the effect of the local atmospheric environment on

THE EFFECT OF THE LOCAL ATMOSPHERIC ENVIRONMENT ON ASTRONOMICAL OBSERVATIONS

THÈSE No 1394 (1995) PRÉSENTÉE AU DÉPARTEMENT DE GÉNIE CIVIL

ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE POUR L’OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES TECHNIQUES

PAR

Lorenzo ZAGO Lauréat en génie aéronautique, Ecole Polytechnique de Milan, Italie de nationalité italienne et suisse

acceptée sur proposition du jury: Prof. G. Sarlos, directeur de thèse Prof. C.-E. Coulman, corapporteur Dr. J.-A. Hertig, corapporteur Prof. D. Huguenin, corapporteur Prof. J. Stenflo, corapporteur Dr. R. Wilson, corapporteur

“La nuit étoilée”, Vincent van Gogh (1889)

Copyright ©1995 EPFL, Lorenzo Zago Copyright ©2010 Lorenzo Zago

THE EFFECT OF THE LOCAL ATMOSPHERIC ENVIRONMENT ON ASTRONOMICAL OBSERVATIONS Abstract Modern astronomy requires ever better performances from its instruments. A main limitation of ground-based telescopes is due to the thermal and aerodynamic disturbances in the atmosphere surrounding the telescope, which are largely caused by the telescope itself and its enclosure. This thesis presents in a comprehensive manner the issues related to the interaction of a modern telescope with its local atmospheric environment, which are key aspects in the design of astronomical observatories. Several new notions and methods are described which allow a better understanding of the turbulent phenomena occurring near and inside different types of telescope enclosure. The knowledge acquired on these effects is then applied to new procedures for a global evaluation of telescope performance and contributes to the general progress of the engineering of telescope enclosures. The wind effects on a large telescope in different enclosure types are described. Wind turbulence affects on the one hand the guiding performance and on the other hand may cause on the relatively thin primary mirrors of large telescopes dynamic deformations which produce significant optical aberrations. The central topic of this work is the study of local ”seeing” effect due to turbulent fluctuations of the refraction index close to the telescope and in particular on the primary mirror. The derivation of theoretical parameterizations, similarity scales and empirical laws applicable to the different phenomena of local ”seeing” allows the interpretation and comparison of measurements done by several researchers in very different conditions. This possibility to quantify and understand all aerodynamic and seeing effects allows to take into account in the design of the observatory all the dynamic and optical effects that affect the telescope performance.

c Copyright 1995 by Lorenzo Zago and EPFL c Revised edition - Copyright 2010 by Lorenzo Zago

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´ L’INFLUENCE DE L’ENVIRONNEMENT ATMOSPHERIQUE LOCAL SUR LES OBSERVATIONS ASTRONOMIQUES R´ esum´ e L’astronomie moderne exige des performances toujours plus poussées de ses instruments. Une limitation majeure des télescopes au sol se rencontre dans les perturbations aérodynamiques et thermiques de l’atmosphère environnant le télescope qui sont en grande partie induites par le télescope même et son enceinte. La thèse adresse de manière globale le sujet de l’interaction d’un télescope moderne avec son environnement atmosphérique local, qui constitue un aspect fondamental pour le projet des observatoires astronomiques. On y décrit plusieurs nouvelles notions, méthodes et relations paramétriques qui permettent une meilleure compréhension des phénomènes de turbulence qui se déroulent l’intérieur et autour des différents types d’enceinte de télescope. L’objectif général tant de développer des outils de connaissance qui serviront particulièrement aux ingénieurs civils chargés du projet des enceintes et des infrastructures d’un moderne observatoire astronomique, cette recherche a intégré des notions, expériences et méthodes dans les domaines de l’optique, de l’aérodynamique du vent, de la physique de l’atmosphère ainsi que du génie civil et de l’analyse des structures. On caractérise le champ aérodynamique créé par le vent autour d’un grand télescope dans plusieurs types d’enceintes. La turbulence du vent influence d’une part la performance de guidage et d’autre part peut causer sur le miroir primaire d’un télescope des déformations dynamiques et donc des aberrations optiques importantes. Ensuite le point centrale de la recherche se trouve dans l’étude de l’effet de ”seeing” local, du aux fluctuations turbulentes de l’indice de réfraction dans l’enceinte et en particulier sur le miroir primaire du télescope. La dérivation d’échelles de similitude et de relations paramétriques applicables aux phénomènes de ”seeing” local conduit à pouvoir interpréter et comparer des mesures qui ont été réalisées par plusieurs chercheurs à des échelles et dans des conditions très différentes. Cette possibilité de mesurer et comprendre tous les effets aérodynamiques et de seeing permet d’intégrer dans le projet de l’enceinte la totalité des effets dynamiques et optiques qui influencent la performance du télescope et donc de l’optimaliser.

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Acknowledgements The author is most grateful to the Ecole Polytechnique Fédérale de Lausanne and its Laboratoire de Systèmes Energetiques - LASEN for the opportunity to present the present thesis. Particular thanks to Prof. G. Sarlos, head of the LASEN, for accepting and carrying the function of thesis director, and to Dr. J.-A. Hertig who first supported the idea of this dissertation and followed it all along with extremely useful discussions and comments. My warm thanks also to C. Alexandrou for his careful reading of the draft and helpful suggestions. I thank Prof. H. van der Laan, former Director General of ESO, for his encouragement to propose this thesis and his recommendation to EPFL. My employment at ESO for 9 years on the development of the Very Large Telescope observatory constituted a great professional opportunity. This research work is quite inter- and pluri-disciplinary and integrates results obtained in collaboration with several ESO colleagues in the framework of the VLT project: the contributions of L. Noethe on the evaluation of optical quality of a deformed mirror and the one of F. Plötz in the evaluation of telescope performance under wind, are particularly acknowledged. I also thanks M. Sarazin for the many exchanges of information and views on the issues of atmospheric turbulence and seeing, as well as Ph. Diericks who is the author of the computer program SuperIMAQ which has been a key tool of this work. Many experimental results reported in this work have been obtained during contracts to various laboratories issued by ESO and coordinated by the author. I would like to cite in particular the Technical University of Aachen (Dr. A. Ruscheweyh), the LASEN (Dr. J.-A. Hertig and C. Alexandrou), and the Danish Maritime Institute (Dr. T. Reynold). A special acknowledgement shall go to the CFHT observatory and its director Dr. Couturier for making available the data log files recording the image quality of 3 complete years of observation. Those data represent the most complete experimental measurements done so far on the local seeing problem in a large telescope and the author is very grateful for the possibility of analyzing them. Many thanks also to Dr. F. Rigaut of the CFHT who transmitted me the data and answered many questions on their correct interpretation.

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Contents 1 Introduction 1.1 General presentation . . . . . . 1.2 Scope and summary . . . . . . 1.3 Original contributions . . . . . 1.4 The ESO Very Large Telescope

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1-1 1-1 1-4 1-5 1-7

2 The image quality of a telescope 2.1 Seeing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Thermal turbulence, light propagation and image size . . . . . . . . . 2.2.1 The microstructure of the temperature field in the atmosphere 2.2.2 The microstructure of the index of refraction . . . . . . . . . . 2.3 Effects of wind loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Wind turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Guiding errors . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Wind buffeting on ”thin” primary mirrors . . . . . . . . . . . . 2.4 The overall image quality and its budget . . . . . . . . . . . . . . . . .

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2-1 2-3 2-6 2-6 2-8 2-11 2-11 2-12 2-13 2-16

3 Telescope enclosures 3.1 The requirements of telescope enclosures . . . . . . . . . 3.2 Evolution of design concepts . . . . . . . . . . . . . . . . 3.2.1 Classical domes . . . . . . . . . . . . . . . . . . . 3.2.2 The MMT and its rotating building . . . . . . . 3.2.3 Improvements in conventional domes . . . . . . . 3.2.4 The ESO New Technology Telescope . . . . . . . 3.2.5 Average seeing at different telescopes at La Silla 3.2.6 The ESO Very Large Telescope . . . . . . . . . . 3.2.7 A summary of outstanding problems . . . . . . .

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3-1 3-2 3-3 3-3 3-5 3-6 3-7 3-9 3-9 3-13

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4-1 4-3 4-4 4-4 4-4 4-9 4-14 4-17 4-19 4-20 4-20

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4 Telescope aerodynamics 4.1 Wind loading on telescopes . . . . . . . . 4.1.1 Classical domes . . . . . . . . . . . 4.1.1.1 Measuring equipment and 4.1.1.2 Results . . . . . . . . . . 4.1.2 NTT rotating building . . . . . . . 4.1.3 Cylindrical enclosure (VLT) . . . . 4.1.4 Retractable enclosure . . . . . . . 4.1.5 Synthesis . . . . . . . . . . . . . . 4.2 Wind loading on the primary mirror . . . 4.2.1 Outline of the problem . . . . . . .

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4.2.2 4.2.3

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Wind tunnel tests with the telescope exposed . . . . . . . . . . . . . 4-22 Tests with the 3.5-m mirror dummy . . . . . . . . . . . . . . . . . . 4-24 4.2.3.1 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 4-24 4.2.3.2 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . 4-24 4.2.3.3 Relationship between pressure fluctuations and wavefront aberrations4-26 Wind tunnel measurements of the pressure/velocity field on the mirror4-30 4.2.4.1 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 4-31 4.2.4.2 Pressure-speed correlation . . . . . . . . . . . . . . . . . . 4-31 4.2.4.3 Correction of wind deformations by active optics systems . 4-34 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-36

5 Local ”seeing” 5.1 The relationship of C2T to the mean velocity and temperature fields . . 5.2 Dome seeing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Causes of dome seeing . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 The ”steady local air” dome effect . . . . . . . . . . . . . . . . 5.2.4 Scaling variables and similarity of dome seeing . . . . . . . . . 5.2.5 An order-of-magnitude estimate of dome seeing . . . . . . . . . 5.2.6 Mirror seeing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.7 Analysis of telescope image quality data data . . . . . . . . . . 5.2.7.1 Data bases . . . . . . . . . . . . . . . . . . . . . . . . 5.2.7.2 Analysis procedure . . . . . . . . . . . . . . . . . . . . 5.2.7.3 HRCam data . . . . . . . . . . . . . . . . . . . . . . . 5.2.7.4 FOCam data . . . . . . . . . . . . . . . . . . . . . . . 5.2.7.5 Analysis summary . . . . . . . . . . . . . . . . . . . . 5.2.8 Seeing caused by heat generation at the secondary mirror unit 5.2.9 Seeing and natural ventilation . . . . . . . . . . . . . . . . . . . 5.2.10 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Mirror seeing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Physical description of mirror seeing . . . . . . . . . . . . . . . 5.3.1.1 Free convection . . . . . . . . . . . . . . . . . . . . . . 5.3.1.2 Mixed and forced convection . . . . . . . . . . . . . . 5.3.1.3 The cold mirror case . . . . . . . . . . . . . . . . . . . 5.3.2 Experimental studies . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2.1 A mirror seeing experiment with a 4-cm mirror . . . . 5.3.2.2 Seeing tests on a 62-cm mirror . . . . . . . . . . . . . 5.3.2.3 Seeing tests on a 254-mm mirror . . . . . . . . . . . . 5.3.2.4 Other laboratory measurements . . . . . . . . . . . . 5.3.3 Analysis and modeling . . . . . . . . . . . . . . . . . . . . . . . 5.3.3.1 Mirror in free convection . . . . . . . . . . . . . . . . 5.3.3.2 Ventilated mirror . . . . . . . . . . . . . . . . . . . . 5.3.3.3 Active correction of mirror seeing . . . . . . . . . . . 5.3.4 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Numerical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Seeing computation by means of a fluid flow numerical model . 5.4.2 CFD for evaluating mirror seeing . . . . . . . . . . . . . . . . . 5.4.3 Application to a 1.25-m telescope project . . . . . . . . . . . .

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5-1 5-2 5-8 5-8 5-10 5-11 5-11 5-13 5-15 5-16 5-16 5-18 5-20 5-26 5-28 5-30 5-33 5-36 5-37 5-38 5-38 5-40 5-42 5-43 5-43 5-49 5-52 5-54 5-55 5-55 5-59 5-61 5-62 5-63 5-63 5-64 5-66

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5.4.4 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . Surface layer seeing . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 The optimum height of a telescope base . . . . . . . 5.5.2 Reduced scale simulation of near-ground seeing . . . 5.5.2.1 Similarity rules for near-ground flow . . . . 5.5.2.2 Pilot test for direct measurement of seeing

6 Systems Engineering 6.1 Engineering criteria and guidelines . . . . . . . . . . . . . . 6.1.1 Wind turbulence on the telescope . . . . . . . . . . . 6.1.2 Wind buffeting on the primary mirror . . . . . . . . 6.1.3 Dome seeing . . . . . . . . . . . . . . . . . . . . . . 6.1.4 Mirror seeing . . . . . . . . . . . . . . . . . . . . . . 6.2 Random conditions and operational aspects . . . . . . . . . 6.3 A statistical model of telescope image quality . . . . . . . . 6.3.1 Parameterization of seeing and guiding effects . . . . 6.3.1.1 Wind versus seeing for the primary mirror 6.3.1.2 Guiding errors . . . . . . . . . . . . . . . . 6.3.1.3 Computation of the CIR figure . . . . . . . 6.3.2 Computation procedure . . . . . . . . . . . . . . . . 6.3.3 Results and discussion . . . . . . . . . . . . . . . . . 6.3.4 Synthesis . . . . . . . . . . . . . . . . . . . . . . . .

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7 Conclusions

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6-1 6-3 6-3 6-4 6-5 6-6 6-7 6-8 6-9 6-9 6-9 6-11 6-12 6-12 6-15 7-1

Bibliography

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APPENDICES A The enclosure of the VLT 8-m telescopes B Aerodynamic measurements on mirrors B.1 Measurements with the 3.5-m mirror dummy . . . . B.1.1 Measurements in the NTT . . . . . . . . . . . B.1.2 Measurements in the inflatable dome . . . . . B.2 Wind tunnel measurements . . . . . . . . . . . . . . B.2.1 Velocity measurements above the mirror . . . B.2.2 Differential pressure measurements across the C Curriculum vitae of the author

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B-1 . B-1 . B-1 . B-3 . B-5 . B-5 . B-8 C-1

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List of Figures 1.1 1.2 1.3 1.4 1.5

Optical schematics of an astronomical telescope . . . . Schematic plan view of the VLT observatory . . . . . Artist’s view of the VLT unit telescope in its enclosure Main components of the VLT 8-m unit telescope . . . The four VLT enclosures - photo ESO . . . . . . . . .

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2.1 2.2 2.3 2.4 2.5 2.6

The atmospheric influence on the image quality of a double star . Point spread function (PSF) of a star image . . . . . . . . . . . . Seeing FWHM as a function of mean CT2 and integration distance Active optics concept for a modern telescope . . . . . . . . . . . Structure of the error budget tree for the ESO VLT . . . . . . . CIR image quality budget of the ESO VLT . . . . . . . . . . . .

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The concurrent engineering process for the design of telescope ESO 3.6-m telescope building at La Silla . . . . . . . . . . . . Building of the 2.2-m telescope . . . . . . . . . . . . . . . . . The building of the MMT . . . . . . . . . . . . . . . . . . . . The first design of the NTT building. . . . . . . . . . . . . . . The final building of the NTT . . . . . . . . . . . . . . . . . . Average seeing at various telescopes at La Silla . . . . . . . . The first artist’s view of the VLT (1984). . . . . . . . . . . . The retractable enclosure which was envisaged for the VLT .

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4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18

Measurement locations in the 3.6-m dome. . . . . . . . . . . . . . . . . Vortex anemometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6-m dome: ratio of mean flow velocity ratio U/U∞ . . . . . . . . . . 3.6-m dome: absolute turbulence intensity σu /U∞ . . . . . . . . . . . 3.6-m dome: turbulence scale Lu divided by the slit width . . . . . . . 3.6-m dome: normalized gust spectra . . . . . . . . . . . . . . . . . . . Enclosure of the NTT with the stowable wind screen . . . . . . . . . . Drawing of the wind tunnel model of the NTT building . . . . . . . . NTT enclosure: flow on telescope upper part . . . . . . . . . . . . . . Normalized rms of dynamic pressure on the telescope upper part . . . Pressure spectral density at 6 Hz for a free flow wind speed of 18 m/s Photograph of the test model . . . . . . . . . . . . . . . . . . . . . . . Measuring point for wind loading on the telescope . . . . . . . . . . . Cylindrical enclosure: flow on telescope upper part . . . . . . . . . . . Normalized rms of dynamic pressure on the telescope upper part . . . Model of the retractable enclosure in the LASEN wind tunnel . . . . . Vertical profile of mean speed, turbulence intensity and length scale . ”Open air” telescope model in the LASEN wind tunnel . . . . . . . .

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4.19 4.20 4.21 4.22 4.23 4.24 4.25 4.26 4.27 4.28

Pressure taps and sectors on the 1/80 models of the primary mirror Mean and rms cp values of modes defocus and astigmatism . . . . . Position of the dummy mirror in the inflatable dome . . . . . . . . . Distribution of the sensors on the surface of the dummy mirror . . . Wavefront aberrations versus pressure fluctuations . . . . . . . . . . Rms of the total wavefront aberration in the inflatable dome . . . . Photograph of test model . . . . . . . . . . . . . . . . . . . . . . . . Plots of σcp on the mirror for different configurations . . . . . . . . . Correlation between σcp and mean wind speed on the primary mirror Scatter plot of peak frequencies versus the velocity ratio U/U∞ . . .

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4-22 4-23 4-25 4-25 4-28 4-29 4-30 4-32 4-33 4-35

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 5.18 5.19 5.20 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.30 5.31 5.32 5.33 5.34 5.35 5.36 5.37 5.38 5.39 5.40

The function f(Ri) in equation (5.7) - from [Wyngaard] . . . . . . . . . . CT2 versus dT /dz in the surface layer . . . . . . . . . . . . . . . . . . . . . Relationship between CT2 , height and surface flux in free convection . . . . Causes commonly held to be source of dome seeing . . . . . . . . . . . . . Seeing FWHM caused by a warmer dome floor . . . . . . . . . . . . . . . The Canadian-French-Hawaii Telescope . . . . . . . . . . . . . . . . . . . Log-normal histogram of FWHM data from HRCam . . . . . . . . . . . . ∆T ’s in the CFHT dome . . . . . . . . . . . . . . . . . . . . . . . . . . . . HRCam FWHM versus mirror-air ∆Tm . . . . . . . . . . . . . . . . . . . HRCam FWHM versus ∆Td . . . . . . . . . . . . . . . . . . . . . . . . . . HRCam FWHM versus sec γ in absence of mirror and dome seeing . . . . HRCam computed natural seeing θno versus ∆Tt . . . . . . . . . . . . . . HRCam computed natural seeing θno versus sec γ . . . . . . . . . . . . . . FOCam FWHM versus mirror-air ∆Tm . . . . . . . . . . . . . . . . . . . FOCam FWHM versus ∆Td . . . . . . . . . . . . . . . . . . . . . . . . . . FOCam FWHM versus sec γ in absence of wind and mirror seeing effects FOCam FWHM versus wind speed. . . . . . . . . . . . . . . . . . . . . . . Seeing caused by a free convection plume from the M2 unit. . . . . . . . . Comparison of seeing measurements at the NTT and at the DIMM. . . . Seeing at the NTT versus mirror-air temperature difference. . . . . . . . . Effect of flaps on the seeing at the NTT. . . . . . . . . . . . . . . . . . . . Convection regimes as a function of Ra and Ls . . . . . . . . . . . . . . . Free convection over a horizontal plane . . . . . . . . . . . . . . . . . . . . Temperature and velocity fluctuations in presence of forced flow . . . . . . Optical schematic of the mirror seeing experiment. . . . . . . . . . . . . . The test mirror on steel plate, itself laid on the floor of the laboratory. . . The cardboard dome. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Power spectrum of the image motion. . . . . . . . . . . . . . . . . . . . . Comparison of measured seeing sequences . . . . . . . . . . . . . . . . . . Layout of the mirror seeing experiment by Iye . . . . . . . . . . . . . . . . Strehl ratios versus mirror-air ∆T for the 62-cm mirror . . . . . . . . . . FWHM versus Strehl ratio for a 62-cm mirror . . . . . . . . . . . . . . . . Seeing FWHM versus mirror-air ∆T for the 62-cm mirror . . . . . . . . . FWHM versus 75% intensity diameter for a 254-mm mirror . . . . . . . . Seeing FWHM for the 254-mm mirror. . . . . . . . . . . . . . . . . . . . . Mirror seeing for an horizontal mirror in free convection for Tm > Ta . . . Computed profile of the temperature structure coefficient CT2 . . . . . . . θ/∆T as a function of the Froude number for a ventilated mirror . . . . . General procedure for evaluating seeing from a CFD model . . . . . . . . The CFD ”square” model with respect to the actual telescope shape . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5-4 5-4 5-7 5-10 5-14 5-17 5-20 5-22 5-22 5-23 5-23 5-25 5-25 5-27 5-27 5-29 5-29 5-31 5-33 5-34 5-35 5-39 5-39 5-41 5-44 5-45 5-45 5-48 5-48 5-50 5-50 5-51 5-51 5-53 5-53 5-57 5-58 5-60 5-64 5-66

xii

. . . . . . . . . .

. . . . . . . . . .

5.41 5.42 5.43 5.44 5.45 5.46 5.47 5.48 5.49 5.50

The grid of the CFD model . . . . . . . . . . . . . . . . . . . . . Mean speed plot . . . . . . . . . . . . . . . . . . . . . . . . . . . CFD model results . . . . . . . . . . . . . . . . . . . . . . . . . . Seeing FWHM versus total fans airflow . . . . . . . . . . . . . . CT2 profiles from various observatories . . . . . . . . . . . . . . . Ratios CT2 10 /CT2R20 and CT2 20 /CT2 30 versus wind speed . . . . . . . . Integral values z30 CT2 dz in the ground layer at La Silla . . . . . . Scaling relationship for the wind tunnel simulation . . . . . . . . Wind tunnel profiles of mean speed, turbulence and temperature Schematic of optical measurements in the wind tunnel. . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

5-67 5-67 5-69 5-69 5-72 5-74 5-74 5-77 5-79 5-79

6.1 6.2 6.3 6.4 6.5 6.6 6.7

Comparison of rms pressure fluctuations in different enclosures . . . . . Rms pressure fluctuations with frequency > 1 Hz in different enclosures Total image quality (θm + θw ) of the VLT 8-m primary mirror . . . . . CIR error budget for the terms caused by local turbulence . . . . . . . . Cumulative distribution of the CIR loss due to the primary mirror . . . Histogram of the mean wind speed distribution on the primary mirror . Cumulative distribution of the CIR loss due to guiding errors . . . . . .

. . . . . . .

. . . . . . .

6-3 6-4 6-10 6-11 6-14 6-14 6-15

A.1 Schematic cross-section of the VLT enclosure . . . . . . . . . . . . . . . . . A-2 B.1 Location of hot wire probes above the mirror surface . . . . . . . . . . . . . B-6 B.2 Tap locations on upper and lower surfaces of the mirror . . . . . . . . . . . B-6

xiii

xiv

List of main symbols A, B a, a2 , b CN2 CT2 cp D DT (∆r) Fr f e g h Ic It KM KH L Lu l N n P Q q qs Ra Re Ri ro S T t U u∗ v z

parameterization coefficients constants structure coefficient of the index of refraction temperature structure coefficient adimensional pressure coefficient (mirror) diameter temperature structure function Froude number focal distance turbulent kinetic energy gravity acceleration heat transfer rate central intensity ratio turbulence intensity eddy diffusivity for momentum eddy diffusivity for temperature Monin-Obukhov length length scale of turbulence along mean flow direction inner scale of turbulence index of refraction frequency pressure dissipated power heat flux normalized by cp ρ surface heat flux Raleigh number Reynolds number Richardson number Fried parameter for seeing Strehl ratio (mean) temperature thickness wind or air flow speed friction velocity water vapor pressure height

α β γ θ κ κw λ λi ν ρ

telescope azimuth angle ratio KH /KM zenithal angle of the direction of observation dissipation rate of kinetic energy dissipation rate of temperature thermal diffusivity of air wave number light wavelength similarity scale for quantity i kinematic viscosity air density

xv

σi σw θ θn θg

root mean square of quantity i wavefront rms error long exposure angular image size on the sky (generally FWHM) image size due to natural seeing rms of high frequency guiding errors

MAIN ACRONYMS USED IN THE TEXT

AAT CFHT CIR DIMM ESO FWHM MMT M1 M2 NTT PSD PSF VLT

Anglo-Australian Telescope Canadian French Hawaii Telescope Central Intensity Ratio, a measure of the optical quality of a telescope Differential Image Motion Monitor, a special 35-cm telescope for measuring seeing European Southern Observatory Full Width Half Maximum of the point spread function Multi-Mirror Telescope Primary mirror of a telescope Secondary (upper) mirror of a telescope New Technology Telescope, the newest 3.5-m telescope located at ESO’s La Silla observatory Position sensing detector Point Spread Function (light intensity profile) Very Large Telescope, a 4×8-m telescope project presently under construction

xvi

Chapter 1 Introduction 1.1

General presentation

Modern astronomy makes use of optical telescopes for the observation of sky objects in the wavelength range from ultraviolet to infrared, that is from about 300 nm to 30 µm . Although the recent years have seen the development of space astronomy from automatic telescopes carried by satellites, the huge cost of these satellites and some of their inherent limitations will mean that ground based telescopes will be still for many decades and perhaps centuries the main instruments of astronomers. Indeed this last decade has seen the start of a number of new projects for telescopes larger than any in operation today. These telescopes, thanks to the high quality of optical systems and their electronics, aim at being almost as performing as satellite instruments, with a much lower cost. Two main developments are presently being pursued in this field. One aims at the manufacturing of larger primary mirrors, with diameters from 6 to 10 meters, which constitute a significant technological leap with respect to the 4-m class mirrors used in the best telescopes built until the mid 80s. The advantages sought with larger mirrors are the increased light collecting performance which is proportional to the mirror area and the improvement of the theoretical resolution which is proportional to the ratio between wavelength and mirror diameter. The other development line aims at decreasing the disturbances caused by the atmospheric environment on the optical performance of a telescope. This objective is sought on the one hand by locating new telescope on high mountain sites with favorable atmospheric characteristics, and on the other hand by reducing local effects, mainly of thermal origin, caused in and by the observatory itself. Ground based telescopes must of course observe through the atmosphere, which has two main consequences on the quality of observations. The first consequence is a degradation due to the turbulent variations of the index of refraction. This causes the image of a star to appear as a randomly moving patch with an angular size which is often quite

1-1

1-2

CHAPTER 1. INTRODUCTION

larger that the theoretical limit size due to diffraction from the telescope optics. This degradation is called the seeing and is often quantified as the mean angular apparent diameter of a star image. Although contributions to this seeing effect come from all atmospheric layers, it is now known that some of the largest disturbances are generated close to the telescope itself and are ultimately caused by differences of temperature between air and the observatory structures. These negative effects tend to disappear when the telescope is exposed to wind, which, however, creates then another problem. This second disturbing effect is caused by vibrations of the telescope due to the wind mechanical turbulence. During the observation the telescope must track the star with very high accuracy. If the telescope is even partly exposed, the wind will tend to shake it. The guiding accuracy required even for short integration times is such that the telescope oscillations due to the wind load cannot be absorbed by the structural rigidity of the telescope alone and must be corrected by an active control loop. There is nonetheless a limit to the amplitude and frequency bandwidth of the wind disturbance that can be corrected by the control system. Moreover the primary mirrors of the large telescopes of the newest generations are much thinner and less stiff, for a number of reasons, than those of predecessor telescopes, and therefore may also have the figure of their optical surface deformed by the wind loads. Thus the wind flow has a twofold action on the overall telescope performance: on the one hand it improves the seeing quality but on the other hand it degrades the guiding accuracy; conversely if the telescope is well shielded from the wind, guiding will be very accurate but seeing will inevitably worsen. It is important to note that both seeing and guiding inaccuracies have similar effects on the image quality of the telescope inasmuch they both cause an enlargement of the apparent size of a star image recorded during the exposure time. The engineer designing the enclosure of a telescope has therefore the difficult task of finding a compromise in the exposure of the telescope to the wind, which will maximize the overall quality of the observation. Telescope enclosures are a very particular type of buildings, which must fulfill an unusual set of requirements. This situation has produced many different technical solutions, depending on a variety of parameters such as the size and type of the telescope, its geographic and meteorologic location, the type of observations pursued at and various other requirements concerning maintenance, access and operation. It is important to underline that the problem, such that it is set nowadays, is quite new. Until a few years ago, the design of a telescope enclosure was deemed to a quite straightforward matter and was based on a tradition of dome building which had been inherited since the time of refractive telescopes. These traditional concepts were applied uncritically to make domes for reflective telescopes with primary mirror sizes larger than 2 ∼ 3 meters, and constituted an established practice of the art which was in fact hiding a basic ignorance of the interaction between a telescope

1.1. GENERAL PRESENTATION

1-3

and its local atmospheric environment, particularly with respect to the seeing problem. Moreover objective difficulties, such as the great variability of the atmospheric environment, hindered comparisons and benchmarks among the best and largest telescopes with respect to the real physical limitations to ground based astronomy. It was then only when particular circumstances proved unequivocally that some of the concepts traditionally used for the design of telescope enclosures were counterproductive, that innovative research work was undertaken on the subject. Most of the work presented in this dissertation was performed in the framework of the development of the new Very Large Telescope (VLT) observatory by the European Southern Observatory (ESO). The VLT observatory will be constituted by four 8-m telescopes which will eventually be able to combine their light beams into a single image. When completed near the year 2000, the VLT will be the largest astronomical observatory in the world1 . Because the VLT project was started without prejudiced ideas, the development of the VLT covered a wide spectrum of conditions and design solutions. As a consequence this work should have applications well beyond the scope of the VLT project, and has the ambition to become a reference for the design of telescope enclosures.

1

It may be useful to note that the VLT is just one case of the extraordinary development of new large astronomical telescopes which is now taking place. At the time of writing this report, there are, beside the VLT, several other ongoing projects: • The first Keck 10-m telescope is completed on Hawaii island and in the tuning phase, while a twin telescope is being fabricated. • The american Gemini project for two identical 8-m telescopes for different sites (Hawaii and Chile) • The japanese Subaru 8-m telescope project, also to be located on Hawaii. • The american privately funded Magellan project for a 6-m telescope in Chile. Other large telescope projects are still in an earlier planning and development phase, such as the Columbus project for a telescope with a twin ”binocular” mount with two 8-m mirrors, and several national projects in Germany, Spain and Great Britain.

1-4

1.2


Scope and summary

This dissertation intends to describe and summarize in a comprehensive manner several studies, both theoretical and experimental, on the effects of seeing and wind turbulence associated with various types and configurations of telescope enclosures. The knowledge acquired on these effects will then be integrated into new methods and procedures for a global evaluation of telescope performance and will provide improved design guidelines for the project of future telescopes and their enclosures. Therefore the scope of this dissertation is twofold: 1. A description of the effect of local atmospheric turbulence on the observation performance of astronomical optical telescopes. This description includes a number of new developments and experimental results which allow to get both useful engineering parameterizations and a global view and interpretation of these phenomena. 2. A contribution to the development of engineering criteria and guidelines, which draws the practical conclusions from the research results and which should assist the civil engineer assigned to the design of a telescope enclosure. One may note that this work is of interdisciplinary nature. While its main objective is to provide civil engineers with a better understanding of the design drivers of telescope enclosures, this research comprehends notions, experiments and methods in the fields of optics, wind aerodynamics, atmosphere physics and structural engineering. In the next chapter the main factors that influence the image quality of an astronomical telescope are summarized. The definitions underlying the seeing phenomenon are given together with its relationship with the temperature fluctuations of the atmosphere. One then introduces the errors caused by wind loading on the telescope: guiding errors due to vibrations of the telescope structures and dynamic deformations of the primary mirror. All these contributions are summarized in an error budget tree (fig. 2.4). Chapter 3 describes the main requirements of telescope enclosures and outlines the concurrent engineering approach required to achieve an optimal design. Through the description of history cases of telescope projects, we introduce the main issues and open questions related to local atmospheric turbulence and their consequences on the telescopes’ performance and on the engineering of telescope enclosures. The last section of the chapter (§(3.2.7, page 3-13) summarizes these outstanding problems which constitute the main research object of the dissertation and are then expanded in the next chapters. Chapter 4 describes the aerodynamic environment surrounding a telescope. Two distinct aspects are studied by means of wind tunnel and full scale experiments: the

1.3. ORIGINAL CONTRIBUTIONS

1-5

first one concerns the characterization of the wind turbulence on the upper part of the telescope, which is responsible for high frequency guiding errors. The second aspect analyzed concerns the turbulent pressure fluctuations on the primary mirror and their relationship with optical aberrations. In chapter 5 we analyze the local seeing effects, due to refractive turbulent inhomogeneities of the atmosphere caused by the telescope and by the observatory itself. The various contributions from the primary mirror of the telescope, the enclosure and the atmospheric surface layer are elucidated by means of experimental measurements, theoretical analysis and numerical simulations. Chapter 6 introduces a systems engineering approach in which the different contributions to the telescope image quality can be combined for a global evaluation of performance of the telescope and the influence of the enclosure.

1.3

Original contributions

In view of the large scope of this dissertation it may be useful to outline the main original contributions that are brought into this work. At a general level this work aims at bringing together and developing concurrently a number of interrelated topics that determine fundamentally the concept and the design of an astronomical observatory. In this sense this work aims at becoming a scientific reference, which the author felt was missing. Chapter 2 essentially reorders the main existing definitions and notions related to seeing and wind effects on telescopes and provides a common base for their quantification with respect to the telescope performance. Chapter 3 is a critical appraisal of the problems arising in the existing observatories, which leads to define more concretely the needs for new developments. Chapter 4 presents the results and the evaluation of several aerodynamic measurements both at full scale and in the wind tunnel. While the test methods used are quite established, they had not before been applied in that context. The accurate quantification of the mechanical turbulence caused on a telescope by several different types of enclosure is here published for the first time. Also the analysis of the optical effects of wind buffeting on a large mirror represents an original contribution to the further development of advanced active and adaptive optics. While some parts of this work benefited from the collaboration of a large team at ESO (see the authors’ list of [Noethe 92]), the definition of the wind engineering aspects as well as the final evaluation and conclusions presented here are by the author. Chapter 5 includes mostly original and unpublished material. We will cite here the

1-6


parametric estimates for the seeing in domes and the one caused by the telescope’s secondary mirror. The largest set of seeing data from one of the world best observatories is analyzed statistically for the first time. The core of the work lies then in the study of mirror seeing, identified as the likely most important effect in a modern telescope: an original physical description of the phenomenon is presented as well as the analysis and comparison of various experiments, leading to engineering parameterizations reliably applicable to an actual telescope design. Chapter 6 draws the main consequences of the scientific results on the engineering of astronomical observatories. The systems engineering statistical approach presented here takes its ground stones from the parameterizations obtained in this work and follows from the author’s considerations on the complexity and interrelationship of all topics studied. Secondary mirror (M2)

Nasmyth focus Altitude axis

Primary mirror (M1)

Cassegrain focus

Figure 1.1: Optical schematics of an astronomical telescope

1.4. THE ESO VERY LARGE TELESCOPE

1.4

1-7

The ESO Very Large Telescope

A large part of the present work was performed in the framework of the a project for a new generation telescope named the Very Large Telescope (VLT). It is then useful to illustrate briefly this project and by the same occasion to introduce an essential nomenclature of the terms and concepts relative to large optical telescopes which are used throughout this report. The European Southern Observatory (ESO) is an intergovernmental organization constituted by eight European countries, including Switzerland, for the purpose of providing and managing astronomical observatories in the southern hemisphere. ESO owns the observatory of La Silla, in the Chilean Andes, which includes 15 telescopes of different size and characteristics, among which is the 3.5-meter New Technology Telescope (NTT) which is deemed to be the best telescope presently in operation. In 1984 ESO started the VLT project for a new observatory on the site of Cerro Paranal, which will be constituted by four unit telescopes, each with a primary mirror with a diameter of 8 meters. A schematic plan view of the future observatory is shown in fig. 1.2. The telescope and its main components are schematically illustrated in figures 1.4 and 1.1. The mounting is altitude-azimuth. The primary mirror is only 17 cm thick and is supported by a so-called active optics system which consists of 150 combined hydraulic-electromechanic actuators capable of correcting the mirror shape for gravity and other low frequency deflections by applying controlled forces. The secondary mirror is provided with a fast tilt control called field stabilization for precision guiding. For observations in the infrared wavelength range, a chopping motion of the secondary mirror allows astronomers to measure the difference between the signal and sky background, but in this case the field stabilization may not be as effective. The telescope is protected by an enclosure of cylindrical shape (fig. 1.5). The upper part co-rotates with the telescope and has a large upside-down-L shaped slit, closed with two sliding doors. The two slit doors are supported on two protuberances of the dome, which also integrate a set of pneumatically activated bars that constitutes a wind screen with different levels of wind permeability across the slit. In the lower fixed part there are 5 large doors (one 10x4m and four 5x4m) while in the rotating upper part there are about 150 1.5x0.5m openings equipped with louvers.

1-8


Figure 1.2: Schematic plan view of the VLT observatory

Figure 1.3: Artist’s view of the VLT unit telescope in its enclosure

1.4. THE ESO VERY LARGE TELESCOPE

Figure 1.4: Main components of the VLT 8-m unit telescope

1-9

1-10


Figure 1.5: The four VLT enclosures - photo ESO

Chapter 2 The image quality of a telescope The first requirement that astronomers will set for the design of a new telescope and its enclosure is that it should have the best possible image quality and the lowest possible seeing. If the atmosphere behaved as a purely refractive medium, the image of a star as seen in a telescope with a perfect optical surface would consist of a bright central spot surrounded by weak circles constituting the diffraction rings. This is due to the wave character of the light in combination with the effect of the finite diameter of the telescope mirror. In this case one says that the image is diffraction limited. In reality the optical image quality of a ground-based astronomical telescope is limited by several other factors, among which: 1. Figuring and alignment errors of the optics which produce optical aberrations. 2. Atmospheric seeing effects. 3. Wind loading on the telescope which causes guiding control errors, and on the primary mirror, where pressure fluctuations may deform the figure of the optical surface. It is interesting to note that all these factors will have similar effects on the quality of an exposure of the focused image: the diffraction rings are broken up and both they and the central spot loses its sharpness, so that the profile of the star image becomes larger and tends to takes the general form of a Gaussian. Figuring and alignment errors of the telescope optics are unrelated to the scope of this work. The other two contributions depend chiefly on the conditions of the atmospheric environment surrounding the telescope and are generally quite influenced by the type and configuration of the telescope enclosure.

2-1

2-2

CHAPTER 2. THE IMAGE QUALITY OF A TELESCOPE

Figure 2.1: Illustration of the atmospheric influence on the image quality: on the right hand the image of a double star as it may appears at a large telescope; on the left hand the resolved image that has been obtained by a very experimental adaptive optics instrument able to correct1 the wavefront distortions caused by atmospheric effects.

1

Adaptive optics systems are still very experimental and presently have many limitations. Eventually, probably in 10 or 20 years, they will constitute the keystone of future telescopes.

2-3

2.1. SEEING

2.1

Seeing

The seeing effects are caused by atmospheric turbulence through which some of the light arriving from a star is scattered by refractive inhomogeneities. As the light wave propagates through the turbulent atmosphere it experiences fluctuations in amplitude and phase. An image formed by focusing this wave exhibits fluctuations in intensity, sharpness and position which are commonly referred to as scintillation, image blurring and image motion. The seeing observed by a telescope on the ground is contributed by the whole atmosphere crossed by the light wave front and one distinguishes three main contributing causes: 1. The turbulence in the high atmosphere, which has a maximum near the tropopause at about 12 km. This layer is, in particular, the cause of the scintillation effect. 2. The turbulence of the atmospheric boundary layer (between 30 and 500 m). 3. The turbulence in the ground surface layer (up to about 30 ∼ 50 m) and the one generated by the artificial structures of the observatory itself. This work will concern only this latter contribution, while we will refer to natural seeing to mean the seeing from the boundary layer and the high atmosphere. A rigorous quantification of the seeing effect depends on the exposure time. For most astronomical observations, seeing is quantified for the so-called long exposure case, in which the exposure is longer than the time in which the wavefront phase inhomogeneities larger than the telescope pupil pass through it. In practice for a large telescope this is an exposure of a duration of the order of 10 to 30 seconds. As a consequence the image motion effect of seeing will be summed-up in an overall blur effect. Several figure of merit are used for quantifying seeing: • Atmospheric coherence length or Fried parameter r0 defined as the diameter of the circular pupil for which the diffraction limited image and the seeing limited image have the same angular resolution. • Full width half maximum (FWHM) of the seeing disk the angular diameter at half height of the star image profile, generally called the point spread function (PSF) - see fig. 2.2. The FWHM angle θ for a telescope of large diameter (D ro ), expressed in seconds of arc (arcsec) on the sky, is related to the ro parameter as θ = 2.013 · 105

λ ro

(2.1)

where λ is the wavelength. In the practical case of a limited diameter telescope, expression (2.1) defines the contribution of the seeing effect to the total FWHM

2-4


Figure 2.2: The point spread function (PSF) of a star image: above for a perfect diffraction limited 8-m telescope in vacuum; below for the same telescope in the atmosphere with ro = 0.25 m at λ = 500 nm, resulting in a FWHM of 0.4 arcsec. Note the change of vertical scale: the Strehl ratio is here 0.001 . The units on the x-axis are arcsec.

2-5

2.1. SEEING

of the image, which results from the convolution of the diffraction pattern of the telescope with the optical aberrations and the seeing. • The Strehl intensity ratio the ratio between the heights of the PSF peak of the actual image and the ideal diffraction limited image. • The diameter enclosing 80% total energy (or some other percentage) For a telescope of large diameter (D ro ) it is: θ80 = 3.812 · 105

λ ro

(2.2)

In this work one will generally use the FWHM angle of the seeing disk as a unit of measure for seeing. Different methods exist to measure or estimate seeing. With a large telescope a good estimate of seeing may be obtained by measuring the object size or by looking at the smallest resolution in the image. In order to have a small transportable instrument for testing the quality of different sites, ESO has developed a 35-cm telescope with a differential image motion monitor (DIMM) based on a method in which the image motion of short exposures is related to the long exposure image size [Sarazin 92]. A main problem for the analysis of seeing effects is due to the fact that measurements of the optical image quality hardly allow separating the different sources. Therefore other instruments are used to characterize and separate the effects from the different layers of the atmosphere such as the scintillometer, used for evaluating high altitude turbulence and the acoustic sounder or SODAR (SOund Detection And Ranging) for measuring turbulence profiles in the atmospheric boundary layer. There exist, however, no direct means to discriminate the different causes of seeing in the immediate environment of the telescope.

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2.2


Thermal turbulence, light propagation and image size

We have already mentioned that the seeing effect is due to turbulent fluctuations of the index of refraction. The index of refraction N varies with the density and composition of the medium. In air it may be expressed by Cauchy’s formula (extended by Lorenz for humidity) as a function of wavelength λ, pressure P (mb), absolute temperature T (K) and water vapor pressure v (mb): N −1=

77.6 · 10−6 v 1 + 7.52 · 10−3 λ−2 P + 4810 T T

(2.3)

Fluctuations of humidity are only significant in extreme cases like fog or near the sea surface which are not relevant to astronomical observations. In fact the best astronomical sites, such as Mauna Kea on Hawaii and La Silla in Chile, experience very low humidity values (generally < 20%). Therefore the effects of humidity can be safely neglected in the discussion of astronomical seeing. Since also pressure fluctuations have negligible effects on the index of refraction, this quantity is affected practically only by the air temperature fluctuations. Therefore the turbulent fluctuations of the index of refraction are intimately linked to the structure of thermal turbulence in the atmosphere.

2.2.1

The microstructure of the temperature field in the atmosphere

[Tatarskii] describes the microstructure of the temperature field in a fluid with homogeneous and isotropic turbulence, characterized in particular by its dissipation rate of kinetic energy , similarly to Kolmogorov’s analysis of the turbulent velocity field. The analysis leads to the definition of an inner scale corresponding to the smallest temperature variations, which is determined by the thermal diffusivity κ and the dissipation rate of momentum: l=

κ3

!1 4

.

(2.4)

Continuing the analogy with the velocity field, Tatarskii finds then an inertial domain, between the outer scale of turbulence L and l where the temperature structure function DT (∆r) =< (T (r) − T (r + ∆r))2 > has the form: 2

DT (∆r) = CT2 ∆r 3

for l ∆r L

(2.5)

2.2

2-7

THERMAL TURBULENCE

where CT2 is the temperature structure coefficient. CT2 characterizes completely the local thermal turbulence at a give time, has units (K2 m−2/3 ) and is therefore formally defined as: < (T (r) − T (r + ∆r))2 > ∆r2/3 for a separation ∆r in the inertial domain. CT2 =

(2.6)

CT2 is also related to the one-dimensional temperature spectrum which in the inertial domain has the form: Φ(κw ) = 0.25 CT2 κ−5/3 (2.7) w where κw is the streamwise component of wavenumber. Moreover, [Tatarskii] notes that in the inertial domain DT (∆r) should be a function of only , ∆r and the temperature dissipation rate θ . Dimensional reasoning leads then to 1 CT2 = a2 θ − 3 (2.8) where a2 is a constant found to be equal to about 3. The value of CT2 at a given point can be measured by special temperature sensors. Sometimes two sensors are used, with a separation ∆r of the order or 1 meter, but often the measurement is taken with one sensor only. The data are then processed assuming the Taylor hypothesis of ”frozen turbulence” in which time and spatial intervals are linked by the mean wind speed as: ∆t = ∆r/U This hypothesis implies that velocity fluctuations are small with respect to the mean value, which is generally the case with not exceedingly gusty winds with a mean speed of at least 4 ∼ 5 m/s. The temperature structure coefficient can then be evaluated from the variations of temperature at a single point as: CT2 =

< (T (t) − T (t + ∆t))2 > (∆t U )2/3

(2.9)

The temperature sensors for the measurement of CT2 must have a high resolution and a large dynamic range. CT2 may vary from 10−6 K2 m−2/3 during the night on an excellent site to 10−1 K2 m−2/3 during the day and convection from the ground. The required bandwidth is determined by the -5/3 slope of the temperature spectrum (2.7) and will generally be at least 100 or 200 Hz. Direct measurements of CT2 from a fixed setup are of course possible only close to the ground while one-time vertical profiles over a larger height can be obtained by aerostatic balloons. The already mentioned SODAR can measure refraction turbulent profiles in the boundary layer with a height range between 50 and 800 m. The profiles of CT2 in the high atmosphere and in the boundary layer have been also the objects of many studies aiming at determining their relationship with height and the atmosphere parameters: see in particular [Coulman 86], [Coulman 88] and [Consortini].

2-8


2.2.2

The microstructure of the index of refraction

Analog statistical properties may be applied to the index of refraction and one may define a structure coefficient of the index of refraction CN2 . From equation (2.3) and ignoring the very minor effect of humidity, CN2 is related to CT2 by: 2

2

CN = CT · 77.6 · 10

−6

1 + 7.52 10 λ

−3 −2

P 2

T2

(2.10)

where λ is the wavelength. Normally one considers as a reference the wavelength λ = 500 nm and the previous equation becomes: 2

2

CN = CT · 80 · 10

−6

P T2

2

(2.11)

The seeing effect through an atmospheric layer of height H can then be expressed an integral function of the index of refraction structure coefficient CN2 , whereby the Fried parameter ro is given by

ro = 0.42(2π/λ)2 sec γ

Z

H

CN2 (z)dz

−3/5

(2.12)

where γ is the zenithal angle of the direction of observation1 . Recalling equation (2.1), the FWHM spread θ of the seeing disk in arcsec is then given by:

θ = 2.591 · 10−5 λ−1/5 (cos γ)−1

Z

H

CN2 (z)dz

3/5

(2.13)

For a vertical direction and λ = 500 nm, the FWHM angle is expressed as: 7

θ = 2.0 · 10

Z

H

CN2 (z)dz

3/5

(2.14)

Combining with equation (2.11), for typical conditions of astronomical mountain sites (pressure 770 mb, temperature 10◦ ) one obtains: θ = 0.94

Z

H

2

CT (z)dz

3/5

(2.15)

The diagram at fig. 2.3 illustrates the order of magnitude of the seeing effect with respect to a mean value of CT2 and the integration distance. Depending on the geometric scale of the phenomenon causing seeing, the critical values of CT2 will be very different: for instance, if we set at ≈ 0.1 arcsec an arbitrary threshold for ”bad” seeing from a single cause, the corresponding critical (mean) value of CT2 will be • for the dome interior (distance scale ' 10 m): ' 6·10−3 K2 m−2/3 1

sec γ is often called airmass in the astronomical jargon.

2.2

2-9

THERMAL TURBULENCE

100 Seeing FWHM (arcsec) 0.02 0.05 0.10 0.20 0.40 0.80

10

z (m)

1

0.1

0.01

0.001 0.0001

0.001

0.01

0.1 CT2

1

10

100

Figure 2.3: Parameterisation of seeing FWHM with respect to a mean value of CT2 (K2 m−2/3 ) integrated over a distance z. • for the atmospheric surface layer (distance scale ' 30 m): ' 10−3 K2 m−2/3 • for seeing caused by convection flow at the surface of the telescope mirrors (distance scale ' 1-40 mm) the critical CT2 values are much higher, of the order of 10 K2 m−2/3 . Equations (2.12) and following show that the overall seeing effects may be considered a 5/3-exponent sum of different terms corresponding to the different atmospheric layers. Thus if θn is natural seeing FWHM, caused by the boundary layer and upward, and θl is the local seeing, the overall seeing is:

5/3 3/5

θ = θn5/3 + θl

(2.16)

The best astronomical sites are reported to have a natural seeing varying between 0.3 to 0.6 arcsec (FWHM), which is roughly equally divided between the high atmosphere and the atmospheric boundary layer. Acceptable sites for astronomical research will have natural seeing up to 2 arcsec. Local seeing, that is the seeing caused by the telescope and the surrounding structures can represent anything from zero to about 2 arcsec and can be the cause of very significant differences of image quality among telescopes located on the same site. Fig. 3.7 (page 3-10) shows the monthly average of seeing values logged at different telescopes located close to one another at the La Silla observatory. The common

2-10


trends of the plot let observe the seasonal variation of the natural seeing at La Silla, which becomes generally worse during the (austral) winter months. One will also note the large differences among the telescopes and with respect to the DIMM seeing monitor, which are often of the order or 0.5 arcsec and sometimes reach 1 arcsec. Understanding and decreasing these differences, unequivocally caused by the enclosure and the atmospheric environment in the immediate surrounding of the telescope, is the challenge faced by all future telescope projects.

2-11

2.3. EFFECTS OF WIND LOADS

2.3

Effects of wind loads

Vibrations and inaccuracies of the guiding system will have the effect of widening the angular image size obtained by a telescope following the course of a sky object during the required exposure time. Modern telescopes benefit from the progress in low-friction bearings and electromechanic drives. Also the performance of active loop control systems has progressed very close to the theoretical limits. Thus the guiding accuracy of a modern telescope is mainly limited only by the mechanical turbulence of the wind acting on the telescope structure. A first quantification of the perturbation brought by the wind will be given by the portion of the energy density spectrum at frequencies greater than the bandwidth of the guiding loop.

2.3.1

Wind turbulence

The longitudinal, vertical and transverse components of the time dependent wind velocity vector at a given location can be expressed as a sum of a constant term and a time dependent function with zero mean: U (t) = U + u(t) V (t) = v(t) W (t) = w(t) The functions u(t),v(t) and w(t) can be assumed to represent stationary random processes at least during a time interval of a few minutes. In general the longitudinal turbulent component u(t) is the most significant with respect to the response of a structure, and of a telescope in particular. A measure of the correlation of u(t) at different time instants separated by a time interval τ is given by the autocorrelation function 1 Z T /2 1 u(t) u(t + τ ) dt (2.17) Ru (τ ) = 2 lim σu T →∞ T −T /2 where σu2 is the variance of u(t). Ru (τ ) is equal to unity for τ = 0 and vanishes for τ → ∞ . One may then define a length scale Lu = U

Z

0

∞

Ru (τ ) dτ

(2.18)

which is a measure of the average size of the turbulent eddies in the mean flow direction. Vertical and lateral turbulence length scales are similarly defined. The power spectrum Su (n) may be obtained as the Fourier transform of the autocorrelation function. The form of the velocity power spectrum in the inertial domain was obtained by Kolmogorov as: nz nSu (n) = 0.04 2 σu U

−2/3

(2.19)

2-12


This expression is valid for (nz/U ) > 1 . Various empirical expressions which account also for lower frequencies have been proposed for use in response computations procedures and building codes: a form which is very convenient for parametric wind response computations is the Von Karman spectrum 4x nSu (n) = 2 σu (1 + 70.8 x2 )5/6

(2.20)

with x = nLu /U Note that the peak frequency of the spectrum can be evaluated from the length scale as U (2.21) nmax = 0.15 Lu

2.3.2

Guiding errors

Wind may be a major source of guiding errors when the telescope structure and particularly the upper part of the telescope tube (see fig. 1.4) are exposed to high frequency fluctuations. The servo control system of the drives on the two axes of a modern telescope may have a bandwidth of about 1 to 3 Hz, effectively compensating quasi-static loads and fluctuating components up to that frequency. A possibility to overcome this limitation will be given in future by servo-controlled tilting secondary mirrors. Such systems are being developed for the VLT and GEMINI2 projects and should dramatically increase the frequency range of corrected fluctuations for observations in visible wavelengths. In the infrared wavelengths however, the requirement for a chopping secondary mirror may still not be compatible with fast tilt control. The drives and bearings of a modern telescope are designed to minimize friction and other non-linear effects. Therefore the response of the servo loop to a varying wind loading can be evaluated with good accuracy by a computation in the frequency domain. Consider the mean aerodynamic torque about one telescope axis y, conventionally defined as: 1 My = CMy ρU 2 2 1 2 where 2 ρU is the usual expression for dynamic pressure and CMy a torque coefficient determined by wind tunnel tests or estimated by computation for each orientation of the telescope. Recalling that the rms of dynamic pressure σp is σp = ρU σu

when U σu

(2.22)

the power spectrum of the aerodynamic torque SMy (n) is expressed as: SMy (n) = (CMy ρU )2 XMy (n) Su (n) 2

See footnote at page 1-3.

(2.23)

2-13


where XMy (n) is the aerodynamic admittance function for the torque about axis y, also determined by wind tunnel tests or computation. The aerodynamic admittance function represents the low-pass character of the telescope structure, which averages out the effect of high frequency turbulence, made of small size vortices. Then the rms of the guiding error angle θy will be computed as: θy =

Z

0

∞

SMy (n)Hθy (n) dn

(2.24)

where Hθy (n) is the guiding response function, determined from the characteristics of the servo loop control systems. The error θx about the other telescope axis can be similarly obtained and the total guiding error is then: θg =

q

θx2 + θy2

(2.25)

The quantities CM and XM (n) will generally depend on the shape of the telescope and the type of enclosure, and will also be functions of the orientation angle. They are therefore best evaluated in wind tunnel tests. Descriptions and data referring to wind tunnel tests performed for the VLT unit telescopes are found in [Zago 89b] and [Alexandrou].

2.3.3

Wind buffeting on ”thin” primary mirrors

The undeformability of the primary mirror is a main requirement for the optical quality of a telescope. While thermal deformation effects are prevented by the use of quasi-zero thermal expansion materials such as Xerodur glass, the effect of static (the change of gravity orientation with respect to the mirror) and dynamic loads (wind and inertia loads) used to be minimized by making the primary mirrors quite thick in proportion to their diameter. The recent development of active mirror support systems, generally called active optics [Wilson 87], has changed this situation. These systems are mainly aimed at maintaining the shape of the mirror through the change of gravity orientation during tracking and can also correct slight alignment and focusing errors. As the shape of the mirror can be adjusted very finely by active actuators that apply controlled forces, the mirror itself does not need to be very rigid. Moreover a too high stiffness would require higher control forces. Adding to this, there are presently technological limitations in the manufacturing of 8-m glass mirror that prevent them from having a thickness of more than 20 cm. Therefore the primary mirrors of the new 8-m telescopes of the latest generation have a relatively low stiffness which results in a larger sensitivity of their shape to externally applied forces. For instance the mirrors of the VLT 8-m telescopes will be intrinsically 37 times less rigid than the one of the 3.5-m NTT (the first telescope with active optics), which is already four times less stiff than the mirrors of predecessor telescopes in the 4-m class.

2-14


Figure 2.4: Illustration of the active optics concept for a modern telescope: • Fine adjustment of the figure of the primary mirror. • Tilt and focus control at the secondary mirror. • Higher frequency correction at a smaller mirror along the optical train: this latest development is also called adaptive optics (see also the note at page 2-2).


2-15

The lower stiffness of the new ”thin” mirrors makes their figure much more sensitive to a varying wind loading. In fact, while the effects of constant or quasi constant pressures can be corrected in closed loop with the active optics system, this has a bandwidth limited by a number of reasons to a period of the order of 1 minute. Pressure variations over shorter times cannot be compensated and will result in dynamic deformations of the mirror and consequent optical aberrations. These are quantified in two ways. One figure of merit is the rms of the surface displacements, hence of the deformation σw of the wavefront, which is generally expressed in nanometers. The other one is the rms of the slope of the wavefront θw , expressed in arcsec, which is also equal to the rms size of the image PSF and then directly comparable to the FWHM angle used for the quantification of seeing. If the main modal components of the deformation are known, the two quantities can be related by analytical or numerical computations.

2-16

2.4


The overall image quality and its budget

The overall image quality, in terms of angular image size and resolution, of an astronomical observation will be given by a quadratic sum of many different terms, among which the main ones are: • Aberrations of the optical components and alignment errors in the telescope.

• Dynamic guiding errors, such as those from the servo loops • The seeing, see expression (2.16)

• Wind dependent high frequency errors In order to guide the design of a telescope, a general error budget tree is formulated. The organization of the error tree for a modern telescope is shown in fig. 2.4. It contains both manufacturing and operation elements. The error budget is divided into two group: on the one hand fixed errors due to manufacturing tolerances and intrinsic limitations of the optical and mechanical systems; on the other hand errors with short time frequencies which depend on the variable conditions of the atmosphere. This second group comprises natural seeing and the effects of local turbulence (local seeing and wind). The creation of an error budget among the various sources of error is often somewhat arbitrary for a complex system. In the case of a telescope an additional difficulty is given by the fact that fixed errors and tolerances should be added to terms of inherently variable nature that depend on the environmental conditions. The error budgets of telescope projects are traditionally given in term of angular image size where the various contributions3 are added quadratically. θ2 =

X

θi2

(2.26)

i

Diericks has criticized this approach and proposed a new criterion for the evaluation of the effects of errors on the final image quality based on a parameter that he called Central Intensity Ratio (CIR) ([Diericks]), defined as Ic =

S S0

(2.27)

where S is the Strehl ratio of the telescope due to all effects: optical aberrations, guiding errors, seeing, etc. and S0 is the Strehl ratio of the equivalent perfect telescope (limited only by diffraction) in the same natural seeing conditions. Therefore the CIR index accounts for all possible sources of errors including local seeing effects with the single exception of seeing of the free atmosphere. It must be noted that the CIR is then a function of natural seeing, and it improves for bad seeing conditions because the telescope errors become more and more masked by the natural seeing. 3

Including the total seeing contribution.

2.4. THE OVERALL IMAGE QUALITY AND ITS BUDGET

2-17

One may note that the CIR criterion has been proposed essentially because of its convenience for defining without risk of over-specification the polishing tolerances of the primary mirror. In this respect the CIR is also more practical than the Strehl ratio, which for a large telescope and poor seeing becomes extremely small (see fig. 2.2). We will show in chapter 6 of this report that the CIR criterion is also a most suitable tool for the objective evaluation of the disturbing influences of atmospheric turbulence on the telescope performance. For large ratios D/ro and as long as it is Ic ≥ 0.8, [Diericks] shows that the relation between the CIR, the FWHM angle θn due to the natural seeing and the telescope errors are: • for local seeing FWHM and/or rms slope error of optical surfaces

• for guiding errors

Ic ' 1 − 2.89 (

θ 2 ) θn

(2.28)

Ic ' 1 − 5.77 (

θg 2 ) θn

(2.29)

where θ is respectively the local seeing FWHM angle and/or the rms slope error and θg is the rms guiding error. Assuming that the individual errors are not correlated the decrease of CIR resulting from a combination of N different errors is simply the sum of the N individual CIR losses: Ic =

N X i=1

(1 − Ici )

(2.30)

Fig. 2.4 shows the error budget of the ESO VLT in terms of the Central Intensity Ratio. It is to be noted that to date there are no established methodologies to verify the performance of the wind and seeing dependent terms in a manner that reflects the actual operation of the telescope and as a consequence also the budget values for these terms are generally set rather arbitrarily. A contribution toward a solution to this problem will be given in chapter 6.

2-18


Figure 2.5: Structure of the error budget tree for the ESO VLT

Figure 2.6: Actual image quality budget of the ESO VLT in terms of the Central Intensity Ratio

Chapter 3 Telescope enclosures Telescopes are delicate instruments and need protection against daylight, atmospheric precipitations and dust. Therefore a closed enclosure is needed when the telescope is not observing the sky. Traditionally this building was topped by a rotating dome with an opening slit in order to give a free field of view to the telescope during the observations. On the other hand it has been also known for some time that the very presence of the dome around the telescope is the cause of seeing effects that degrade the quality of the images observed. This was sometimes expressed by astronomers as ”the best dome is no dome”, a paradox which is not always true since vibrations induced by the wind on an exposed telescope may degrade image quality as much as seeing, but which illustrates the dilemma faced by the designers of telescope enclosures.

3-1

3-2

3.1

CHAPTER 3. TELESCOPE ENCLOSURES

The requirements of telescope enclosures

Telescope enclosures are a very particular type of buildings. They must fulfill an unusual set of requirements, which may be briefly outlined as follows: 1. In the closed position, the enclosure shall provide weather protection and a controlled environment (in particular with respect to thermal conditioning and cleanliness) for the telescope and its instrumentation. 2. In the configuration for observation, the enclosure shall allow a free field of view to the telescope. The enclosure should also provide the best atmospheric environment for the telescope observations. This has multifold aspects from the protection of the telescope from wind loads that may affect its guiding accuracy to the prevention or minimization of local seeing effects. These objectives represent the greatest challenge to the designer. 3. The enclosure shall provide access to the telescope for normal and extraordinary maintenance and include handling facilities for installing and removing large pieces of equipment like the primary mirror and the instruments that have to be removed and replaced regularly. In Appendix A one finds a brief description of the enclosure designed by the author for the ESO VLT 8-m telescopes, which illustrates in particular all the practical aspects related with servicing and maintainance that must be taken into account in the design of these buildings. With all its multifold requirements the design process of a telescope enclosure is a complex matter which should require a rigorous concurrent engineering approach. A main task within this process is constituted by the system analysis of the interaction of the enclosure characteristics with the optical performance of the telescope. Very schematically, the design process may be illustrated by the figure below. The next section outlines the evolution of engineering and design concepts for telescope enclosures during the past 20 years. Some case histories will illustrate the main problems associated with the design of these special buildings. Geometry & configuration requirements

Concurrent design Handling & maintenance requirements

... ... System engineering

Telescope environment requirements

Observation & operational requirements

Telescope characteristics

Figure 3.1: Schematic of the concurrent engineering process required for the design of telescope enclosures

3.2. EVOLUTION OF DESIGN CONCEPTS

3.2 3.2.1

3-3

Evolution of design concepts Classical domes

The classical external shape for a telescope has been for a long time a cylinder topped by a rotating hemispherical dome, which has a slit made such that it can have at any time only the opening strictly required for the view of the telescope. It is interesting to note that this concept was purely based on the intuition that a curved external shape would create less turbulence and therefore limit local seeing. The phenomenon of local seeing was very mysterious and the absence of hard evidence on its causes left dome designers relying on intuitive beliefs, such as that a smooth laminar air flow on the dome would be most favorable for the observation. The dimension of the dome was generally oversized with respect to the telescope, to protect it from wind loads and it was largely believed that any airflow on the telescope should be avoided. It was also thought that the telescope should be raised high above the ground level in order not to be affected by the near ground turbulence of the surface layer. Such ideas, although they were not quantified experimentally, determined the design of most existing telescope buildings. Let us consider for instance the ESO 3.6-m telescope dome at La Silla (fig. 3.2). Its designers believed that they were giving their telescope all best chances by locating it on the highest peak of the ridge; for good measure they built a massive 30-meter high tower topped with an oversize spherical dome (to prevent wind buffeting on the telescope). As a result the whole building is very impressive and the rotating dome is a particularly fine piece of heavy steel engineering. But, as in other examples of 4-meter telescope domes of the same generation, building and dome costed about 60 million DM (of 20 years ago) and accounted for about 60% of the entire telescope project cost. Some evidence that something may have been overdone began to appear a few years later when the ESO-MPG 2.2-m telescope was erected at La Silla. Its building is much more modest than its large predecessor (fig. 3.3). It is also located on a lower location on the main La Silla ridge. The telescope is placed almost at ground level and the dome fits the telescope with a minimal clearance. These choices were at the time dictated by financial budget constraints, nevertheless they did not seem to affect performance: the 2.2-m telescope was reported to have consistently better seeing than the 3.6-m ([Pedersen], see also section 3.2.5 hereafter). While a proper comparison should assess in particular the different thermal designs1 of the two buildings, it is quite obvious that there was an evident disproportion in the 3.6-m dome between means employed and results achieved. 1

The 2.2-m building includes a cooled floor while the 3.6-m now has an active air cooling system in the dome.

3-4


Figure 3.2: The ESO 3.6-m telescope building at La Silla: a 30-m high cylinder topped by a 30-m diameter hemispherical dome.

Figure 3.3: The building of the 2.2-m telescope is not larger than the ones of many smaller telescopes at La Silla.

3.2

EVOLUTION OF DESIGN CONCEPTS

3.2.2

3-5

The MMT and its rotating building

While the success of the ESO 2.2-m telescope already casted doubts on some traditional dome concepts, the real revolution in enclosure design came in the early 80s with the Multi-Mirror Telescope (MMT), in Arizona. The designers of the MMT were led by the particular telescope structure and financial budget constraints to make a box-like sharp-edged building, which rotated together with the telescope about the azimuth axis. The telescope observes through a large opening which makes it quite exposed to the wind and it is also placed quite low on the ground. In all respects the MMT building was exactly the opposite of former standards for telescope enclosures, but it proved itself nevertheless quite adequate. In particular the MMT was reported to have a remarkably good seeing [Beckers 81], which was attributed to the natural wind ventilation allowed by its large opening, the same effect that all earlier domes wanted to avoid. A main lesson of the MMT experience is that it has revealed a fundamental ignorance of the physics of local seeing, which had been hidden behind the effort given to the large and costly constructions of conventional domes.

Figure 3.4: The building of the MMT: the opposite of conventional domes, yet more than adequate for its purpose.

3-6

3.2.3


Improvements in conventional domes

The astronomers had not waited for the MMT to realize that the seeing of the 4-m class telescopes developed in the 60s and 70s was much worse than the natural value of the site. The drawback of bad seeing is greater with large telescopes since it tends to offset for many types of observation the advantage of the large aperture. Great efforts were put in trying to improve the situation. Anecdotal evidence and some early experiments ([Hoag], [Murdin]) pointed to convective heat transfer from heat generating equipment and warm surfaces as the main cause of dome seeing. A ”theory” of dome seeing was formulated ([Woolf 79]), in which the phenomenon was described by the rising of bubbles of warm air in the dome. Thus the corrective actions consisted in insulating the surfaces of floors and walls, trying to eliminate by active cooling all the heat produced by electric equipment items on the telescope and elsewhere within the dome. In some cases ventilators were installed to generate a ”sucking” effect through the slit, supposedly to counteract the upward motion of the bubbles. In some observatories a floor chilling system was installed in order to cause a stable vertical temperature gradient inside the dome to damp natural convection. This course of action was taken in particular for the 3.6-m Canadian-French-HawaiiTelescope (CFHT). The telescope, erected on Mauna Kea on the Hawaii island, which is deemed to be the best astronomical site in the world, had during the first years of operation a seeing in excess of 2 arcsec. As a result of many precautions taken to eliminate heat transfer to the telescope air volume, the average seeing has been improved to 0.6 arcsec ([Racine 84], [Racine 92]). These improvements, as in other observatories, were almost totally empirical, as only occasional measurements of seeing in association with physical quantities of the dome atmosphere were taken. For a long time little information was gathered on correlations usable for engineering work and the effectiveness of single actions was often controversial. For instance, an air conditioning system was installed at the ESO 3.6-m telescope to homogenize and lower the air temperature inside the dome. The author measured once the air temperature at 16:00 on a clear summer afternoon and found only 0.1 K difference between the floor and the top of the dome. So the system was certainly effective in eliminating temperature gradients inside the dome. However, the seeing improved only slightly. Also the effect of dome ventilators was controversial. [Gillingham 82] reported an improvement (not precisely quantified) of seeing in the 3.9-m Anglo-AustralianTelescope after the installation of two ventilators with a total rated flow of 40 m3 /s; this appeared not to depend on the direction of the flow, either up or down the slit. In a later report however, [Gillingham 89] reported on the basis of records totalling a few hours that blowing upwards resulted in better seeing than sucking downward. Nevertheless it was obvious that the various technical changes done in the domes

3.2


3-7

were globally effective even if no clear engineering guidelines could be drawn. Eventually the hypothesis was expressed that a large part of dome seeing was in fact mirror seeing, generated in the immediate vicinity of the surface of the primary mirror ([Woolf 82]). This was confirmed later by the analysis of a large data set taken at the CFHT ([Racine 92]). It is now recognized that the general improvement of seeing at the CFHT was due in a large part to the fact that the chilled floor and all the heat extraction precautions implemented were also helping to keep the temperature of the primary mirror closer to that of the air volume, a welcome effect that had not been deliberately sought. More recently, the CFHT observatory started a project to control more directly the temperature of the mirror. In the meantime the MMT had already announced its good news. It then appeared that seeing could be dramatically reduced also by letting the wind blow away any natural convection flows arising from the mirror and the surfaces of the telescope room.

3.2.4

The ESO New Technology Telescope

Besides the seeing aspects, the concept of a co-rotating building utilized for the MMT was very practical for telescopes with an altitude-azimuth mount. Thus it was also considered in the early 80s by ESO for the New Technology Telescope (NTT) 3.5-m project. The NTT project team had some critical thoughts on the MMT building and looked for further improvements: it was argued that if the MMT could improve seeing with a large frontal opening, adding another one at the back to flush the telescope with the wind flow might improve it further. At the same time it was still considered that smoothing a few edges would improve the quality of the airflow on the telescope. Therefore the initial concept for the NTT building was a mixture of old and new (fig. 3.5): the building was basically a cylinder topped by a hemisphere, chopped in order to have plane walls at the front and back and a flush-through slit. A model of this building was tested in the wind tunnel and the measurements showed that strong, high frequency turbulence was created inside the building by the wind going through the slit, with a peak frequency near to the first eigenfrequency of the telescope. This would have degraded the guiding performance by more than any seeing improvement. Still, a configuration with both ends open remained attractive because it allowed the exchange of the whole volume of air in the dome within a few seconds. The designers added a semi-permeable windscreen at the front (see fig. 4.7 at page 4-8) and closed the back wall with adjustable louvers. Then, realizing that a wind shielding system would be necessary independently of the external shape, they aban-

3-8


Figure 3.5: The first design of the NTT building.

Figure 3.6: The final building of the NTT

3.2


3-9

doned the pretense of an aerodynamic shape and redesigned the building geometry solely on the base of its functional requirements - fig. 3.6. A new, more extensive series of wind tunnel tests were conducted with the new configuration (the main results of which are included in chapter 4), which confirmed the need for a frontal windscreen with a permeability of about 20%. Experience on the telescope, in service at La Silla since 1989, has showed that the windscreen needs generally to be raised when the wind exceeds 6 ∼ 7 m/s. In conditions of light breezes (2 ∼ 4 m/s) without windscreen and the louvers opened, the NTT appears to have virtually no local seeing. However when the wind is stronger and ventilation must be reduced, the seeing effect reappears.

3.2.5

Average seeing at different telescopes at La Silla

Since about 1987, all astronomers observing at the main telescopes of the La Silla observatory are requested to log the seeing angle experienced during their observations. Although this request is not always followed and the seeing values are logged rather irregularly, this data base2 provides significant information on the large differences from telescopes that are in many respects quite similar and located on the same site. Unequivocally these differences can only be caused by the enclosure and the atmospheric environment in the immediate surrounding of the telescope A plot of the data (fig. 3.7) outlines in particular the difference between the 3.6-m and the 2.2-m telescopes. All values are corrected to get the seeing at zenith and at 1 µm wavelength. The data of the DIMM seeing monitor (see page 2-5) starting mid 1991 quantify even more dramatically the degradation of optical image quality at the other telescopes determined by the type of enclosure and building. Also since 1991 onward, the NTT establishes a new quality benchmark at the observatory.

3.2.6

The ESO Very Large Telescope

The favorable experience with the MMT and the NTT influenced fundamentally the design of the next generation of large telescope in the 8-meter class. Now natural ventilation was the word to be followed in designing the new enclosures. In 1984, at the start of the ESO VLT project, the work on the definition of the telescope enclosures began with the objective to study and design a fully retractable type of enclosure, in which the telescope would be largely exposed to the undisturbed wind flow during observations. Beside the reduction of local seeing, another main design driver was the objective to drastically lower the cost of the telescope enclosures and other infrastructures to less than 25% of the overall project cost, 2

The data base is freely available on the Internet World Wide Web at the address http://lw10.ls.eso.org/lasilla/seeing2/seeingmain.html .

3-10


2.5

FWHM (arcsec)

2

1.5

1

0.5

0 87

87.5

88

88.5 year

89

89.5

90

90

90.5

91

91.5 year

92

92.5

93

93

93.5

94

94.5 year

95

95.5

96

2.5

FWHM (arcsec)

2

1.5

1

0.5

0

2.5

FWHM (arcsec)

2

1.5

1

0.5

0

Figure 3.7: Monthly average seeing at various telescopes at La Silla: + 3.6-m telescope 3 2.2-m telescope 2 NTT × DIMM seeing monitor Note that the seeing at the NTT is occasionally even better than at the DIMM seeing monitor. The DIMM is located on a 6-m high tower not far from the 2.2-m dome, therefore at a less favorable location than the NTT (see fig. 3.3).

3.2


Figure 3.8: The first artist’s view of the VLT (1984).

Figure 3.9: The retractable enclosure which was envisaged for the VLT

3-11

3-12


so that the entire VLT project could be realized within a budget frame compatible with what it was felt were the financial possibilities of the ESO organization. Thus the very first artist’s view of the VLT dating from 1984 (fig. 3.8) saw the four 8-m unit telescopes completely exposed during observations and protected during the day by movable roll-on/off shelters. A large windscreen had the function of limiting the wind loads on the telescope. For many reasons this first design was not very practical; however it illustrates well the objectives that were set for the enclosure with respect to the atmospheric environment: the enclosure should allow on the telescope as much wind flow as required for eliminating local seeing, while limiting the amplitude of wind buffeting to levels acceptable for the optimum guiding performance of the telescope. Eventually this design evolved to the retractable dome enclosure represented in fig. 3.9. The fixed base of the enclosure is made of a metal space frame ring-shaped structure and supports the rotating part on a number of roller bearings. The upper rotating part is made of an approximately cylindrical panel clad space frame, which constitutes a wind shielded recess in which the lower part of the telescope is contained, topped by a retractable hemispherical dome consisting of overlapping shell sections. During observations the enclosure leaves the upper part of the telescope essentially in open air. The problem of achieving a good guiding accuracy in open air was overcome by the design of a servo-controlled tilting secondary mirror. The effects of wind buffeting on the primary mirror, however, were not fully quantified until quite late in the project development. Although a possible criticality of this aspect had been recognized at an earlier stage, which led to provide the cylindrical recess for the lower part of the telescope (see fig. 3.9), it was thought that the active mirror support system could be designed capable of dynamic corrections up to a frequency of 1 Hz. Unfortunately the required technological developments could not be achieved within the VLT project envelope ([Noethe & Zago 93]). This issue led to a redesign of the VLT enclosure in form of a more conventional building (fig. 1.5). This choice brings again in the foreground also for the VLT the problem of local seeing.

3.2


3.2.7

3-13

A summary of outstanding problems

This brief presentation of some case histories of telescope projects illustrates how the state of the art in the engineering of astronomical observatories is not yet up to a knowledge level which should be required for designing reliably such complex systems. The trials, errors and design corrections that we have briefly recalled above have been the consequence of missing knowledge on a number of still unclear and controversial issues related to the interaction of a telescope with wind, seeing and the local atmospheric turbulence, in particular: • The relationship between the effects of dome and mirror seeing and the ventilation and temperature conditions of the telescope. • The characterization of the high frequency wind (mechanical) turbulence acting on a telescope during the observations, which is the main responsible of guiding errors. • The wind pressure field on the primary mirror and its relationship with optical aberrations. • The effects of the atmospheric surface layer, which should influence in particular the choice of the height of the telescope pier. The work presented in the next chapters is a contribution toward a better knowledge of these issues. In particular we intend: 1. To provide a larger and improved base of experimental data characterizing the atmospheric environment in several different types of telescope enclosures. 2. To obtain methods and figures for predicting the seeing and guiding performances of a telescope in relationship to the main variables that characterize the local atmospheric environment. 3. To contribute to the development of concurrent design approaches (see page 3-2) aimed at bringing the process of designing telescopes and their enclosures on more rational bases than it has been the case in the past. In pursuing these objectives we will try to maintain a global and general view and a pragmatic approach aimed at providing practical solutions to some main engineering issues related to the design of telescope enclosures. Thus our main aim will be to identify and characterize all the significant phenomena and establish parametric engineering relationships with the quantities which most influence them, sometimes at the price of simplifying approximations and generalizations.

3-14


Chapter 4 Telescope aerodynamics There is little effect from wind on the performance of 4-m class telescopes enclosed in large, oversize domes like the CFHT or the ESO 3.6-m (see chapter 3). In fact one of the main design criteria of those domes was the prevention of any wind loading on the telescope by leaving a large distance between the telescope tip and the slit and including movable windscreens to close those sectors of the slit that are not in the field of observation. The only wind tunnel study performed for these domes concerned static load measurements on a model of the CFHT telescope ([ENSAM]) which concluded that static wind loads were indeed negligible on the telescope. More recently, wind tunnel tests were performed on a model of the hemispherical dome of the 10-m Keck telescope [Kiceniuk], aimed at evaluating the airflow patterns and speeds inside the dome. After that the MMT showed the favorable effects of wind on seeing, several aerodynamics studies were performed on enclosure design concepts in which the telescope volume was flushed by the wind flow. Worth mentioning are some water tunnel tests performed by Japanese and US teams searching for the best arrangement of venting openings in enclosures of hemispherical, cylindrical and various polyhedral form ([Ando], [Siriluk]). We note here that the value of all these tests resides mainly in a qualitative evaluation of the flow patterns surrounding the telescope, since the similarity conditions were not respected sufficiently for drawing accurate quantitative results, generally because of the limitations of the test facilities utilized. Also, these studies generally overlooked the importance of the effect of the slit induced turbulence, first put in evidence by the author [Zago 85] in a preliminary analysis of the wind tunnel measurements of the NTT building. At a time when venting a telescope was reported as the newest and best solution to fight the dome seeing problem (see page 3-9), we pointed out that in the context of the new projects for 8-m telescopes it could also affect negatively the telescope performance in two respects:

4-1

4-2

CHAPTER 4. TELESCOPE AERODYNAMICS

• The edges of the enclosure opening induce higher turbulence intensities in the flow, which result in significant fluctuations of dynamic pressure ( 21 ρU 2 ) acting on the telescope. • Pressure fluctuations may cause deformations, hence optical aberrations, of the primary mirror, which in 8-m telescopes will be much thinner in proportion to its diameter e.g. less stiff than in predecessor telescopes. An accurate quantification of both these effects requires the use of methods and test facilities (i.e. turbulent layer wind tunnels) which respect the similarity conditions that rule wind turbulence. In this regard the experimental results presented in this chapter represent the first accurate and reliable data base for the aerodynamic design of telescopes and their enclosures. It may be useful to underline two aspects that make the subject peculiar with respect to more conventional wind engineering. The first aspect is the extreme smallness of critical structural deflections that must be evaluated and ultimately minimized by proper engineering. With an aimed guiding accuracy of 0.3 arcsec rms , the tip of an 8-m telescope shall keep its deflection under wind to less than 20 µm rms. Therefore optical telescopes are not operated with wind speeds exceeding 80 or 100 km/hr, as in these conditions the enclosure is closed. One of the objectives of this research is the determination of the relatively low wind loads acting on a telescope in a way that is both accurate and suitable for input in parametric studies of the telescope performance. Analogously, the quality of the large primary mirrors starts deteriorating when deflections are greater than 200 nanometers, and the aberration depends strongly on the modal shape of the loading. The second peculiar aspect is consequent to the fully automated active control of guiding and mirror support. These systems have allowed a tremendous progress in maintaining the accuracy of the telescope over the exposure times of the observations but are able to compensate external loads only within a certain frequency bandwidth. Therefore one is interested in particular in the accurate characterization of the high frequency component of wind load, even when this constitutes a small part of the overall load.

4-3

4.1. WIND LOADING ON TELESCOPES

4.1

Wind loading on telescopes

In a typical telescope the top ring with the spiders (see fig. 1.4) represents the largest drag contribution to the aerodynamic torque acting on the telescope. Therefore measurements of the flow characteristics near the upper part of the telescope are representative of the overall aerodynamic action which influences the guiding performance. The guiding rms error will depend on the amplitude of the torque spectra about the two axes of the telescope - equations (2.24) and (2.25). Inserting equation (2.20) in (2.23) the torque spectrum about any axis y can be expressed as: 3

SMy (n) =

4(CMy ρσu )2 ULu 1 + 70.8

n LUu

2 56

(4.1)

We see that SMy (n) is a function of the static torque coefficient CMy = My / 21 ρU 2 , and of the three flow parameters: • U , mean speed • σu , speed rms

• Lu , turbulence length scale

In the following sections, we present the results of measurements of the parameters U , σu and Lu in various types of enclosures, in the region of the upper part of the telescope: [A] Measurements of wind turbulence in the dome of the ESO 3.6-m telescope. [B] Wind tunnel tests on a 1/50 model of the NTT enclosure. [C] Wind tunnel tests on a 1/64 model of the VLT cylindrical enclosure. [D] Wind tunnel tests on a 1/80 model of the alternative retractable enclosure for the VLT. The measurements in the 3.6-m dome were performed by the author with the help of F. Rigaut, who at the time was serving as a cooperant at La Silla. The wind tunnel studies were defined and coordinated by the author and contracted by ESO to specialized laboratories equipped with a boundary layer wind tunnel which allows a realistic simulation of the wind turbulence.

4-4

4.1.1


Classical domes

Here the results of an investigation in the ESO 3.6-m dome at La Silla are presented. The purpose of these measurements was to get a quantitative evaluation of the most critical wind effects in the dome, rather than a systematic survey representative of all observing conditions. 4.1.1.1

Measuring equipment and procedure

The measurements were taken in the upper part of the ESO 3.6-m dome (fig. 4.1), taking advantage of the bridge crane there located, during the evening of a windy day when the dome anemometer indicated almost constantly a mean velocity of 18 m/s from North. The dome slit was entirely opened. A vortex type anemometer (fig. 4.2) was utilized, which is particularly suited for fast response measurements, having a ∆t · U resolution of 6 mm. The measurements consisted of wind velocity sequences of 137 seconds each with 4096 records, therefore at the frequency of nearly 30 Hz. Several such sequences were recorded at different positions along the path of the bridge crane as shown in fig. 4.1. Before each sequence, the dome was rotated forth and back in order to find, rather empirically, the azimuth angle at which one would have the stronger feeling of wind flow and turbulence. Not surprisingly, this was found to be approximately facing the mean wind direction. Therefore the values measured are properly worst case quantities, as one may expect that during observation the slit would be facing the wind only a fraction of the observing time. 4.1.1.2

Results

The main results from the measurements are given in the figures found in the next pages, as a function of the distance from the edge of the slit. Some measurements were taken along the center of the slit, others halfway to the left side, as it was remarked that flow and turbulence were often stronger along the sides than along the slit mid-line. The 3.6-m dome, even with the slit facing the wind, acts as an efficient wind shield in terms of mean flow velocity. Nevertheless, the slit is the cause of velocity fluctuations inside the dome, which are larger than in the original atmospheric turbulence. This dome induced turbulence has a mean scale of the order of the slit width and a peak frequency in the range 0.3 to 1 Hz. In proximity of the slit this effect causes also fluctuations of the dynamic pressure term ( 12 ρU 2 ) that are larger than in the free atmosphere, particularly in the frequency range above 1 Hz where they might directly affect the tracking behavior of an hypothetic telescope whose top structure would come closer to the slit than the present telescope. Further inside the dome,


4-5

because of the large decrease of mean velocity the amplitude of pressure fluctuations is largely below the situation in the free flow.

Figure 4.1: Measurement locations in the 3.6-m dome.

Figure 4.2: The vortex anemometer placed near the slit (left) and further inside the dome (right).

4-6


U/U∞ 0.5

Velocity ratio Center of slit Left side +

0.4

0.3

+ +

0.2

+ + +

+ 0.1

0

0

2

4 6 Distance from slit (m)

8

10

Figure 4.3: Ratio of mean flow velocity ratio U/U∞ .

σu /U∞ 0.2

Absolute turbulence intensity Center of slit 3 Left side + 3

0.15

3 0.1 + + + +

0.05

+ + 3 3 3

0

0

2


3 3 8

10

Figure 4.4: Absolute turbulence intensity σu /U∞ . The free stream value during the measurements was about 0.04 .

4-7


Turbulence length scale / slit width 4 Center of slit Left side

3.5

Length scale / slit width

3 2.5 2 1.5 1 0.5 0 0

2


8

10

Figure 4.5: Turbulence scale Lu divided by the slit width (5 m). The turbulence scale in the free atmosphere at the location and level of the 3.6-m dome is in the range 50 to 200 meters. This free flow turbulence is still a contributing factor close to the edge of the dome (Lu = 14-17 m); further inside we have purely slit made turbulence.

Figure 4.6: Normalized gust spectra at different locations inside the dome and, for reference, in the free flow. In the free atmosphere most of the wind turbulence energy is found in the range 0.01 to 0.05 Hz. In the dome a peak in the range 0.3 to 1 Hz appears, which takes more of the turbulent energy the further away one is from the slit. Note that the spectra are here normalized with the respective σu2 values.

4-8


Figure 4.7: The enclosure of the NTT with the stowable wind screen raised along the front slit.


4.1.2

4-9

NTT rotating building

The ESO NTT has been the first telescope whose enclosure is designed to allow wind through-flow in the telescope volume (see section 3.2.4 above). It has also become a kind of a standard reference for advanced telescopes in the 4-m class. The same design of telescope and enclosure with minor modifications has been adopted for the 3.5-m GALILEO telescope presently in construction for installation at the observatory of La Palma (Canary Islands) and is considered also for a future SouthAfrican telescope. This enclosure is actually a real building, with several volumes and rooms for telescope, instruments and auxiliary equipment which rotates about the azimuth axis accompanying the telescope. The telescope is housed in a kind of corridor between two walls which separate the closed rooms for the Nasmyth instruments which are air conditioned separately. This corridor is closed on the front and upper sides by 2 large upside-down-L shaped sliding doors while the back a wall includes several louvers allowing through ventilation. A semi-permeable windscreen can be raised across the front side of the slit (fig. 4.7). The tests were performed in the turbulent wind tunnel of the Technical University of Aachen with a 1:50 model of the NTT rotating building. The velocity measurements were taken at three locations, indicated in fig. 4.8. The tests were run with several venting configurations of the enclosure O-O-O O-O-20% 50%-u-O 20%-h-O 50%-u-O

Slit open without windscreen, back louvers open. Slit open without windscreen, back louvers with 20% permeability (almost closed). Slit open with windscreen with 50% permeability over the entire height, back louvers open. Slit open with windscreen with 50% permeability over half the front height, back louvers open. Slit open with windscreen with 50% permeability over the entire height, back louvers open.

The measurements covered the range of azimuth angles from 0 to 60◦ with the wind direction. Figures 4.9 and 4.10 show the main results for point TR45: • Ratio of mean speeds U/U∞

• Absolute turbulence intensity, evaluated with respect to the free flow speed It = σu /U∞ • Turbulence length scale, evaluated by approximating a Von Karman spectrum (see equation 2.20)) to the measured spectrum in the inertial range. In this way the derived value of length scale will best represent in parametric studies using the Von Karman expression the actual energy density in the high frequency range most critical for the telescope tracking performance. In the plot the length scale Lu is normalized with the slit width.

4-10


• Fluctuation σp of the dynamic pressure term ( 21 ρU 2 ), normalized with the term 2 ρU∞ . The data show a sharp decrease of mean speed for azimuth angles greater than 20◦ . Without windscreen (configurations O-O-O and O-O-20%), this is associated with a large increase of turbulence, particularly for azimuth angles between 10 and 40◦ where the turbulent fluctuations of dynamic pressure created by the slit are quite larger than in the free wind flow. The turbulence length scale is respectively 0.37 and 0.48 of the slit width at zero azimuth, which signifies the generation of high frequency turbulence by the slit edges even when the telescope faces the wind directly. Fig. 4.11 shows the values of the pressure spectral density at 6 Hz for a free flow mean speed of 18 m/s, a good indicator of the wind influence on the tracking performance as telescopes have generally their first eigenfrequency between 5 and 8 Hz: the amplification with respect to the free flow conditions reaches one order of magnitude. This effect is only corrected when the windscreen is raised to full height across the front side of the slit, such that the mean flow velocity, hence the pressure fluctuations on the telescope (see equation (2.22)) are sharply decreased. On the basis of these results a 20% permeability windscreen was integrated in the final design of enclosure. Observation records of the NTT at La Silla show that in most cases the operator is obliged to raise it when the wind exceeds about 6 m/s, that is almost half of the time of observation.


4-11

Figure 4.8: Drawing of the model of the NTT building (quoted dimensions are full scale) showing the three measurement points.

4-12


Velocity ratio U / U_inf O-O-O O-O-C 50%-u-O 20%-h-O 20%-u-O

1

Velocity ratio

0.8

0.6

0.4

0.2

0 0

10

20 30 40 Azimuth angle (deg)

50

60

Absolute turbulence intensity sigma_U / U_inf 0.6 O-O-O O-O-C 50%-u-O 20%-h-O 20%-u-O

Abs. turbulence intensity

0.5

0.4

0.3

0.2

0.1

0 0

10


50

60

Turbulence length scale / slit width O-O-O O-O-20% 50%-u-O 20%-h-O 20%-u-O

Length scale / slit width

1

0.8

0.6

0.4

0.2

0 0

10


50

60

Figure 4.9: Flow on telescope upper part for different venting configurations - test results

4-13


Pressure fluctuation 0.5 O-O-O O-O-C 50%-u-O 20%-h-O 20%-u-O

Nonpimensional pressure fluctuation

0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0

10


50

60

Figure 4.10: Normalized rms of dynamic pressure on the telescope upper part: σp /(ρU 2 )

80 O-O-O 70

S_p(6Hz) [Pa2/Hz]

60 50 40 30 20 10 0 0

10

20

30 40 Azimuth angle (deg)

50

60

Figure 4.11: Pressure spectral density at 6 Hz for a free flow wind speed of 18 m/s. For reference the free flow value (for L = 100 m) is 3.32 Pa2 /Hz.

4-14


Figure 4.12: Photograph of the test model

4.1.3

Cylindrical enclosure (VLT)

The cylindrical enclosure selected for the VLT unit telescopes is presented in section 1.4 and appendix A. This type of enclosure retains elements of both the NTT building (namely the large upside-down-L shaped slit doors) and conventional domes. The enclosure structure is essentially an envelope protecting the telescope with a rotating upper part. Louvers and other openings are placed along the entire envelope surface and a proportionally larger volume can be ventilated than in the NTT. Wind tunnel tests of this enclosure were performed at the boundary layer wind tunnel of the Danish Maritime Institute. The model included the complete enclosure with a fully modeled telescope inside it at a scale of 1:64 as shown in fig. 4.12. The tests were run with several venting configurations of the enclosure: O-O-O C-C-O O-C-20

O-C-50

C-C-20

Louvers open, bottom ventilation openings open, slit open without windscreen. Louvers closed, bottom ventilation openings closed, slit open without windscreen: only wind direction 0◦ and 20◦ . Louvers closed, bottom ventilation openings closed, slit open with windscreen with 20% permeability over the entire height. Louvers closed, bottom ventilation openings closed, slit open with windscreen with 50% permeability over the entire height. Louvers closed, bottom ventilation openings closed, slit open with windscreen with 20% permeability over the entire height.

We present here the flow properties measured at the location just in front of the top ring of the telescope, as shown in fig. 4.13, which are most determining for the

4-15


guiding performance of the telescope. The test report ([DMI]) describes the results of all the measurements performed, which included also forces and torques on the telescope and the pressure distribution on the enclosure outer surface. Fig. 4.14 shows the measured normalized values of mean speed, turbulence intensity and length scale for the various venting configurations. Fig. 4.15 gives the normalized 2 ). The results show a pattern similar to fluctuation of dynamic pressure σp /(ρU∞ the case of the NTT when the flow can pass through the telescope volume (louvers open): mean speeds decrease sharply for azimuth angles greater than 20◦ ; without windscreen there is a large increase of turbulence for azimuth angles between 20◦ and 40◦ . The fluctuations of dynamic pressure on the telescope will be largest for an azimuth ≈ 20◦ , where the turbulence length scale drops to about 0.2 of the slit width. However, when the louvers are closed and the cylinder surface is air tight except for the large slit (configurations C-C-O and C-C-20%), the flow cannot pass through the telescope volume and the speed near the top of the telescope speed increases with a growing azimuth angle at least until 40◦ . Unfortunately no measurements were performed for these configurations at larger azimuth angles. Like for the NTT, the data conclude to the need of a 20% semi-permeable windscreen which will limit high frequency pressure fluctuations on the telescope by reducing the mean flow velocity.

Slit of enclosure 4m

Measuring point

Figure 4.13: Measuring point for wind loading on the telescope: 4 m (full scale) in front of the top ring

4-16


Velocity ratio U / U_inf O-O90-O O-O180-O O-C-O O-C-20% O-C-50% C-C-O C-C-20%

1

Velocity ratio

0.8 0.6 0.4 0.2 0 0

20


Absolute turbulence intensity sigma_U / U_inf

80

Turbulence length scale / slit width

0.4 O-O90-O O-O180-O O-C-O C-C-O O-C-50% O-C-20% C-C-20%

0.3

0.25 0.2

O-O90-O O-O180-O O-C-O O-C-20% O-C-50% C-C-O C-C-20%

1 Length scale / slit width

Abs. turbulence intensity

0.35

0.15 0.1

0.05 0

0.8 0.6 0.4 0.2 0

0

20


80

0

20


80

Figure 4.14: Cylindrical enclosure: flow on telescope upper part

Nondimensional pressure fluctuation

Pressure fluctuation 0.3 O-O90-O O-O180-O O-C-O O-C-20% O-C-50% C-C-O C-C-20%

0.25 0.2

0.15 0.1

0.05 0 0

20


80

2 Figure 4.15: Normalized rms of dynamic pressure σp /(ρU∞ ) on the telescope upper part


4.1.4

4-17

Retractable enclosure

The test results presented in the two previous sections illustrate well the main problem with ventilated telescope enclosure: the natural wind ventilation desired to get rid of dome seeing effects is associated to high frequency turbulence produced by the slit edges, which then affects the guiding performance of the telescope. An alternative envisaged to overcome this problem consisted a retractable enclosure which leaves the upper part of the telescope completely exposed to open air during the observations. Even if the overall pressure fluctuations on the telescope are larger than in the previous enclosures, their frequency is much lower and the perturbations can be corrected dynamically by the guiding control loop. Wind tunnel tests with a model a retractable enclosure were performed at the EPFL/LASEN boundary layer wind tunnel as part of the feasibility studies of the VLT project (see section 3.2.6). The telescope is exposed to open air for the observations, except for the lower part which is enclosed in a protecting recess. The model was at the 1:80 scale and included a very detailed model of the telescope structure. The edge of the enclosure was horizontal and located 16 mm (model scale) above the altitude axis. The tests were conducted with a mean speed of 16 m/s and a rms of 1.8 m/s, which gives a free flow turbulence intensity of 0.11 .

Figure 4.16: Model of the retractable enclosure in the LASEN wind tunnel

4-18


The profiles of mean speed and turbulence intensity were measured along a vertical line 1.9 cm (model scale) in front of the edge of the telescope pointing at zenith and are shown in fig. 4.17. Note that the height is given in the model scale (1:80 with respect to the 8-m telescope).

700

600

600

500

500 Height (mm)

700

400 300 200

400 300 200

100

100

0

0

-100 -10

-100 -5

0 5 10 Mean speed (m/s)

15

20

0

0.2

0.4 0.6 Turbulence intensity

0.8

700 600 500 Height (mm)

Height (mm)

These measurements show the telescope wind environment as divided in two regions: the top of the telescope is essentially in the undisturbed free flow while the lower telescope structure and the primary mirror are located in a region with recirculating flow.

400 300 200 100 0 -100 0

10

20 30 40 Length scale (m)

50

60

Figure 4.17: Vertical profile of mean speed, turbulence intensity and turbulence length scale (full scale) in front of the telescope pointing at zenith. The height is given in the model scale (1:80 with respect to the 8-m telescope).

1


4.1.5

4-19

Synthesis

The main characteristics of the wind flow acting on a telescope in different types of enclosures have been investigated. The main conclusions of this study are: • In conventional domes the turbulence created by the slit edges will generally not disturb the telescope’s guiding. In the cases where the dome is oversized with respect to the telescope the fluctuations of dynamic pressure on the telescope are negligible and windscreens are not required. Only if the dome is fitted very tightly on the telescope there will be occasionally periods and orientations in which a windscreen will be needed. • In the new types of through-flow enclosures, when no windscreen is set across the slit there is a critical range of azimuth angles between 20◦ and 40◦ in which the turbulence created by the slit is much larger than the one present in the free wind flow. In that range the absolute turbulence intensity σ/U∞ on the telescope is higher for the NTT (' 0.45) than for the cylindrical enclosure (' 0.25), possibly because of the amplifying effect of the parallel walls. For azimuth angles ≤ 10◦ and ≥ 50◦ the turbulence intensity remains around 0.1 . • Windscreens with a permeability of 50% decrease by about half the mean speed but only marginally the turbulence intensity. Windscreens with a permeability of 20% decrease the mean speed to about 20 % and limit also the turbulence intensity to about 0.1 . • The turbulence length scale of the flow acting on the telescope is related to the slit width with factors varying from 0.4 to 1 in the different configurations without windscreen, for azimuth ≈ 0◦ when the telescope is facing the wind. Increasing the azimuth angle, the ratio length scale/slit width decreases respectively to below 0.2 in both enclosures, with large variations depending on the setting of the louvers allowing or denying through-flow in the enclosure. The low values of length scale will cause the wind spectrum at the telescope to have a peak in the range of 1 to 10 Hz (see equation (2.21)), where the amplification of the fluctuating term of the dynamic pressure ( 21 ρU 2 ) with respect to the free wind flow conditions reaches one order of magnitude. As these frequencies will generally be close to or above the bandwidth of the telescope servo system, maintaining a good guiding performance of the telescope will require the use of a 20% windscreen to limit the pressure fluctuations by dramatically reducing the mean flow speed (see equation (2.22)).

4-20

4.2 4.2.1


Wind loading on the primary mirror Outline of the problem

The problem treated here is the evaluation of the loss of image quality caused by wind induced pressure fluctuations on the primary mirror of a large optical telescope. The primary mirror will experience significant optical aberrations already with deflections of the order of 200 nanometers. These aberrations depend strongly on the modal shapes of the deflections which in turn depend on the spatial distribution of pressure fluctuations on the surface and on the mirror eigenmodes. Therefore the study described here joins notions and methods of optics and wind engineering. This special problem will be tackled in the following manner: 1. The features to be investigated are the pressure variations on the mirror surface which shall be measured over times which are somewhat longer than the basic integration time of the active optics system (30 sec to 1 min). These measurements shall allow a decomposition into the main optical aberrations modes of the mirror, described by Zernike polynomials, of which the first eight are: 1 2(x2 + y 2 ) − 1 x y x2 − y 2 2xy x(x2 − 3y 2 ) y(3x2 − y 2 )

piston def tilt-x tilt-y ast-x ast-y tri-x tri-y

piston defocus tilt x-component tilt y-component astigmatism x-component astigmatism y-component triangular coma x-component triangular coma y-component

2. When these optical modes are fitted to measurements of the pressure field on the mirror, one obtains a set of modal pressure coefficients which then characterize the spatial frequencies of the fluctuating pressure field. 3. The wavefront aberrations corresponding to each modal component of pressure can be computed from the modal pressure coefficients with a knowledge of the elastic eigenmodes of the mirror, which are quite similar to the aberration modes. 4. The square root of the quadratic sum of all components of the modal deformation gives finally the total wavefront aberration (expressed in nanometers), which is the measure of the overall optical quality of the mirror shape. 5. We will in particular study the variation of the overall mirror aberration with respect to the average values of fluctuating pressure in the different enclosure types and for various mirror orientations, with the aim to establish relationships suitable for parametric studies. This research ran parallel to the development of the VLT project and was developed in three experimental phases:

4.2. WIND LOADING ON THE PRIMARY MIRROR

4-21

[A] Wind tunnel tests on a 1/80 model of the telescope in open air. [B] Measurements of the pressure field on a 3.5-m dummy mirror located inside the NTT building (see fig. 3.6) just in front of the telescope and in the inflatable dome prototype, also located at the La Silla observatory. [C] Wind tunnel tests on a 1/60 model of the telescope surrounded by a cylindrical enclosure.

Figure 4.18: ”Open air” telescope model in the LASEN wind tunnel

4-22


y

wind flow 2 4 51.25 mm

1 44.5 mm

14

7

19 8

1

3

12

3

23 20 6

10

29.5 mm

5 15 mm

18

17

26

29

31 32

25 13 27

16

2

4

8

6

x 11

24 30

22 28

7

21

5

15 9

Figure 4.19: Distribution of pressure taps and sectors on the 1/80 models of the primary mirror

4.2.2

Wind tunnel tests with the telescope exposed

A first test with pressure measurements on the primary mirror was performed at the LASEN boundary layer tunnel as part of the program for wind loading on the VLT telescope in a retractable enclosure (see section 4.1.4). The 1/80 model of the telescope was surrounded by a low platform, which was at the time one of the alternative designs envisaged for an open air arrangement of the VLT (fig.4.18). Because of its sharp edges the mirror model can be considered to be Reynolds independent. Two types of measurements were done: • Average, peaks and r.m.s. of the pressure field. The measurements were obtained by 32 sensors distributed over the surface (see figure 4.19). The pressure signals were sampled at 250 Hz and the results were taken from 16 runs of 10 sec each. The frequency response of the sensors was flat up to 100 Hz. The following table shows the values of the mean 2 pressure coefficient cp [= P/( 21 ρU∞ )] and its rms σcp for various zenith angles α and zenithal angle γ measured with respect to the wind direction: γ α 10 0 30 0 45 0 80 0 30 45 30 90 30 135 30 180 3 180

cp -0.0668 0.1551 0.2992 0.5698 -0.0341 -0.2554 -0.3356 -0.3553 -0.2282

σcp 0.0532 0.0800 0.1033 0.1650 0.0558 0.0521 0.0494 0.0370 0.0649

4-23


• Mean pressures over eight sectors of the mirror. Since the measuring equipment did not allow the simultaneous measurement of the instantaneous pressure at all pressure taps, an original method was devised to obtain directly the main modal components of pressure. For this test a different model with the same dimensions but altogether 152 pressure taps was used. The pressure taps were grouped into eight sectors, which are shown in figure 4.19, the pressure taps were connected, thereby giving the average pressures over these sectors. By forming (1 + 3 + 5 + 6) − (2 + 4 + 6 + 8) one could measure properties of a mode similar to defocus and by forming (3 + 4 + 8 + 7) − (1 + 2 + 6 + 5) properties of a mode similar to the ycomponent of astigmatism. Both the average values and the r.m.s. values were measured for various zenith angles. The results for α = 0 are shown in figure 4.20. To get the corresponding coefficients of defocus and the ycomponent of astigmatism these data have to be multiplied by a factor of two. If one assumes reasonably that the x- and y-component of astigmatism are of the same √order of magnitude, a multiplication of the second coefficient with a factor 2 2 would give the coefficient of the total astigmatism. 0.15

0.15

_

σp

Cp 0.10

0.10

0.05

0.05 zenith angle

0.00 0

10

20

30

40

50

60

70

80

zenith angle 0.00 0

10

20

30

40

50

60

70

80

Figure 4.20: Mean and rms cp values of modes defocus (circles) and y-component of astigmatism (crosses)

4-24


4.2.3

Tests with the 3.5-m mirror dummy

4.2.3.1

Measurements

The measurements were performed on a dummy mirror with a diameter of 3.5 m, made of wood on a support structure of the same material. The altitude axis of the dummy was 2.5 m above the base and its inclination could be set in a range from 0◦ to 90◦ . The dummy mirror integrated 13 differential pressure sensors, located as shown in fig. 4.22. All pressures were measured at 50 Hz over 82 sec. The offsets of the 13 sensors could drift from one measurement to another. Average data computed from these measurements are therefore not very reliable. In total 76 measurements were done inside the NTT building where the dummy mirror was located just in front of the telescope. The measurements were performed over the complete range 0 ≤ γ ≤ 90◦ of zenith angles with the dummy mirror mostly facing the wind, with angles α between the wind and the azimuth of the enclosure in the range 0 ≤ α < 70◦ . The anemometer for the measurement of the reference wind was installed on a 2-m mast at the top of the building. 56 measurements were performed in the inflatable dome. The center of the dummy mirror was at a height of 2.5 m and was therefore largely shielded by the 3.5-m high concrete wall. The degree of this protection can be further controlled by setting different elevations of the inflatable segments. The measurements were performed over the complete range 0 ≤ γ ≤ 90◦ of zenith angles with three azimuth angles with respect to the predominant wind direction: 0, 135◦ and 180◦ . The reference anemometer was located on a mast approximately 10 meters away from the inflatable dome at a height of approximately 10 meters. The main test results are listed in appendix B.1. We will describe here the main results of this work and those of most general application. 4.2.3.2

Main results

The following table shows the averages cp (referred to U∞ and which, as mentioned above, are only approximately accurate) and the averages σcp of the rms pressure coefficients in the NTT for α ≈ 0 and various zenith angles γ. γ cp σcp

0 0.139 0.152

15 0.136 0.191

30 0.266 0.157

45 0.672 0.161

60 0.869 0.143

75 1.089 0.246

90 1.068 0.188

Whereas the average pressure p depends strongly on the inclination γ of the dummy, the pressure variations σcp are virtually independent of γ. The following table shows as an example the rms values σci of the temporal variations of the normalized modal coefficients and of the residual rms for the measurements

4-25


wind direction

ΦN

ΦS

Figure 4.21: Position of the dummy mirror in the inflatable dome

y 8 7

9 3

1750 mm

1500 mm 750 mm 2

10

4

6

1

x

5 13

11 12

Figure 4.22: Distribution of the sensors on the surface of the dummy mirror

4-26


in which α is ≈ 0 with various zenith angles γ. They are for all γ of the same order of magnitude. γ 0 15 30 45 60 75 90

α -12 -7 -6 6 -15 3 4

piston 0.1377 0.1135 0.0867 0.1107 0.0873 0.1894 0.1414

def 0.0434 0.0878 0.0694 0.0543 0.0740 0.1272 0.0987

tilt-x 0.0646 0.0745 0.1072 0.1407 0.0873 0.1721 0.0979

tilt-y 0.0545 0.1110 0.1335 0.0851 0.1307 0.1389 0.1349

ast-x 0.0514 0.1272 0.1157 0.1094 0.0922 0.1046 0.1046

ast-y 0.0524 0.1015 0.1348 0.0928 0.1105 0.1331 0.0861

tri-x 0.0590 0.1488 0.1284 0.1055 0.0983 0.1123 0.0908

tri-y 0.0431 0.0942 0.1486 0.0832 0.0815 0.0826 0.0636

res 0.0138 0.0389 0.0343 0.0261 0.0255 0.0249 0.0204

The data for defocus and astigmatism can be compared with the corresponding data from the LASEN wind tunnel experiments (fig. 4.20). A comparison √ with figure 4.20, where the data have to multiplied by two for defocus and about 2 2 for astigmatism, shows indeed the good agreement between the two experiments. The power spectra of the pressure at the locations of the 13 sensors and those computed for the various modes depend strongly on γ. For γ = 90◦ the highest energy density is at about 0.2 Hz. For smaller zenith angles the turbulence is shifted to much higher frequencies up to about 2 Hz. 4.2.3.3

Relationship between pressure fluctuations and wavefront aberrations

The rms surface error, hence the total wavefront aberration incurred by a real mirror under the measured pressure fluctuations may be computed from the modal pressure coefficients and the structural parameters of the mirror. This computation was done for the case of the VLT primary mirror, which has the following main characteristics: Material Density Diameter Form Thickness Young modulus Poisson ratio

Xerodur glass ρ = 2550 kg/m2 D = 8.2 m Meniscus with constant thickness t = 0.17 m E = 91·109 Pa ν = 0.24

The VLT mirror is supported by three hydraulic whiffle-trees, each acting the same pressure on 50 points over a 120◦ sector. The centers of the three sectors constitute the three virtual fix-points of the mirror. 150 active optics actuators are integrated into the hydraulic supports and are astatic, as they only produce controlled forces and are not reacting to external loads. The predominant deformations produced by external forces are the elastic eigenmodes of the mirror with the lowest eigenfrequencies. The deflections in these

4-27


eigenmodes are proportional to the corresponding components in the pressure field, with scaling factors which are inversely proportional to the square of the eigenfrequencies of these modes. The wavefront aberrations generated by the wind pressure fluctuations can then be computed as the sum of the lowest eigenmodes generated by the corresponding pressure fields and the reaction forces on the fixed points. The computation method is rather complex and is described in [Noethe 91]. The computation for the VLT mirror was performed by L. Noethe of ESO and is reported in [Noethe 92]. Hereby we will only present some main results and draw their general consequences. The following table shows the dependence of the rms of the wavefront aberration in the main optical modes on the zenith angle γ of the dummy for α ≈ 0. The data are from the measurements 1 to 7 in the NTT (see section B.1.1 of appendix B) and are normalized to an external wind speed of 10 m/s: γ σw,def σw,ast σw,tri σw,total

0 162 626 99 654

15 330 1476 246 1532

30 254 1604 273 1647

45 198 1344 185 1371

60 253 1187 172 1225

75 429 1651 190 1716

90 367 1189 144 1252

The bulk of the wavefront aberration is contained in the astigmatic mode which is very similar to the first eigenmode of the mirror, which has symmetry two. Fig. 4.23 shows for all measurements the correlations between the average σp of the rms values of the pressure variations and the rms σw of the computed total wavefront aberration. The figures suggest a linear relationship between the two parameters, independently of mirror azimuth and zenith, with a factor ≈ 150 in the NTT building and slightly lower in the inflatable dome. Recalling also that the modal pressure coefficients were similar in the NTT and in open air, it appears that the normalized modal pressure patterns on a mirror are determined to a greater extent by the disk shape itself than by the particular wind flow field inside the enclosure. Therefore it is possible, at least for the purpose of engineering parametric studies to express the total wavefront aberration simply from pressure measurements with few sensors on the mirror. The relationship σw ' 150 σp applies of course only to the VLT mirror but can be scaled to other mirror dimensions. Recalling that the displacement of a loaded plate is proportional to x4 /(Et3 ), for a mirror of arbitrary stiffness, diameter and thickness, supported on three equidistant virtual points, one obtains: D4 σw ' 2.17 · 10 σp Et3 5

(nm)

(4.2)

4-28


σw (nm) Mirror in the NTT building 6000 3 3 3 3 5000 3 3 33 4000 3 3 3 3 3 3 333 3000 3 3 3 3 3 33 2000 3 3 333 3 3 33 3 3 3 3 1000 3 3 3 3 3 3 3 3 3 3 3 3 33 3 3 3 3 3 3 3 3 33 03 3 3 0 5 10 15 20 25 30 35 40 σp (Pa)

σw (nm) Mirror in the inflatable dome 800 700

3 3

600 500 400 300 200

3

33 100 33 3 3 3 3 3 33 3 33 03 3 3 333 0 1

3 3 3 33 3 3 3 3 3 3 3 3 333 33 3 3 3 3 3 33 3 33 3

2 3 σp (Pa)

4

5

Figure 4.23: Rms of the total wavefront error versus the average rms of pressure fluctuations. The line represents the relationship σw = 150 σp . Recalling that the wavefront aberration caused by the pressure fluctuation consists predominantly of astigmatism, we have computed by means of the SuperIMAQ1 program the rms slope error of the optical aberration θw as a function of the wavefront error σw obtaining: σw (arcsec) θw = 0.00141 D where following the usual conventions σw is expressed in nanometers and D in meters. Inserting equation (4.2) we obtain: θw ' 306

D3 σp Et3

(arcsec)

(4.3)

Another aspect of general interest is the reduction of rms surface error when the mirror is shielded from the direct wind approach, as in the inflatable dome (see fig. 4.21). The degree of this protection can be further increased by raising the inflatable segments. Fig. 4.24 shows the influence of the elevation of the northern (windward) segment of the dome on the wavefront aberrations.

1

The SuperIMAQ program [ESO] was written by Ph. Diericks of ESO to compute the PSF and all image quality parameters of a telescope mirror, accounting for all diffraction effects, surface wavefront errors and seeing by the method described in [Diericks].

4-29


σw (nm) 800

Mirror in the inflatable dome

700

+ +

600 500

+

400

3 + 33 3 3

300 200

3

3

3 3 3

100 0

3

+

0

50

100

0◦ 30◦ 60◦ 90◦

3 + 2 ×

++

2 ×2 ×

3

ΦN = ΦN = ΦN = ΦN =

2 2

× ×

150 200 2 Uext (m2 /s2 )

250

300

Figure 4.24: Rms of the total wavefront aberration in the inflatable dome as a function of external wind speed (squared) for different elevations of the northern (windward) sector of the dome - see fig. 4.21.

4-30

4.2.4


Wind tunnel measurements of the pressure/velocity field on the mirror

In the previous section we have found a general, if approximate relationship between the average rms of pressure fluctuations on a primary mirror and the optical aberrations caused by dynamic deformations. It is also of interest to establish correlations between the wind speed measured on the mirror and the pressure fluctuations so that the ventilation of the enclosure can be planned optimally. In fact the wind has a twofold effect on the mirror: on the one hand it affects negatively the optical performance by deforming the mirror, on the other hand it has a positive effect as it decreases mirror seeing2 . We will present here some wind tunnel measurements taken for the VLT cylindrical enclosure.

Figure 4.25: Photograph of test model

2

Mirror seeing will be treated extensively in section 5.3.


4.2.4.1

4-31

Measurements

These wind tunnel tests were performed at the boundary layer wind tunnel of the Danish Maritime Institute as part of the test program with the cylindrical enclosure selected for the VLT (see section 4.1.3). The model included the same complete enclosure with a fully modeled telescope inside it at a scale of 1:64 (see fig. 4.25). The tests were run at a nominal wind speed of about 12 m/s, with several venting configurations of the enclosure as described in section 4.1.3 above and covered the range of wind directions 0, 10, 20, 40, 90 and 180◦ in combination with telescope zenith angles of 10, 35 and 60◦ . Two types of measurements were performed: • Measurements of the pressure difference between the upper and lower faces of the primary mirror. Pressure taps were mounted on opposite sides of the primary mirror at four symmetrical locations. The scanivalve setup was such that instantaneous pressure differences were measured. These instantaneous pressures were then expressed as coefficients normalized by the reference external wind speed. • Measurement of wind velocity close to the upper surface of the mirror, by two single-wire hot-wire probes, respectively vertical and horizontal, located about 10 mm (model scale) above the mirror surface. Appendix B.2 includes sketches with the location of the measurement points and tables with the means, minima, maxima and rms of all pressure coefficients and wind speed measurements close to the mirror surface measured. The tables also give the peak frequency (corrected for the 8-m full scale) of the pressure fluctuations. This varies between 0.1 Hz and 0.6 Hz, which is the same range as found at the dummy in the NTT, considering the factor 2 in geometric scale. The measured rms of the pressure coefficients are plotted in fig. 4.26 versus the azimuth with the wind direction for different telescope altitudes and enclosure configurations. 4.2.4.2

Pressure-speed correlation

The test measurements were analysed in order to find some general relationships useful for parametric design analysis. No correlation is found between mean cp values and wind speed on the mirror. The reason is that we have in many cases large differences in mean pressure on the four pressure taps and also in some instances a reversed flow on the mirror, whereby the mirror upper surface is actually under a mean negative pressure. On the contrary a correlation between σcp and wind speed is well established and is independent of the wind direction. Recalling that σcp is referred to the external reference speed U∞ : 1 2 σP = σcp ρ U∞ 2 we introduce a similar coefficient referred to the wind speed U measured on the

4-32


Zenith angle = 10 deg 0.25 O-O-O O-C-O C-C-20

rms_Cp

0.2

0.15

0.1

0.05

0 0

20

40

60

80 100 120 Azimuth angle

140

160

180

Zenith angle 35 deg 0.25 O-O-O O-C-O C-C-20

rms_Cp

0.2

0.15

0.1

0.05

0 0

20

40

60


140

160

180

Zenith angle = 60 deg 0.25 O-O-O O-C-O C-C-20

rms_Cp

0.2

0.15

0.1

0.05

0 0

20

40

60


140

160

180

Figure 4.26: Plots of σcp (rms of the pressure coefficients, normalized to the external wind speed) versus the azimuth angle with respect to the wind direction for different telescope altitudes and enclosure configurations (see the table at page 4-14).

4-33


mirror:

1 σP = Cσp ρ U 2 2

obtaining the relationship σcp = Cσp

U U∞

(4.4)

2

(4.5)

Fig. 4.27 is a scatter plot of this relationship. The correlation is independent of the azimuth angle and of the venting configuration of the enclosure. The coefficient Cσp depends only on the zenith angle: Cσp ' 1.1, for zenith angle ≤ 55◦ Cσp ' 0.3, for zenith angle = 80◦ Although it cannot be generalized to other types of enclosures, this result suggests that simple parameterizations between speed measurements and pressure fluctuations should be looked for in the study of a new enclosure. Since the ratio U/U∞ is a parameter that can be adjusted by acting on the ventilation devices of the enclosure (louvers, windscreen), a relationship of the type (4.4) will be particularly useful for parametric design analysis as well as for operational simulations of the use of the enclosure venting devices. σ cp 0.25 zenith 60◦ 3 zenith 35◦ + zenith 10◦ 2 Cσp = 0.3 Cσp = 1.1

3 0.2 3

+ + +

0.15

3 3

2

+ 0.1

3

2

3 + +

+ 2 3 0.05 3 + + + 22 332 3 3+ 3 2 +2 + 3 + 2+2 3 + 3 0 ++ 0 0.05 0.1

2

2 2

0.15

2

0.2 0.25 0.3 (U/U∞ )2

0.35

0.4

0.45

0.5

Figure 4.27: Correlation between σcp (rms of the pressure coefficient) and mean wind speed on the primary mirror.

4-34

4.2.4.3


Correction of wind deformations by active optics systems

Two important results were mentioned above: 1. The deformations caused by wind buffeting are contained in the basic (low order) elastic/optical modes of the mirror. 2. The peak frequency of the pressure fluctuations was in the range 0.2 to 2 Hz at the NTT and in the range 0.07 and 0.56 Hz (full scale for an 8-m mirror) in the wind tunnel tests. Both these facts invite the possibility of considering a dynamic corrections of the wind-buffet deformations of a large flexible mirror by the active optics system (see page 2-14). Recalling that existing active optics systems, such the one installed on the NTT have a bandpass of about 1/30 Hz, [Wilson 89] analyzes in some detail the possible implementation and limitations of improved active optics systems with an extended bandpass up to 1 Hz and eventually 10 Hz. Various technical solutions are proposed and it is concluded that such systems are technically feasible. It is therefore interesting to elaborate the test results obtained during this work also in terms of the peak frequencies of the pressure fluctuations on the mirror. Fig. 4.28 presents a scatter plot of peak frequencies versus the velocity ratio U/U∞ at an 8-meter primary mirror inside the cylindrical enclosure. The data include all test configurations with varying azimuth angles and venting conditions and are here only separated according to the pointing zenithal angle. Recalling the relationship (2.21) and that the test wind speed was about 12 m/s, we derive a range of turbulence length scales for the pressure fluctuations between 0.9 and 3.6 m (full scale). With respect to the mirror diameter the length scale range is then 0.11 < Lu /D < 0.45 During the mirror dummy tests at the NTT, the wind speed was not measured close to the mirror, so that a similar analysis is unfortunately not possible. However several power spectra of pressure fluctuation measurements were evaluated ([Noethe 92]) in which the peak frequency was within the range 0.2 to 2 Hz, which is exactly the same (in view of the 1:2 geometrical scale) as the range recorded in the cylindrical enclosure. This confirms also with respect to the frequency characteristics the general conclusion already drawn for modes and amplitudes of wavefront fluctuations: wind buffeting effects on the mirror depend first on the geometrical scale and only to a smaller extent of particular venting conditions. We can then pragmatically conclude an upper bound for the worst case peak frequency of pressure fluctuations on a primary mirror, which is quite independent on the particular pointing angle or venting configuration: nmax < 1.7 U/D

(4.6)

4-35


Peak frequency (Hz) 0.8 zenith 60◦ 3 zenith 35◦ + zenith 10◦ 2

0.7 0.6

+ ++

2

2

2222

0.5 ++

0.4 0.3

3

+ 3+ 33 3

2

0.2 3 3 3 2 + 2 + 3

0.1 0

0

0.2

0.4 0.6 Velocity ratio U/U∞

0.8

1

Figure 4.28: Scatter plot of peak frequencies versus the velocity ratio U/U∞ . The frequency data were obtained by visual interpretation of the power spectra reported in the test report [DMI]. This result, which stipulates that the peak frequency of significant wind buffeting effects on a large telescope mirror will in no case exceed the range of 1 to 2 Hz, will hopefully encourage the development of active optics systems into a frequency bandwidth which should be realistically achievable with present state technology.

4-36

4.2.5


Synthesis

The pressure patterns on the primary mirror of a telescope exposed to wind have been investigated in three different configurations: with the telescope in open air, in the slit of the NTT building and in a cylindrical recess. While the spatial distribution of mean pressures shows, as expected, considerable differences in the different types of enclosure, the patterns of pressure fluctuations are quite similar. As a consequence their effect on optical aberrations resulting from dynamic deflections of the mirror surface can be predicted with reasonable accuracy by a general relationship between the average rms of pressure variations on the mirror and the total rms surface error. For an astatically supported mirror with three reacting virtual support points, this parameterization is given by expression (4.2): D4 (nm) σw ' 2.17 · 105 3 σp Et The optical aberration is found predominantly in the astigmatic mode, which allows us to relate the rms surface error to the image spread angle θw obtaining expression (4.3): D3 θw ' 306 σp (arcsec) Et3 Simple approximate relationships can also be found between the local speed values and the rms of pressure variations on the mirror, but they will likely depend on the enclosure type. In the particular case of the VLT cylindrical enclosure, a parameterization is found between the average speed measured 60 cm (full scale) from the mirror surface and the rms of pressure variations, which does not depend on the azimuth angle. These relationships will be particularly useful for parametric analysis of the overall wind+seeing effects of the primary mirror and for determining the optimum operation of the venting devices (windscreen, louvers) of the enclosure. The study results outline the great sensitivity of large primary mirrors to wind buffeting. For example in the instance of the VLT, according to equation (4.2), the set limit of a wavefront error σw of 200 nm implies a maximum allowed pressure fluctuation σp of 1.3 Pa only.

Chapter 5 Local ”seeing” We will describe in this chapter the seeing effects of the turbulence found in the immediate vicinity of the telescope, namely that generated by the enclosure, the telescope itself and in the ground surface layer (up to about 30 ∼ 50 m). Until a few years ago, the various effects which will be described in this chapter were encompassed under the general term of dome seeing. Although the problem has been well recognized at least since the mid-70s when several new telescopes of 4-m class were commissioned, experimental measurements remained for a long time scarce and episodic, also because of the objective difficulty in devising and interpreting valid experiments. Citing [Woolf 82] ”... [dome] seeing in telescope design has been treated as a magician treats a rabbit. A number is pulled out of a hat, to great applause, it is handed to an attendant waiting in the wings, and it is seen and thought of no more.” The successive decade provided indeed some more data from which it has now been possible to attempt an improved understanding of this phenomenon. This chapter intends to present a description, interpretation and parameterization of the main local seeing effects. These can be separated in different types: • Dome seeing • Mirror seeing • Surface layer seeing

5-1

5-2

5.1

CHAPTER 5. LOCAL ”SEEING”

The relationship of C2T to the mean velocity and temperature fields

We have seen in section 5 that the effect of seeing can be quantified by the FWHM spread angle θ which can be evaluated as the integral along any given line of sight of the local temperature structure coefficient CT2 (see section 2.2). We will here describe how the temperature structure coefficient CT2 is related to the quantities which characterize the turbulent velocity and temperature fields. The starting point is given by the relationship (2.8), derived by [Tatarskii] among others, which relates CT2 to the dissipation rates of kinetic energy and temperature: 1

CT2 = a2 θ − 3

(5.1)

where a2 is a constant equal to about 3. Introducing the eddy coefficients KM for momentum and KH for temperature, the respective dissipation rates can be expressed in tensor notation as: θ = K H

∂T ∂xk

1 = KM 2

!2

(5.2)

∂ui ∂uk + ∂xk ∂xi

!2

− KH

g ∂T T ∂z

(5.3)

The last term at the right side accounts for buoyancy effects. If the mean characteristics generally depend only on one geometrical coordinate, as it is the case in a stationary atmospheric boundary layer with the height z above the ground, the above expressions become: θ = K H

dT dz

!2

= KM

du dz

!2

(5.4) − KH

g dT T dz

(5.5)

Inserting in (5.1) one gets: CT2 = a2

KH KM

du dz

2

dT dz

−

2

KH Tg dT dz

1

(5.6)

3

[Wyngaard] has analyzed in detailed, on the basis of experimental data, the parameterization of CT2 in terms of the temperature and velocity fields in the atmospheric surface layer using the so-called similarity theory. Similarity theory is a method by which statistical mean and turbulent values in a flow/temperature field, when properly adimensionalized, are assumed to be universal

5.1

CT2 AND THE FLOW PARAMETERS

5-3

constant or functions of a stability parameter. The adimensionalizing quantities, called scaling variables, and the stability parameter can be chosen in different ways by obeying to some simple rules (see for instance [Hull], pp. 347-361). Here the scaling variables taken are the height z and the temperature gradient dT /dz, while the Richardson number was used for the stability parameter: dU dz

g dT Ri = T dz

!−2

Noting that similarity theory predicts that θ and , hence CT2 , when adimensionalized are universal function of Ri, [Wyngaard] derived the expression CT2

dT = f (Ri) dz

!2

4

z3

(5.7)

The function f(Ri), obtained from experimental measurements is plotted in fig. 5.1 and is a good illustration of the fundamental asymmetry of thermal turbulence, hence seeing, with respect to the sign of the temperature gradient. As a numerical exercise we have computed CT2 by means of expression (5.7) as a function of dT /dz for three different speed rms σu values at 15 meters height above the ground (fig. 5.2). One will note that the effect of small variations of dT /dz on the local CT2 is very significant. The achievement of low seeing implies very small temperature gradients, particularly in unstable conditions. An exception is given by the case of a stable gradient with low mechanical turbulence. This is possibly the plainest demonstration that quiet inversion layers have very favorable seeing characteristics. The variations of mechanical turbulence have opposite effects on CT2 depending if the thermal conditions are unstable or stable. For unstable conditions and a same dT dz , CT2 decreases with increasing turbulence. For stable conditions CT2 increases dramatically with increasing turbulence. This means for instance that the artificial inversion obtained by chilling the dome floor in some observatories (CFHT, ESO 2.2-m) does achieve a low seeing only as long as no wind turbulence enters the dome. By choosing other scaling variables, namely the friction velocity u∗ and the normalized surface heat flux q (in K m s−1 ), and as the stability parameter the ratio z/L, where L is the Monin-Obukhov length L=−

u3∗ T kgq

[Wyngaard] obtains another expression for CT2 : CT2

q = g(z/L) u∗

2

2

z− 3

(5.8)

5-4


Figure 5.1: The function f(Ri) in equation (5.7) - from [Wyngaard]

Figure 5.2: Computation of CT2 versus above the ground

dT dz

in the atmospheric surface layer, 15 m

5.1


5-5

where g(z/L) is an empirical function evaluated from experimental data as: z g(z/L) = 4.9 1 − 7 L

− 2

z 0 L

3

g(z/L) = 4.9 1 + 2.75

z L

− 2 3

(5.9) (5.10)

In presence of a strong turbulent flow, L is large and therefore g(z/L) close to the surface is constant ' 4.9 and equation (5.8) becomes: CT2

q ' 4.9 u∗

2

2

(5.11)

z− 3

We note that this expression may be derived also directly from the general expression (5.6). When friction effects predominate over buoyancy the second term of equation (5.5) may be neglected. Putting KH /KM = β we obtain: 

2 KM

CT2 = a2 β  

du dz

1

3

dT dz

 2 

!2

(5.12)

With this approximation and using a common parameterization for the K factors: KM = kzu∗ = k 2 z 2 dT dz

=

dU = k 2 zσu dz

q KH

(5.13) (5.14)

where k is the Von Karman constant (' 0.4), u∗ is the friction velocity, σu the velocity rms and q the vertical heat flux, expression (5.6) can be elaborated as CT2 =

a2 βk

2 3

q u∗

2

2

z− 3

(5.15)

Near the surface the heat flux q is practically equal to the surface flux qs , which in a turbulent surface layer is proportional to (∆T u2∗ /U ). Therefore in a turbulent near-neutral surface layer CT2 is proportional to (u∗ /U )2 hence to (σu /U )2 which is the square of turbulence intensity It2 . One then finds that CT2 is directly related to both the squares of turbulence intensity and temperature difference: " # 2 h i u∗ 2 q 2 2 ∝ · ∆T ∝ It2 · ∆T 2 (5.16) CT ∝ u∗ U CT2 can also be put in relation with the outer scale of turbulence Lu . Following [Tatarskii], the outer scale of turbulence is related to KM as KM =

L2u

dU dz

5-6


inserting this expression into (5.12) we obtain CT2

=a

2

dT dz

βL4/3 u

!2

(5.17)

The free convection case When the flow is strongly unstable, that is when, approaching the free convection condition, buoyancy predominates over friction effects such that −7z/L 1, expression (5.9) becomes 2 z −3 g(z/L) ' 1.52 − L inserting in equation (5.8)and using the definition of L, one obtains an expression in which u∗ disappears: CT2

g = 2.68 T

− 2 3

z · qs

!− 4 3

(5.18)

This relationship between surface flux, height and CT2 is graphically illustrated in fig. 5.3 below. Another expression for the free convection case can be obtained quite simply from equation (5.7), noting that the function f (Ri) becomes about 3.6 for Ri 0 (see fig. 5.1): !2 4 dT 2 (5.19) z3 CT ' 3.6 dz which has the same form as equation (5.17) and where the distance z may be interpreted as a length scale parameter which characterizes flow mixing in the free convection circulation process.

5.1


5-7

100 Q = 0.5 W/m2 1 W/m2 2 W/m2 5 W/m2 10 W/m2 20 W/m2

10

z (m)

1

0.1

0.01

0.001 0.0001

0.001

0.01

0.1 CT2

1

10

100

Figure 5.3: Relationship between CT2 (K2 m−2/3 ), height and surface heat flux in free convection over a horizontal surface

5-8

5.2


Dome seeing

The dome seeing phenomenon began to attract serious attention in the mid-70s, when astronomers realized that observations made with new larger telescopes and improved optics did not achieve all the expected quality and resolution as the seeing generated at and by the telescope became more and more the limiting factor in image quality. While the general cause of this dome seeing was immediately recognized in the thermal turbulence created by free and weakly mixed convection inside the dome, a realistic description and parameterization of the phenomenon was for a long time matter of conjectures, supported by very scarce experimental data.

5.2.1

Literature review

In an early report on the matter [Hoag] measured at the Flagstaff 1.5-m telescope of the US Naval Observatory, housed in a dome with a diameter of 20 m, the correlation between seeing and the temperature difference between the inside and outside air, finding a mean dependency of 0.28 arcsec/K. [Murdin] measured the increase of image size caused by dissipating large powers inside the dome volume. The heat was generated by electrical fan-heaters. In the Isaac Newton Telescope dome (located at that time at Heastmonceux, GB) which has a diameter of 18 m, the increase of seeing FWHM was found to follow approximately a linear relationship with slope 0.052 arcsec/kW. At the Yapp 90-cm telescope dome (diameter 9 m) the slope was 0.11 arcsec/kW. In both cases the warm air was blown inside the dome but not directly in the telescope beam. When the air blown by an electric fan heater rated 3 kW was directed into the telescope beam the degradation climbed to a few arcseconds per kW. Although these experiments were not representative of actual dome seeing conditions, since the average heat dissipation of telescopes and instruments seldom exceeds a few kilowatts and of course warm air is never blown into the optical beam, the results prompted telescope designers and operators to require the active cooling of the electro-mechanical and electronic systems of most following telescope. In other tests, the experimenters also dissipated 90 kW just outside and upwind of the dome slit, but could not detect a sensible degradation. Nevertheless it is also customary to require that the heat dissipation from all telescope circuits is done away and downwind from the dome. [Woolf 79] formulated a theory of dome seeing based on the assumption that turbulent ”bubbles” of warm air fill the dome volume. We note that this assumption is in contrast with a correct description of free convection in a large volume (see for instance [Townsend]) whereby the regions away from the surfaces may experience large velocity means and fluctuations but negligible temperature fluctuations, which are confined to the wall regions. Later, however, Woolf himself relativized

5.2. DOME SEEING

5-9

the significance of his early interpretation in [Woolf 82] and [Woolf 82a] (which is a very comprehensive review of the seeing subject) and expressed the hypothesis that mirror seeing is more responsible for poor seeing than any other factor in telescope design. [Gillingham 82] measured at the Anglo-Australian Telescope a correlation of 0.28 arcsec/◦ C between seeing and the temperature difference between the inside and outside air. Some of his observations on the effects of blowers on dome seeing have been cited in section 3.2.3 above. [Forbes 82] performed some measurements of temperature fluctuations inside the enclosure of the Multi-Mirror Telescope (see section 3.4 and fig. 3.4 above). He noted a loose relationship between local microthermal activity inside the dome and image blur. [Woolf 88] did some order-of-magnitude estimates of possible dome seeing effects. He analyzed experimental measurements from the AAT, the CFHT (see section 3.2.3) and the University of Hawaii 88-inch telescope, which indicated the likelihood that seeing was caused mostly by a mirror-air temperature difference. The CFHT observatory (see section 3.2.3) brought a particular attention to the analysis and improvement of seeing quality. [Racine 92] analyzed 562 image frames from the HRCam instrument (for high resolution imaging) taken during 25 nights for correlations with temperature differences. He found that the main contribution to local seeing was due to occurrences of positive surface-air temperature differences at the optical surface of the primary mirror, while a less significant dependency was found with the temperature difference between the dome inside and outside air.

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5.2.2


Causes of dome seeing

The occurrence of dome seeing has been linked by researchers to a variety and cumulation of several sources of heat transfer and air flow phenomena inside the telescope enclosure. Fig. 5.4 below shows schematically the main causes that are generally considered to be possible source of dome seeing.

Figure 5.4: Causes commonly held to be source of dome seeing: A Convective air flow near caused by a surface-air temperature difference at the primary mirror: this causes the so-called mirror seeing B Convective air flow from the Cassegrain instrumentation located behind the primary mirror C Air flow through entrance doors to the telescope volume D Turbulence across the observation slit of the enclosure E Convective air flow from the members of the telescope structure F Convective air flow from the secondary mirror unit G Convective air flow from the heat generating equipment inside the enclosure H Convective air flow from the enclosure floor I Convective air flow from the dome and enclosure walls

Most observatories have taken actions in the course of time to reduce most of these effects by insulating wall and floor surfaces and by extracting the heat generated by electric equipment items by means of active cooling circuits. However the relative importance of the different causes, the quantification of their effect and consequently

5.2. DOME SEEING

5-11

the definition of the technical actions best suited to provide a seeing-free environment has remained controversial. In fact, the key for understanding the dome seeing phenomenon lies in a correct appreciation of the different free convection flow patterns which may be found in the air volume crossed by the optical beam. A main characteristic of free convection flow lies in the fact that temperature gradients and fluctuations are greatest close to the heat exchange surface while the far region experiences the largest velocities (see for instance [Townsend], pp. 381-392). Thus one shall expect that the seeing disturbance, being caused by temperature fluctuations, decreases rapidly with the distance from the heat exchange surface.

5.2.3

The ”steady local air” dome effect

We have so far linked the seeing phenomenon to turbulent temperature fluctuations. An apparent seeing effect can, however, also happen in absence of turbulence fluctuations if steady variations of temperature, hence index of refraction, are present along and across the light beam of the telescope. This situation may occur when the air inside the enclosure is globally at a different temperature than the exterior and it experiences a temperature gradient across the aperture. In such conditions the light rays across the aperture will be steadily refracted along slightly different paths and the focused image will experience a blurring effect similar to seeing (but no particular image motion). Because the phenomenon is stationary or has anyway a very slow evolution in time, it can be eliminated by a ventilation of the telescope volume. The image blurring will also be readily corrected by an active optics telescope (see fig. 2.3.3 at page 2-14). One such a case is illustrated by [Wilson 91]. While such effects may have been confused with ”turbulent” seeing in the past, it should be clear that this ”quasi-static” image blurring is a different phenomenon, much simpler to understand and to correct, either by providing ventilation at some time intervals or by an active optics system. We will therefore consider hereafter only the seeing caused by turbulent fluctuations of the index of refraction.

5.2.4

Scaling variables and similarity of dome seeing

A general characterization of free convection at a surface of characteristic length L is given by the following dimensionless numbers which are derived from the governing equations (see for instance [Incoprera], p. 493): • the (densimetric) Froude number, which represents the ratio of kinetic to potential energy: T U2 (5.20) Fr = ∆T gL

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• the Reynolds number, which represents the ratio of kinetic energy to that dissipated by friction and characterizes the turbulence regime: Re = • the Prandl number:

UL ν

(5.21)

ν (5.22) κ Consider a simple situation in which the air volume inside the dome enclosure sketched in fig. 5.4 is affected by free convection generated by temperature differences between air and the floor of the dome. The floor-air temperature difference will generate a system of convection cells by which the heat is carried in the dome inner air volume. Since the flow conditions around a telescope are generally too complex to allow a rigorous modelisation of theair volumes affected by the seeing effect, it will be of interest to understand the similarity that rules the effect of changes of one or more parameters on the seeing, thereby deriving the criteria for interpreting the data obtained from mirrors and telescopes of different scales and conditions. Pr =

In an extreme simplification we will consider the height from the floor as the only geometrical parameter. Mean statistical values of turbulent quantities may then be obtained through similarity theory (see section 5.1). Following [Wyngaard], we take as scaling variables of the free convection field from a plane horizontal surface the quantities g/T , q and z. Dimensional reasoning leads then to CT2

z

4 3

g T

2 3

4

q− 3 = b

where b is a constant. Rearranging gives: CT2

g =b T

− 2 3

z · q

!− 4 3

(5.23)

which, within the constant factor, is equation (5.18) which had been derived for the unstable limit conditions of a turbulent boundary flow. Equation (5.23) is a convenient expression to derive a relationship of the integrated seeing θ with the flow scaling variables. Noting that g and T , as well as air density and specific heat are not scalable, and assuming further that the height dependency will be constant through all scales, the scales λCT2 and λθ of seeing are related to the scale λq of surface flux (the normalized heat transfer rate) as 4

λCT2 = λq3 and, recalling equation (2.15), h

λθ = λCT2

i3

5

4

= λq5

(5.24)

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5.2. DOME SEEING

Noting that q is a likely function of temperature difference and upward flow speed, dimensional analysis gives: λq = λ∆T · λU From the Froude number criterion, we have: U∝

s

∆T gz T

Thus λU is approximately:

(5.25)

1 2 λU ' λ∆T

One gets: 3 2 λq = λ∆T

(5.26)

and finally 6 5 λθ = λ∆T

5.2.5

(5.27)

An order-of-magnitude estimate of dome seeing

Equation (5.23) may also be used for a simple order-of-magnitude estimate of the effect on seeing caused by the temperature fluctuations caused by free convection from a warmer dome floor. Consider the geometry of fig. 5.4. If the dome diameter is Dd , the mean height of the air volume crossed by the optical beam with respect to the heat exchange surface will be about Dd /4. Assuming for the constant b the value of 2.68 determined for the atmospheric surface layer (see equation (5.18)) and taking T = 10◦ C, we find: CT2

qs ≈ 25.2 · Dd /4

!4 3

(5.28)

Considering that the light beam travels three times between the primary and the secondary mirror1 , the total light path inside the protected volume of the dome will be ≈ 1.1 Dd and from equation (2.15), a rough estimate of the dome seeing θd will be given by h

i3/5

θd ≈ 0.94 CT2 (1.1Dd )

−1/5 4/5 qs

= 20.9 Dd

(5.29)

qs is the normalized surface heat flux (i.e. divided by air density and specific heat, typically a factor 1000) with dimentions [K·m/s]. Equation (5.29)) is plotted in fig. 5.5 for two typical values of enclosure size: free convection flow in the enclosure volume will begin to cause significant seeing effects 1

The wavefront of light is reflected by the primary mirror toward the secondary mirror and then again downwards to an instrument focus (see fig. 1.1 at page 1-6).

5-14


Figure 5.5: Order-of-magnitude value of seeing FWHM caused by a warmer dome floor. (≈ 0.4 arcsec) in the light beam with a heat flux of the order of 15 W/m2 . Considering that a typical free convection heat transfer rate would be 3 W/m2 K at the floor, one should then expect a seeing contribution of about 0.1 arcsec per degree K of floor-air temperature difference. Relationship of the same quantitative order between heat flux, distance from the exchange surface and seeing are likely applicable also to other potential sources of free convection located inside the enclosure (e.g. items G and I in fig. 5.4). However, in view of the smaller exchange surface areas of walls and other heat dissipating objects with respect to the inner air volume, the seeing rate per deg K of surface-air temperature difference will be quite lower than for the floor. The rate of dome seeing per floor-air ∆T of 0.06 to 0.08 arcsec/K which is estimated here indeed explains the high seeing values experienced during the first years of operation by many telescopes of 4-m class built in the 70s, like the ESO 3.6-m and the CFHT. These telescopes are enclosed in large concrete/steel buildings with no natural ventilation and, as the inner dome thermal environment was hardly or poorly controlled, the different heat capacities of the concrete base, the primary mirror, the telescope structure and the dome inevitably caused large differences of temperatures. Measurements at the ESO 3.6-m telescope performed by the author [Zago 84] and [Schmider] before the installation of an improved thermal control system in the dome, show that the temperature difference between the dome floor

5.2. DOME SEEING

5-15

and the interior air is frequently of the order of 5 K and raise at times up to 10 K. As we have already mentioned in section 3.2.3 above, the thermal control of most of these domes has been improved in the meantime, so that surface-air ∆T now hardly exceed 1 or 2 K in the worst cases. Newer telescopes such as the MMT and the NTT have been built inside lighter enclosures which also allow natural ventilation. As a consequence, dome seeing, in the proper meaning of seeing created by large convection flow patterns in the dome enclosure, is no more a critical factor of telescope performance nowadays. Therefore there is not much opportunity nor perhaps interest to investigate in detail a matter which appears pragmatically solved.

5.2.6

Mirror seeing

Free convection at the surface of the primary mirror, the cause of so-called mirror seeing, does remain an important issue for telescope designers. In earlier telescopes, the evidence of mirror seeing was possibly hidden in the background of larger dome seeing effects and this effect was first suspected by [Woolf 82], [Woolf 82a], to be the main seeing contribution in the telescopes of the latest generation. More recently, experimental measurements by [Racine 92] showed that at the CFHT, mirror seeing is indeed the main cause of observatory-made seeing. [Racine 92] analyzed 562 image frames from the HRCam instrument (for high resolution imaging) during 25 nights over an 8-month period for correlations with temperature differences. He found that the main effect came from the primary mirror and evaluated it at: θm = 0.4 arcsec · ∆Tm6/5 where θm is the seeing FWHM contribution and ∆Tm is the temperature difference between the mirror surface and the surrounding air. A lower dependency was found with the temperature difference between the dome inside and outside air: 6/5 . θd = 0.1 arcsec ·∆Td In the next section we report the results of the analysis by the author of a much larger set of image quality data of the CFHT. Then a more extensive analysis of the mirror seeing phenomenon is found in section 5.3 below.

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5.2.7


Analysis of telescope image quality data data

To this date, experimental data useful for understanding the dome seeing phenomenon may appear surprisingly scarce if one consider the impact of the problem on the quality of observations (see section 3.2.5). There are some reasons for this lack of reliable measurements. One reason is due to the difficulty of measurements methods. Dome seeing is only one of several sources of image spread, which include in particular natural seeing which has a very high variability. There are no direct methods for the distinct evaluation of the local contribution to seeing which is caused by thermal turbulent inhomogeneities in and around the telescope. Only if a large collection of homogeneous and precise data of image quality together with all relevant environmental parameters are available, it is possible to perform a statistical analysis in which the local seeing effects effects can be outlined through the fluctuations of the natural seeing. Local seeing is of course more easily detectable on sites where the average natural seeing is low. Unfortunately the operating procedures of most astronomical observatories do not particularly facilitate such measurements. Astronomical observatories are generally operated as service institutions for the use of individual astronomers. Requests for observing time on the best telescopes far exceeds the available resource. A severe selection is done on proposed observing programs and successful astronomers typically obtain observing runs of 2 to 4 nights, during which they are hard pressed to perform all the intended observations. Therefore this continuous shift of observers, whose priorities are their own immediate observation objectives, is an operational obstacle to the establishment of research programs on local seeing, which will take a fraction of observing time over long periods, and only offer eventually a perspective for quality improvements. To this date the Canadian-French-Hawaii Telescope is the only observatory in which image quality, temperature and wind data are systematically taken and therefore provides the best database for studying dome seeing. Thanks to the courtesy of the CFHT direction, the author had access to this important set of data, which was analyzed for the first time in its entirety. 5.2.7.1

Data bases

The CFHT is a 3.6-m telescope (see fig. 5.6) housed in a large dome with a diameter of 32 m, located on Mauna Kea, Hawaii island, at the altitude of 4200 m. This site is deemed among astronomers to be the best in the world for natural seeing. The observations with the telescope, which started operating in 1979, experienced during the first years of operation an average seeing in excess of 2 arcsec [Racine 84]. As a result of many technical actions taken to eliminate heat transfer to the telescope air volume, the average seeing has been improved to 0.6 arcsec [Racine 92]. A main fac-

5.2. DOME SEEING

5-17

Figure 5.6: The Canadian-French-Hawaii Telescope tor in this achievement was the installation of a chilled floor for the telescope volume. The floor creates a stable temperature vertical gradient, thus effectively eliminating sustaining free convection flows inside the dome. It also acts as a powerful cold sink for any heat generated or entering in the dome volume, contributing in particular to keeping down also the temperature of telescope structure and primary mirror. We have analyzed the data log files concerning all observations done during the years 1991, 1992 and 1993. They record the FWHM image quality of all observations taken with the two main imaging instruments used on the telescope prime focus, which are respectively named FOCam and HRCam. The latter one has a fast tip-tilt guider aimed at correcting automatically telescope guiding errors (wind induced fluctuations in particular). Thus image quality from HRCam is typically 20% better than from FOCam. The records of the log files include for each observation the zenithal angle of the telescope, the integration time, the number of FWHM measurements averaged in that time, meteorological data of the external environment (wind, air

5-18


temperature) as well as the temperature measured at several locations around the telescope and in the dome: Sensor ref. TM1 TaM1a TaM1b TaTRa TaTRb TabM1 Tout Ta6f Ta6i Tf1-4

Location Mirror surface temperature Air temperature near the mirror (one side) ditto (other side) Air temperature at top ring level ditto (other side) Air temperature below the mirror Outside air temperature Air temperature 6 feet above the floor Air temperature 6 inches above the floor Floor temperatures

Table 5.1: Location of main temperature sensors in the CFHT dome Only the records in which the FWHM was actually recorded (> 0) were retained for the analysis. Since the vast majority of observations are taken at the prime focus, the relatively few Cassegrain observations have been discarded. Also all observations with integration periods of less than 10 seconds are discarded, since they may not average correctly image motion due to seeing effects, as well as all those in which the FWHM measure was fluctuating excessively (i.e. with σθ > 0.33). A few observation sequences in which the FWHM remained at very high values (> 2 arcsec) were also eliminated as it was considered that this could only be attributed to occasional very bad natural seeing or to a non-optimal optical setup, both effects being out of the scope of the present analysis while they could introduce bias in the evaluation of local seeing effects. 5.2.7.2

Analysis procedure

The purpose of the analysis was to discriminate statistically between the different contributions to the overall image spread and quantify in particular the local seeing effects. The main analysis guideline will be given by the assumption that the overall image quality can be parameterized as a sum of various terms dependent on few driving quantities such as the zenithal distance γ and various temperature deltas. Recalling that the amplitudes of various seeing FWHM contributions sum up with the power 5/3, while all other contributions should be added quadratically, one has:

5/3 6/5

θ2 = θo2 + θn5/3 + θl

2 + θW

(5.30)

where • θo is the telescope/instrument image FWHM. For the HRCam case this was reported after calibration tests to be about 0.35 arcsec, practically independent on the zenithal angle [Racine 92].

5-19

5.2. DOME SEEING

• θn is the natural seeing, here defined as the contribution which is independent from particular conditions of telescope and dome. From equation (2.13) one has θn = θno (sec γ)3/5 where θno is the natural seeing at zenith. • θl is the local seeing, for which parameterizations will be sought with respect to various temperature deltas as well as wind speed and direction. • θW is the contribution due to wind shaking of the telescope. Following the steps of the analysis by [Racine 92] of a subset of HRCam data, we will investigate in particular dependencies on temperature differences. Recalling equation (5.27) one will assume that local contributions to the seeing angle depend on the power 6/5 of the corresponding ∆T s: θl '

X

6/5

ai ∆Ti

(5.31)

The following thermal indices will be considered (see fig. 5.4 and table 5.1): ∆Tm ∆Tt ∆Td

between the mirror surface and the surrounding air (TM1 - TaM1a/b) the temperature gradient along the tube (TaTRa/b - TaM1a/b) between the dome interior and the outside (TaTRa/b - Tout)

Since the scattering of the global seeing is exceedingly dominated by the fluctuations of natural seeing, it is not advisable to use direct multivariate least square regressions to evaluate all contributions in one computation and a more careful stepwise approach is required. Therefore we shall attempt to isolate the different influences and derive their parameterizations by using suitable subsets of the data.

5-20

5.2.7.3


HRCam data

After the preliminary screening 1662 observation records were retained. The general statistics of the FWHM measurements is Average: Median: Rms: Minimum:

0.65 0.61 0.18 0.35

arcsec arcsec arcsec arcsec

One should note here that the median values are more significant of general performance than arithmetic averages. Image quality and seeing statistics follow an approximately log-normal distribution (see fig. 5.7) in which the average is significantly larger than the median. Therefore plain regression techniques, which assume a Gaussian distribution, cannot be applied directly on distributions of FWHM values and we will here use the method of collapsing the data to median values binned over small intervals of a dependent variable before applying fitting techniques. A first verification establishes that the HRCam FWHM distribution does not appear to show a significant dependency on wind speed: Median Median Median Median

for for for for

U < 5 m/s: 5 < U < 10 m/s: 10 < U < 15 m/s: U > 15 m/s:

0.61 0.64 0.64 0.58


The temperature data measured at several locations around the telescope and in the dome (see table 5.1) confirm that the CFHT dome environment is almost permanently characterized by a stable thermal stratification. In the vast majority of

Figure 5.7: Histogram of FWHM data from HRCam: note the typical log-normal distribution.

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5.2. DOME SEEING

the observations the air temperature above the primary mirror is lower than the one near the top ring, which in turn is lower than the external air temperature - see fig. 5.8. This stratification effectively ”damps” free convection flow patterns and any related turbulence. Indeed one does not find any seeing that could be attributed to ∆T ’s between air and floor and dome surfaces. The temperature of the primary mirror stays generally very close to the one of air just above it: the average of the mirror surface-air temperature difference ∆Tm is + 0.05K, with a rms of 0.47K. As shown by fig. 5.8, ∆Tm and ∆Tt are visibly correlated (the correlation coefficient is 0.75) while this hardly appears to be the case of the pairs consisting of ∆Tm and ∆Td , although the correlation coefficient is nevertheless 0.14 . Fig. 5.9 shows a scatter plot of FWHM values with respect to ∆Tm . In order to avoid bias from the airmass effect only observations with sec γ < 1.2 are taken (984 records). Binned medians are also shown. For ∆Tm > 0 a trend to larger median FWHM is noticeable. For ∆Tm < 0 no influence is noted, if one excepts a group of values for which ∆Tm is less than -1K, which belong all to a same observation sequence. Therefore the higher average seeing of this sequence may well be due to increased natural seeing accidentally occurring at the time. Fig. 5.10 shows a scatter plot of FWHM values with respect to the temperature difference ∆Td between the dome interior and the outside air. Again only observations with sec γ < 1.2 are considered. Note that because of the dome floor cooling system, the dome interior is amost always colder than the outside air. For ∆Td < 0 no dependency is appearing. For ∆Td > 0 there may seem to be a trend toward increased seeing, but too few data points exist to derive any significant conclusion. In order to find correlation coefficients that would fit equations (5.30) and (5.31), it is necessary to get first an estimate of the fixed telescope/instrument error θo . By correlating with respect to sec γ a subset of FWHM values for which the temperature dependent effects are absent, one can estimate the mean natural seeing and the fixed error due to the instrument. This subset, which includes only FWHM values corresponding to |∆Tm | < 0.3K and ∆Td < 0.4K (858 records), is plotted in fig. 5.11. Noting that, when θl and θW are nil, equation (5.30) becomes θ2 = θo2 + θn2 o (sec γ)6/5 a least square fit on the binned median values of the selected subset gives a fixed error due to the instrument θo = 0.395 arcsec while the median natural seeing is evaluated as θno = 0.397 arcsec

5-22


Figure 5.8: Left: Scatter plot of ∆Tm versus ∆Tt . Right: Scatter plot of ∆Tm versus ∆Td .

Figure 5.9: Scatter plot of HRCam FWHM versus the temperature difference ∆Tm between the mirror surface and the surrounding air. Binned median values and the are also shown.

5.2. DOME SEEING

5-23

Figure 5.10: Scatter plot of HRCam FWHM versus the dome-outside temperature difference ∆Td .

Figure 5.11: HRCam FWHM versus sec γ in absence of mirror and dome seeing

5-24


To find a parameterization for the FWHM versus ∆Tm relationship, we consider a subset with sec γ < 1.2 (fig. 5.9). Noting that θn ' θno in this case, equation (5.30), combined with (5.31) gives

2 θ2 = θo2 + θn5/3 + a5/3 m ∆Tm o

6/5

(5.32)

For ∆Tm > 0, a least square fit gives am = 0.38 which results in the following parameterization for the mirror seeing contribution: θm = 0.38 ∆Tm6/5

arcsec

(5.33)

This fit is also plotted on fig. 5.9. For −1K < ∆Tm < 0 the slope is practically nil, while for ∆Tm < −1K, the data are inconclusive, as explained above. So far then, recalling that no dependency appears with respect to the temperature difference ∆Td between the dome interior and the outside air, the HRCam performance appears represented by the following relationship:

θ2 = 0.3952 + θn5/3 sec γ + 0.385/3 ∆Tm2 o

6/5

(5.34)

Other possible dependencies were sought by analyzing the values of natural seeing extracted by means of equation (5.34) θno =

h

(θ2 − 0.3952 )5/6 − 0.385/3 ∆Tm2 cos γ

i3/5

(5.35)

versus other temperature differences obtainable from the sensors listed in table 5.1. None could be determined. For instance, fig. 5.12 shows a plot of θno values computed from (5.35) with respect to the temperature gradient along the tube ∆Tt : no correlation is apparent. Noting that we had not taken into account the mirror orientation in the parameterization for mirror seeing (5.33), we have analyzed also a subset of θno values in which ∆Tm is > 0.5K with respect to sec γ - fig.5.13. Also in this case no correlation is apparent. Finally, the median of θno over the entire data set (1662 records) is 0.39 arcsec, very close to the value of 0.397 arcsec evaluated previously. Equation (5.34) can thus be considered as verified for the HRCam observations.

5.2. DOME SEEING

5-25

Figure 5.12: HRCam computed natural seeing θno with respect to the temperature gradient along the tube ∆Tt .

Figure 5.13: Check for unaccounted effects of telescope orientation on mirror seeing: HRCam computed natural seeing θno with respect to sec γ (only data with ∆Tm > 0.5K)

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5.2.7.4


FOCam data

After the preliminary screening to eliminate spurious data, 1446 observation records were retained. The Average: 0.79 general arcsec statistics of the FWHM measurements is: Median: Rms: Minimum:

0.75 arcsec 0.205 arcsec 0.32 arcsec

Because tracking and guiding errors are not corrected by a fast tilting mirror as it was the case with HRCam, the FOCam image sizes are larger than the ones obtained by HRCam and also show a higher dependency on wind speed: Median Median Median Median

for for for for

U < 3 m/s: 3 < U < 6 m/s: 6 < U < 10 m/s: U > 10 m/s:

0.74 0.75 0.78 0.91


Fig. 5.14 shows a scatter plot of FWHM values with respect to ∆Tm . Only observations with sec γ < 1.2 and U < 6 m/s are plotted. For ∆Tm > 0 a trend to larger FWHM values can be noticed. However the values of ∆Tm are less uniformly scattered than it was the case with HRCam data: for ∆Tm > 0.7K there are only three clusters of data each belonging to a same observation sequence. For ∆Tm < −0.6K, seeing even appears to decrease but the scarcity of data does not allow us to attribute a statistical significance to the trend. Fig. 5.15 shows the scatter of FWHM values with respect to the temperature difference ∆Td between the dome interior and the outside air. The FOCam data also cover the range of positive ∆Td up to 4K and, although here also the data points are very unevenly scattered, no trends are apparent. The airmass effect is then evaluated by analyzing a subset with ∆Tm < 0.3K and U < 6 m/s (fig. 5.16). Noting that the median FWHM for sec γ ' 1 is 0.71 arcsec, a least square fit on the binned median values gives a fixed error due to the instrument θo = 0.466 arcsec while the airmass dependent variable is evaluated as θno = 0.509 arcsec While we had expected the value of θo from FOCam to be larger that in HRCam, we find that also the apparent natural seeing is larger. Barring the possibility that HRCam can correct seeing image motion to such an extent, this suggests the presence of mechanical effects from the telescope which cause the tracking performance to depend on orientation. As the data set does not allow the discrimination of this particular effect, we will proceed in the analysis on the basis of the values evaluated above, since the effect of an inaccuracy in the relative weighting on other seeing effects is anyway minor (see equation (5.30)).

5.2. DOME SEEING

5-27

Figure 5.14: FWHM from the FOCam data as a function temperature difference ∆Tm between the mirror surface and the surrounding air. The full line represents a best fit of binned median values: for ∆Tm > 0 the mirror seeing contribution θm is evaluated 0.3 ∆Tm6/5 . The dashed line corresponds to a factor of 0.38, as obtained from the HRCam data.

Figure 5.15: FWHM from the FOCam data as a function of the temperature difference ∆Td between dome interior and outside.

5-28


Inserting the computed values of θo and θno in equation (5.32), a least square fit on the mirror seeing data (fig. 5.14) gives for ∆Tm > 0 : θm = 0.3 ∆Tm6/5 arcsec

(5.36)

One should remind that the value of this coefficient is determined to a large extent by only three data sequences and therefore carries less confidence than the value found in the HRCam case (which was 0.38 arcsec/∆T 6/5 ). Both trend lines are drawn for illustration on fig. 5.14. Fig. 5.17 shows a scatter plot of FWHM with respect to wind speed. This subset only includes data for which sec γ < 1.2 and ∆Tm < 0.3K (562 records). This plot shows the overall effect of wind on the FOCam performance, averaging out the influence of relative azimuth of observation with respect to wind direction. Assuming that the median of the wind induced errors are proportional to the square of wind speed θW = aW U 2 a best fit of equation θ2 − θo2 = θn2 o + a2W U 4 gives then θW = 0.0035 U 2 5.2.7.5

Analysis summary

In conclusion, the analysis of three years of CFHT seeing records shows that mirror seeing is the only significant local seeing effect generated inside the observatory. It is found when the mirror is warmer than ambient air and is correlated with the surface-air temperature difference at a rate of 0.38 arcsec/K6/5 , which confirms the outcome of the analysis by [Racine 92] of a smaller set of HRCam data. [Racine 92] noted also a correlation between seeing and a positive temperature difference ∆Td between the dome interior and the outside air with a factor of 0.1 arcsec/K6/5 . The HRCam data analyzed here are not incompatible with a trend of this kind, but too few data points exist for ∆Td > 0 to draw a positive conclusion. The range 0 < ∆Td < 4K is better represented in the FOCam data but in that case no apparent trend is detectable (fig. 5.15). Thus we do not have conclusive evidence for the existence of this seeing contribution.

5.2. DOME SEEING

5-29

Figure 5.16: FOCam FWHM versus sec γ in absence of wind and mirror seeing effects.

Figure 5.17: FOCam FWHM versus wind speed.

5-30

5.2.8


Seeing caused by heat generation at the secondary mirror unit

In modern telescopes the secondary mirror (often called M2) is attached to electromechanical actuators which allow fine adjustment of the optical alignment and focusing. The latest telescopes projects also provide for fast motion of the secondary mirror, either to switch rapidly between the observed object and the sky background, or to correct guiding errors due to wind loading. All these systems produce some heat which, if it is not removed by a cooling circuit, will dissipate right into the telescope light-beam and may then cause a seeing degradation. In order to evaluate this issue, Jacques Beckers of ESO performed a series of measurements at the ESO 2.2-m telescope using a CCD array to measure FWHM image size ([Beckers 92]). Three different types of heating gadgets were used to produce heat: a metal square box 22×22×22 cm and a metal plate 220×27.5×1.1 cm. They were mounted on top of the 2.2-m telescope, the plate across the light-beam, simulating two opposite spiders (see fig. 1.4), and the box mounted on it on thermal insulating legs. The measurements were performed on stars about 30◦ from zenith while either the box or the plate were heated. The box was heated with 135 Watts and the plate with 560 Watts. Both wattages resulted in a surface-air temperature difference of about 60 K. The mean heat transfer coefficient was respectively 7.5 W/m2 for the box and 7.8 W/m2 for the plate. The wind velocity was low during the experiment (3 m/s or less), which let us assume that the air flow motion near the top of the telescope was around 1 to 2 m/s (although no measurements were done inside the dome). A measurement cycle (heating to maximum temperature starting from ambient and cooling off to near ambient) lasted 2 hours. The CCD images were fit with a Gaussian profile and the FWHM were recorded. The natural seeing was recorded by the DIMM seeing monitor2 operating at La Silla and was near 0.8 arcsec during the three nights of the experiments. The experimenters had expected to record a significant increase of seeing with the heating elements in the telescope light-beam, and were surprised when the effects were very small, barely noticeable through the variability of natural seeing. The measurements were analyzed by least square fitting of θ = θn2 + θo2 + (a∆T )2 where θn was the natural seeing measured by the DIMM and θo a general fixed error contribution from the telescope.

2

The DIMM was introduced at page 2-5.

5.2. DOME SEEING

5-31

The factor a was the quantity of interest, as the FWHM contribution was assumed to be linear with ∆T , and was evaluated as: • a = 0.0037 arcsec/K, for the box

• a = 0.006 arcsec/K, for the plate/spiders For the maximum ∆T = 60 K the seeing contributions were respectively 0.22 arcsec for the box dissipating 135 Watts and 0.36 arcsec for the plate (560 Watts).

Figure 5.18: Seeing caused by a free convection plume from the M2 unit. We can transpose these experimental data also to telescopes of different sizes provided that a geometry similarity is approximately maintained in the proportions of the test. Consider the telescope configuration sketched in fig. 5.18. Heat is dissipated by the secondary mirror unit causing a vertical plume across the light-beam. Let us assume that the plume spreads in proportion to its distance from its origin. A circumferential cross-section at a distance r from the optical axis has then dimensions zl along the line of sight and yl across it. We assume further that the thermal turbulence in the plume is described by a relationship of type (5.23). The seeing spread through a line of sight at a distance r from the optical axis (see fig. 5.18) will be proportional to: 4 3 3 q 5 5 5 2 θl ∝ CT zl ∝ zl r

5-32


where CT2 and q are respectively the average temperature structure coefficient and heat flux along a line of sight across the plume. The total seeing spread of the light beam will be obtained by integrating over the plume cross-section seen by the telescope, normalized by the mirror area: 1 Z θ ∝ 2 θl yl dr D where D is the pupil (mirror) diameter. Since both zl and yl are proportional to r, it is: 4 1 Z q 5 8 θ∝ 2 r 5 dr D r

Noting that the total heat flow Q from the secondary unit is proportional to (q zl yl ) ∝ (q r2 ), we obtain: 4 9 4 1 Z Q 5 dr ∝ Q 5 D− 5 θ∝ 2 D r Therefore the scaling relationship based on the experimental results is: θ Q = 0.22 135

4/5

2.2 D

9/5

(5.37)

or: θ = 0.018 Q4/5 D−9/5

(5.38)

This relationship may be used to specify the maximum allowable heat dissipation for a given seeing requirement. For instance, if we consider a 8-m telescope and a requirement that the seeing budget due to M2 heating shall be ≤ 0.025 arcsec, the allowable heat dissipation from the secondary mirror unit will be about 108 Watts.

5-33

5.2. DOME SEEING

5.2.9

Seeing and natural ventilation

It is generally acknowledged among astronomers that the telescopes which have enclosures that allow for wind ventilation have a low dome seeing. Unfortunately here also the evidence is mostly anecdotal and few actual data exist. Even at the NTT which is possibly the best example of a ”ventilated” telescope in operation, multifold reasons and technical problems have prevented comprehensive measurements of the local seeing phenomenon over long periods of time. We can therefore present here only some individual measurements, obtained in collaboration with S. Ortolani of Padoua Observatory and M. Sarazin of ESO, which nonetheless illustrate the performance of the NTT with respect to seeing. Fig. 5.19 shows a comparison of seeing sequences taken at the NTT [Ortolani 94] and the corresponding measurements at the DIMM telescope3 . The agreement is very good and shows that the NTT experiences virtually only the natural seeing. One should note that the sequence of May 16 is one of exceptionally low natural seeing. In both cases the wind was weak: during the May 16 sequence it was between 0 and 3 m/s, while during the May 17 sequence it was 4∼5 m/s. The primary mirror was about 1 to 2 degrees K colder than ambient air. May 16, 1994

May 17, 1994

2

2 DIMM NTT 1.5 FWHM (arcsec)

FWHM (arcsec)

1.5

1

0.5

1

0.5

0

0 0

0.5

1 1.5 GMT (hour)

2

2.5

7

7.5

8

8.5 9 GMT (hour)

9.5

10

10.5

Figure 5.19: Comparison of seeing measurements at the NTT and at the DIMM. However the NTT does not behave always so favorably. On a previous occasion some seeing measurements which let appear the presence of mirror seeing ([Ortolani 93]) were taken during a night in which the primary mirror was significantly warmer than ambient air (fig. 5.20). Here the wind was 6∼7 m/s but was facing the back of the telescope building. The effect of opening/closing the louvers at the back of the telescope was investigated during a test run: the flaps were alternatively opened and closed every about ten 3

see footnote at page 5-30.

5-34


June 13 and 15, 1994 4 3.5

FWHM (arcsec)

3 2.5 2 1.5 1 0.5 0 0

1

2 3 Mirror-air Delta_T (K)

4

5

Figure 5.20: Seeing at the NTT versus mirror-air temperature difference. minutes. Although the seeing measured by the DIMM4 was very variable, the difference of seeing between the two flaps conditions was very noticeable: see fig. 5.21. The wind speed was about 7 m/s. When the flaps are closed the ventilation of the telescope volume is much reduced and the seeing increases immediately. This conclusion joins much anecdotal evidence by NTT observers complaining that raising the windscreen (see fig. 4.7) to maintain a good guiding performance in windy conditions often degrades the seeing quality. In conclusion, even with the limitations due to the scarcity of objective data, the experience of the NTT brings the following elements of knowledge: • A ventilated enclosure can provide conditions in which local seeing is virtually nil. • Mirror seeing is still present when the primary mirror is warmer than ambient air. • Local seeing generally reappears when the ventilation is limited by the closed louvers and the windscreen.

4

In that case the DIMM was located 2 meters above the ground, 40 m south (downwind) of the NTT.

5-35

5.2. DOME SEEING

NTT (arcsec) 4

October 1989

3.5 3

3 3

2.5

3

3 3 33 3 3 3 +3 +3 + + ++ ++ ++ +++ ++

2 1.5 1

3

flaps closed 3 flaps open +

0.5 0

0

0.5

1

1.5 2 2.5 DIMM (arcsec)

3

3.5

Figure 5.21: Effect of flaps on the seeing at the NTT.

4

5-36

5.2.10


Synthesis

Dome seeing, in its general meaning of seeing generated by turbulent fluctuations of the index of refraction inside a telescope enclosure, can be distinguished into different phenomena: • Seeing caused by free convection in the entire enclosure volume, generated typically by a floor warmer than ambient air. • Mirror seeing, caused by a temperature difference between the surface of the primary mirror and air. • Seeing from the secondary mirror unit. A number of parameterizations have been derived from theoretical approximations, experimental measurements and similarity relationships which may be used to quantify these effects in the context of the design of a telescope enclosure. From the engineering standpoint, there are two different avenues to prevent the occurrence of dome seeing in a telescope enclosure. One way requires a very tight thermal control of the telescope air volume. Chilling the floor of the telescope volume below the exterior air temperature, with the establishment of a stable stratification, does prevent the occurrence of dome seeing. In the CFHT observatory, where such a cooling system is installed, no seeing related to convection flow inside the dome can be detected, except for mirror seeing due to free convection on the surface of the primary. And even that phenomenon penalizes the telescope only for a small fraction of the observing time, because the chilled floor keeps also the temperature of the primary mirror always at a close range with the dome’s ambient air. The second possibility consists of planning the natural ventilation of the telescope volume by the wind. The NTT, typical example of this configuration, often achieves virtually zero local seeing in this manner. However, when the ventilation is reduced by closing the back louvers a significant seeing reappears. Also, when the mirror is warmer than ambient air, mirror seeing appears present in the NTT. Thus in conclusion, both the general evidence and the engineering experience point to mirror seeing as the main obstacle toward the removal of local seeing effects in modern observatories. This aspect will therefore be studied in more detail in the next section.

5.3. MIRROR SEEING

5.3

5-37

Mirror seeing

Laboratory studies of image deterioration due to convection above heated mirror have been published by a few researchers: • Lowne [Lowne] performed tests on a 254-mm spherical mirror at different elevations and studied also the effects of forced air blowing. • Barr et al. [Barr] studied mirror seeing on a 1.8-m horizontal mirror but for a number of reasons the results obtained are poor and hardly usable. • Iye et al. [Iye] performed the most comprehensive tests available so far, using a 62-cm horizontal mirror with and without forced air convection. All these laboratory measurements constitute an important body of data but, perhaps because different methods were used, they have never been generalized and interpreted in a way that would lead to a general theory of the mirror seeing phenomenon from which one could obtain engineering parameterizations reliably applicable to an actual telescope design. In the next section we will describe the mirror seeing phenomenon as it appears from a fluid dynamics standpoint. Section 5.3.2 will summarize the available experimental data, including some obtained by the author during this work, and reduce them to common units of measure. Then in section 5.3.3 the various data sets will be analyzed, interpreted in the light of similarity relationships and utilized to develop and validate approximate computational models which will provide a useful theory for understanding and controlling the mirror seeing phenomenon in telescopes.

5-38

5.3.1


Physical description of mirror seeing

One should distinguish between the case of free convection in which the flow on the mirror is not affected or disturbed by externally driven air motion, and the case of mixed and forced convection in which an external air flow interferes with the free convection flow pattern. 5.3.1.1

Free convection

Free convection at a plate surface develops typically through large convective cells the regime of which is characterized by the three dimensionless numbers F r, Re, P r (see page 5-11). The Froude number characterizes the buoyancy force but is inconvenient in its present form, because it is expressed in terms of a reference velocity U which is not clearly defined. It is therefore customary to work with the Raleigh number: g∆T L3 Re2 P r = Ra = Fr T νκ At low Raleigh numbers the flow is deemed laminar, although it may be unstable, until a transition at Ra ' 4 · 107 to a fully turbulent regime. Recalling that telescope enclosures will typically have during night-time a stable stratification due to the daytime interior air cooling, even where the floor is not deliberately chilled, we may find some analogy with studies relative to the urban ”heat island” problem which is also characterized by an ambient stable stratification. Experiments reported by [Hertig 86] and [Giovannoni] have shown that for a large single surface and particularly in presence of an ambient stable stratification the convective cell can become unstable already at Ra > 6 · 105 and form a turbulent central nucleus if the length gL3 Ls = νκ 9 is greater than 3 · 10 m. Fig. 5.22 from [Hertig 86] illustrates the different regimes found experimentally for a convective cell with an ambient stable stratification. The height of the cell will depend theoretically on the stratification of ambient air. In a free neutral medium the plume would simply ascend until its energy is exhausted (free plume). Since the temperature fluctuations are greater very close to the surface-air interface, here is where we would expect that the mirror seeing effect is generated. Looking more in detail at the mechanism of free convection heat transfer from a horizontal plane, one distinguishes three regions (fig. 5.23): 1. A viscous-conductive layer in which heat is transferred by molecular conduction. The thickness z0 of this layer may be estimated equal to the free convec-

5-39

5.3. MIRROR SEEING

Figure 5.22: Convection regimes as a function of Ra and Ls

TURBULENT REGION Maximum velocity fluctuations

Rising plumes

2

CT

WALL REGION

Maximum temperature fluctuations

VISCOUS-CONDUCTIVE LAYER Figure 5.23: Temperature and velocity fluctuations in free convection over a horizontal plane

5-40


tion wall scale [Townsend]: z0 =

κ3 T gqs

!1

4

(5.39)

2. A wall region characterized by the emergence of rising plumes of warm fluid (and falling plumes of cold fluid) in which the mean temperature gradients, hence the temperature fluctuation intensity, are largest. 3. A farther region in which mean velocities and velocity fluctuations are largest but temperature gradients are negligible. The temperature fluctuations are largest at the base of the wall layer and strongly intermittent as they are caused by the plumes of fluid coming from the top of the conductive layer. The intermittency of these temperature fluctuations is in particular driven by the velocity fluctuations in the upper layer, which in turn depend on the form and general characteristics of the whole convective cell. In such circumstances it is understandable that the wall layer will hardly ever see an ideal laminar free convection flow as even tiny velocity fluctuations in the farther region will determine a flow pattern characterized by the eddy diffusivities KM and KH rather then the fluid viscosity ν and thermal diffusivity κ. Therefore most of the mirror seeing is generated in a thin region just above the viscous-conductive layer, itself quite thin (in the range of millimeters) where the temperature fluctuations are largest. If it could be visualized, seeing would appear almost ”floating” above the surface. This fact suggests that the mean value of mirror seeing, as it takes its origin so close to the surface, should predominantly be a function of the surface flux and could also be described by the expression (5.18) derived by Wyngaard for the atmospheric surface layer, that is at a much larger geometric scale. In section 5.3.3 we will indeed verify the hypothesis that equation (5.18) is valid to a good approximation also for the mirror seeing scale down to the height of the conduction layer (see fig. 5.23). 5.3.1.2

Mixed and forced convection

If a forced flow interacts with buoyancy forces the wall region and, in part, the conductive layer will be destabilized by the velocity gradients. In the turbulent region (see fig. 5.24) the turbulent diffusivity will increase rapidly with the distance from the surface, with a consequent reduction of the temperature fluctuations. The profile of CT2 above the surface will be such that the maximum is at the interface between the viscous-conductive layer and the overlying turbulent layer but will decrease more rapidly than in the free convection case.

5-41

5.3. MIRROR SEEING

2

CT

TURBULENT FLOW

Maximum temperature fluctuation

VISCOUS-CONDUCTIVE LAYER Figure 5.24: Temperature and velocity fluctuations in presence of forced flow over a horizontal plane All the experimental and anecdotal evidence shows that very little seeing will be produced if a forced convection regime is fully established as in that case the viscousconductive layer becomes very thin and the temperature turbulence profile decreases very rapidly. A more significant case is the intermediate situation in which a weak air flow interacts with free convection producing a mixed convection regime. This will be characterized by the Froude (5.20) and Reynolds (5.21) numbers. When the Froude number is large, forced convection is dominant and therefore mirror seeing should disappear. When the Froude number is small, free convection is dominant. The amplitude of the temperature turbulence profile is determined by the turbulent eddy diffusivity so that for our purpose the turbulence regime similarity is defined by the turbulent Reynolds number, proportional to the turbulence intensity - see (5.13): UL ∝ It (5.40) Re = KM Therefore in the mixed convection case, identity of the Froude number and turbulence intensity is required for any similarity between tests at different scales. In section 5.3.3 we will show that the rate of seeing produced by a given mirror-air temperature difference is indeed a function of the Froude number.

5-42

5.3.1.3


The cold mirror case

All the considerations above apply to the case where the flow is thermally unstable. For a colder mirror the convection cell cannot become unstable or turbulent unless mechanical energy is supplied in form of a turbulent draft. The seeing will then be a function of the velocity gradient as described by equation (5.7) with Ri > 0 and will generally be negligible (see fig. 5.1).

5-43

5.3. MIRROR SEEING

5.3.2

Experimental studies

A number of experiments have been realized by several researchers to understand and analyze the mirror seeing phenomenon. These tests have been performed with different methods and quantities measured also differed. Perhaps for this reason the various data have never been generalized toward the derivation of engineering parameterizations reliably applicable to an actual telescope design. We will present hereafter an original experiment aimed at verifying the possibility of simulating and measuring the seeing phenomenon by mean of reduced scale tests. Then we will briefly describe also the other main experiments reported and reduce all the measured quantities to a common unit of measure. The test results will be compared to those of similarity and computation models in order to provide a useful theory for understanding and controlling the mirror seeing phenomenon in telescopes. 5.3.2.1

A mirror seeing experiment with a 4-cm mirror

The experiment described here was performed by the author in the ESO optical laboratory. Description of the experiment The experiment is schematically illustrated in fig. 5.25: a parallel laser beam with a diameter of 3 cm is reflected on a flat horizontal mirror of a diameter of 4 cm and focused on a position sensing detector (PSD). The mirror was heated by selfadhesive film resistances in order to produce seeing which was evaluated from the rms of the image motion on the PSD and converted in terms of equivalent FWHM angle. We use here the expression, reported by [Sarazin 92], relating the variance of shortexposure angular image motion to Fried’s parameter ro for the long exposure: 1

− 35

σ 2 = 0.35 λ2 D− 3 ro

(5.41)

where λ is the wavelength, in the presently case 680 nm, and D the beam aperture of 3 cm. Noting that only the variance along one direction was measured on the PSD: 2 σxy (f · σ)2 2 = σx = 2 2 one obtains: " #3 λ2 f 2 5 ro = 0.18 1 (5.42) D 3 σx2

5-44


LASER DIODE

f = 30 cm

Beam D = 3 cm

MIRROR

Figure 5.25: Optical schematic of the mirror seeing experiment. where f is the focal distance on the PSD, which was 30 cm in this experiment. σx was computed from the image motion data recorded by the PSD over an integration time of about 30 seconds. The value for the FWHM angle θ is then evaluated by equation (2.1): θ = 2.013 · 105

λ ro

Different power settings of the heating resistances fixed around the mirror were set and the corresponding temperature of the mirror surface was measured by means of a contact thermometer. Because of the heating method, the temperature of the mirror is not completely homogeneous so the values given in the table of results below represent averages with an accuracy of a few percents of the mirror-air ∆T . The resolution of the PSD used is about 3 µm, which corresponds to a computed seeing (FWHM) of about 1.3 arcsec. Therefore, in order to get seeing measurements with good resolution, the mirror was heated up to a ∆T of 100 K. The tests were performed in two configurations: 1. In the first configuration the mirror was simply laid on the floor of the laboratory, in ”open air” - fig. 5.26. 2. The second configuration consisted in having the mirror enclosed by an octagonal cardboard dome of diameter 30 cm and a 6-cm wide slit as shown in fig. 5.27.

5.3. MIRROR SEEING

5-45

Figure 5.26: The test mirror on steel plate, itself laid on the floor of the laboratory.

Figure 5.27: The cardboard dome.

5-46


Results For all tested configurations (which included presence/absence of dome and different mirror-air ∆T ), seeing measurements were taken continuously over a period of typically half-hour, sometimes longer. From these sequences the mean and rms values were then obtained. A summary of the main test results for both open-air and dome configurations is found in the table below. Test Power Mirror FWHM (arcsec) configuration (W) ∆T (◦ C) mean rms notes Dome 0.84 10 4 2 3.3 15 17 6 7.5 22 20 10 13.5 50 25.4 11.2 31.4 100 54.6 10.6 31.4 100 38.8 7 1) Open air 0.84 10 0 0 3.3 15 0 0 7.5 22 4 1 13.5 50 25 11 31.4 100 56 28 31.4 100 41.8 14 1)

a= 6 F/∆T 5 0.25 0.54 0.48 0.23 0.21 0.15

0.23 0.22 0.17

Table 1: Summary of test results. 1) External disturbances minimized.

The use of equation (5.41) to evaluate the results in terms of FWHM or image size assumes that the turbulence follows Kolmogorov’s law. In order to verify this point, power spectra of the image motion have been computed on the 30-sec sequences. As the example of fig. 5.28 shows, the spectrum have clear Kolmogorov’s characteristics with an inertial range with slope − 35 . A fact apparent from these results is that the dome configuration starts showing seeing at lower ∆T s than the open-air one: however for larger ∆T s the results are quite the same. It looks like there is an anticipated stable-to-unstable transition in the dome due to interaction of the mirror convective flow with the internal dome surface, most likely linked to the tiny geometrical scale of the model. Therefore no undue extrapolation of these curious results should be done to full scale. Another important feature shown by the measurements is the large scattering of seeing values recorded during a same measurement sequence. This variability depended very much on the ”room turbulence” caused by the presence of the experimenters and by other external disturbances, such as opening and closing a door, happening

5.3. MIRROR SEEING

5-47

during a measurement sequence. One should remark here that the air motions in the generally very quiet optical lab, which could be caused by people occasionally moving some meters from the experiment, are very small in absolute terms and certainly not of turbulent nature. Nevertheless when such tiny air motions interact with the convective flow from the mirror, they apparently cause strong increases of seeing. One should underline that this increase of seeing values appears to be clearly due to some interaction of the ”room turbulence” (which, as said, is not really one) with the convection flow immediately above the mirror and is not a purely added ”room seeing” effect. If the mirror is not heated, the ”room turbulence” produces no measurable seeing effect. This indicates the extreme sensitivity of seeing caused by natural convection to even minimal air motions and turbulence that have an external cause. Typically at full scale, this would correspond to the often reported case of seeing allegedly caused by leaving a door open on the observing floor in a telescope dome. One can also remark that ”room turbulence” affects to a proportionally larger extent the seeing of a mirror with a small ∆T , which creates weak convective flows. Stronger convective flows from larger ∆T s tend to predominate over external disturbances. Some subsequent measurements were taken outside of working hours in order to minimize disturbances that may affect ”room turbulence”, which resulted in sequences - noted with 1) - with substantially less mean seeing and variability. Fig. 5.29 shows two comparisons between couples of sequences taken in the same test configurations.

5-48


Figure 5.28: Power spectrum of the image motion.

Figure 5.29: Comparison of measured seeing sequences taken with the same configuration: left the data measured in normal conditions in the ESO optical lab, right the data measured after working hours, in quiet conditions. The average seeing is definitely lower in the latter case.

5-49

5.3. MIRROR SEEING

5.3.2.2

Seeing tests on a 62-cm mirror

A Japanese team from the National Astronomical Observatory, Tokio, performed a mirror seeing experiment ([Iye]) with a 62-cm mirror setup which had been originally conceived to verify the feasibility of a new active optics system. The test setup is shown in fig. 5.30: the wavefront from a 65-cm horizontal mirror was measured by means of a Shack-Hartmann analyzer and expanded by Zernike polynomials. The image quality under the presence of seeing degradation was expressed by evaluating the Strehl ratio by the expression S ' 1 − π2

σw2 λ2

(5.43)

where σw is the measured wavefront rms error. The mirror was not actively heated or cooled but its temperature as well as that of ambient air followed slightly different diurnal variation cycles so that most of the time there was a mirror-air temperature difference. In order to measure the effect of forced ventilation, the upper surface of the mirror was flushed by the air flow created by an electric fan with a flow-guide nozzle as illustrated in fig. 5.30. Unfortunately the experimenters did not measure the value of turbulence intensity of the air flow from the fans. An estimate may be obtained from the measured velocity profile. The measurements were carried automatically over 90 full days. Fig. 5.31 shows the average Strehl ratio measurements reported by [Iye] as a function of the mirror-air ∆T for different flushing speeds. We note that the method used to derive the Strehl ratio from the wavefront aberrations through equation (5.43) becomes more and more inaccurate for σw > λ/10 or S < 0.7 . When the mirror was colder than ambient air the image quality remained perfect and no seeing was found for the range of mirror-air ∆T s up to -3K covered by the experiment. For the purpose of comparison we have converted the Strehl ratio values to FWHM seeing values by means of the SuperIMAQ computer program for the analysis of mirror image quality [ESO]. The seeing values in term of seeing FWHM are then plotted in fig. 5.33 .

5-50


Figure 5.30: Layout of the mirror seeing experiment by Iye et al.

1

2

2 × 2 × × × × + + + 2 2 3 3 × × + 2 2 3 + 3 + + + 3

0.8

0.6

U U U U

= = = =

0.0 0.2 0.5 1.0

m/s m/s m/s m/s

3 + 2 ×

3

S 0.4

3 3

0.2

0

3 3

0

0.5

1 ∆Tm (K)

3

1.5

2

Figure 5.31: Measured Strehl ratios versus mirror-air temperature difference for the 62-cm mirror (as reported by [Iye]).

5-51

5.3. MIRROR SEEING

Mirror D = 0.62 m at 700 nm 2

FWHM (arcsec) = 0.98*l/r0

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

0.1

0.2

0.3

0.4 0.5 0.6 Strehl intensity

0.7

0.8

0.9

1

Figure 5.32: Relationship between seeing FWHM and Strehl ratio for a 62-cm mirror (computed with the SuperIMAQ program).

0.6

Seeing FWHM (arcsec)

0.5

0.4

0.3

0.2 U = 0.0 m/s U = 0.2 m/s U = 0.5 m/s U = 1.0 m/s

0.1

0 0

0.5

1 Delta_T_m (K)

1.5

2

Figure 5.33: Seeing FWHM versus mirror-air temperature difference for the 62-cm mirror.

5-52

5.3.2.3


Seeing tests on a 254-mm mirror

C. M. Lowne of the Royal Greenwich Observatory performed an experiment to investigate the degradation of image quality in a heated mirror [Lowne]. The beam from a HeNe laser was diverged by a 20x microscope objective and than directed to a 254-mm spherical mirror. The return image was accepted by the microscope objective and relayed over a further 2 meters, giving an image magnification of 250x with image scale 2.5 mm to 1 arcsec. A calibrated iris was placed at this focus and the beam was then led to a CdS photo-conductive cell, which measured the light intensity. The mirror was tested at three zenith angles (0◦ , 20◦ and 50◦ ) and was heated and cooled artificially over a range of temperatures from -2K to +8K with respect to ambient. The measurements consisted in recording in each test case the iris diameter through which passed 75% of the light intensity. These data, expressed in arcsec, are listed in the tables below.

Zenith angle 0◦ 20◦ 50◦

Free convection (U = 0) ∆T (K) -2 0 2 4 6 8 1.74 1.01 2.26 3.97 5.53 6.30 1.01 1.50 2.08 2.21 2.81 1.2 1.01 1.36 1.58 1.69 1.89

Forced convection ∆T = 6K Zenith U (m/s) angle 0.1 1.0 0◦ 3.40 1.66 20◦ 2.82 1.85 ◦ 50 1.75 1.75

75% intensity diameters (arcsec) recorded by [Lowne] We have converted the 75% intensity diameters to FWHM seeing values by means of the SuperIMAQ computer program (fig. 5.34). Noting that the 75% intensity diameter for a diffraction limited (perfect) mirror is 0.73 arcsec, an aberration of 70 nm astigmatism was assumed in order to fit the reference measured value of 1 arcsec. The converted measurements are then plotted in fig. 5.35.

5-53

5.3. MIRROR SEEING

Mirror D = 0.254 m 4 SuperIMAQ calculation


3.5 3 2.5 2 1.5 1 0.5 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 Diameter of 75% encircled energy (arcsec)

Figure 5.34: Relationship between seeing FWHM and 75% intensity diameter for a 254-mm mirror with 70 nm astigmatism. Free convection


6 deg 0 20 50

5 4 3 2 1 0 -4

-2

0

2 4 Delta_T (K)

6

8

10

Forced convection (delta_T=6K)


6 0 m/s 0.1 m/s 1.0 m/s

5 4 3 2 1 0 0

10

20 30 Zenith angle (deg)

40

50

Figure 5.35: Seeing FWHM for the 254-mm mirror.

5-54

5.3.2.4


Other laboratory measurements

[Barr] studied the mirror seeing of a 1.8-m horizontal mirror in the range of mirrorair temperature differences -1.5 K ≤ ∆Tm ≤ 1.9 K by analyzing interferograms of the front surface. Unfortunately the large aberrations of the mirror and the change of tilt and focus between and during the test runs limit exceedingly the accuracy of the results and the comparison of different mirror conditions. The researchers also intended to verify the utility of small blowers placed around the mirror to create an artificial airflow . However their power was too weak to create a sustaining airflow capable to predominate the free convection flow pattern. Possibly the most significant result of this work is the analysis performed on the phase structure functions of the interferograms which concluded that they follow well the form predicted for Kolmogorov turbulence for separation distances up to 80 cm. Since the largest temperature fluctuations are found at a much shorter distance from the surface and are therefore associated to small turbulence length scales, this result of [Barr] makes admissible to use a CT2 parameterization also in the case of mirror seeing.

5.3. MIRROR SEEING

5.3.3

5-55

Analysis and modeling

In this section the experimental data described above will be analyzed and compared to those of mathematical models in view of deriving and validating some general procedures for the evaluation of the mirror seeing effect. 5.3.3.1

Mirror in free convection

Discussion of experimental data We have seen that mirror seeing due to pure free convection should be proportional to ∆T with an exponent of 1.2. Examination of the experimental measurements leads to the following conclusions: • The data from the CFHT telescope, analyzed in section 5.2.7 indicate a proportionality factor of 0.38 arcsec/K−1.2 . • In the Japanese 62-cm mirror experiment the factor to ∆T 1.2 lies between 0.25 and 0.34, although in fact the data would be better fitted with an exponent greater than 1.2. • For the 254-mm experiment of Lowne the factor to ∆T 1.2 lies between 0.28 (for ∆T = 8K) and 0.45 (for ∆T = 2K). The exponent would appear here to be lower than 1. • The experimental measurements of the author with a 4-cm mirror indicate for ∆T s up to 22K factors between 0.25 and 0.54. The discrepancies between the various experiments must not surprise as the measurement methods, the experiment set-ups, the range of temperatures explored and the environmental conditions differed greatly. Nevertheless the basic concordance of data over the large range of mirror diameters and other conditions provides some useful indications: 1. Mirror seeing in free convection conditions appears approximately independent of mirror size. 2. As the range of experimental conditions must have covered many different flow regimes (see fig. 5.22) it appears that mirror seeing is a quite ”robust” phenomenon as its quantification does not depend exceedingly on the particular conditions of the flow regime. 3. As seeing appears already in small mirrors with low ∆T s, associated with very low Raleigh numbers, it must be concluded that also fluctuations and instabilities in laminar flow regimes do produce seeing whose magnitude is of the same order as in fully turbulent regimes.

5-56


Emphasizing the weight to the CFHT data, we will here propose the following relationship for the purpose of engineering parametric studies: θ = 0.38 · ∆T 1.2

(5.44)

One should make allowance for possible variations of the order to ±25%. Fig. 5.36 shows the reasonable agreement of equation (5.44) with respect to all the laboratory data. Similarity theory model In section 5.3.1.1 we have illustrated how the production of mirror seeing takes place very close to the surface, in the region near the interface between the viscous conductive layer and the emerging plumes of warmer air. It follows that the phenomenon depends essentially only on one, namely vertical, geometrical coordinate. The hypothesis was expressed that the profile of the temperature structure coefficient CT2 above the viscous conductive layer over a mirror should follow the same similarity law (5.18) as in the atmospheric surface layer, in spite of the large difference of geometric scale. The maximum value of CT2 will be found at the top of the viscous conductive layer, the thickness of which is computed by the expression from [Townsend] as: κT gqs

z0 =

!1 4

CT2 is zero at the surface and will be linearly interpolated in the viscous conductive layer. Thus the vertical profile of CT2 is described by CT2 (z, qs )

g = 2.68 T

− 2 3

CT2 (z, qs ) = CT2 (z0 , qs ) ·

!− 4

z qs

3

z z0

for z ≥ z0

(5.45)

for z < z0

(5.46)

The seeing FWHM angle is then obtained by integrating equation (2.13) twice5 over the height significant for seeing effects: (

θ = 2 · 2.591 · 10

−5

λ

−1/5

Z

H

CN2 (z)dz

3/5 )

where CN2 is given by equation (2.10):

CN2 = CT2 · 77.6 · 10−6 1 + 7.52 10−3 λ−2 5

See fig. 1.1

P 2

T2

5-57

5.3. MIRROR SEEING

1 62-cm experiment (Iye) 0.38 dT^1.2 similarity model


0.8

0.6

0.4

0.2

0 0

0.5

1 Delta_T (K)

1.5

2

8 25-cm experiment (Lowne) 0.38 dT^1.2 similarity model


7 6 5 4 3 2 1 0 0

1

2

3

4 5 Delta_T (K)

6

7

8

60 4-cm experiment (this work) 0.38 dT^1.2 similarity model


50 40 30 20 10 0 0

10

20

30 Delta_T (K)

40

50

60

Figure 5.36: Mirror seeing for an horizontal mirror in free convection for Tm > Ta . Laboratory data from experiments performed in various ranges of temperatures are compared with expression (5.44) and with the similarity profile model of equations (5.45-46).

5-58


0.1 0.09 0.08

Height (m)

0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0

2

4

6 CT2

8

10

12

Figure 5.37: Example of computed profile of the temperature structure coefficient CT2 (mirror diameter 62-cm, ∆T = 1K, sea level conditions). The integrated FWHM is 0.4 arcsec. obtaining: θ = 5.182 · 10

−5

λ

−1/5

80 · 10

−6

P T2

3/5 Z

H

CT2 (z)dz

3/5

(5.47)

This model has been used to simulate all the laboratory experiments described above. In these simulations, the surface flux qs was computed by the textbook6 relationship between the Nusselt and Raleigh numbers for the laminar regime (Ra < 107 ): N u = 0.54 Ra0.25 A computed profile of CT2 is shown in fig. 5.37. One may note that in this typical example (mirror diameter 62-cm, mirror-air ∆T = 1K) the near totality of mirror seeing is produced in the first 2 cm above the mirror surface. The integral seeing values resulting from the simulations are plotted in fig. 5.36 over the experimental data. The good agreement indicates that a similarity model described by equations (5.45-46) does account well for the observed seeing effects.

6

See for instance [Incoprera], p. 506.

5-59

5.3. MIRROR SEEING

5.3.3.2

Ventilated mirror

The data from the 62-cm experiment suggest an approximately linear relationship between the seeing FWHM angle and the temperature delta for any given airflow speed. This reflects the fact that also in these conditions the seeing is caused by buoyant intermittent fluctuations like in the free convection case. Forced ventilation reduces this seeing by creating a mixed convection regime, which should be here characterized by the non-dimensional Froude number: Fr =

T U2 ∆T gD

(5.48)

where D is the mirror diameter. We would therefore expect that the Froude number has the role of a stability parameter with respect to the FWHM normalized with the mirror-air temperature temperature difference. If this is the case the rate of mirror seeing with respect to the mirror-air temperature temperature difference is a function of the Froude number: θ/∆T = f (F r)

(5.49)

The results of both the 25-cm and 62-cm experiments are plotted against the Froude number in fig. 5.38. They do follow a function of the Froude number as assumed by equation (5.49), which has the form: f (F r) = 0.18 F r−0.3

(5.50)

Equations (5.49) and (5.50) allow us to derive an empirical similarity law for the scale λθ of mirror seeing from a ventilated mirror: λθ =

λ∆T λF−0.3 r

= λ∆T

λ2U λ∆T λD

!−0.3

It follows that −0.6 0.3 λD λθ = λ1.3 ∆T λU

(5.51)

The dependency on the Froude number and the similarity relationship (5.51) suggests a relationship with the mirror size which would mean that larger mirrors have more seeing in the same condition of ventilation, although this is still to be verified on large mirrors.

5-60


1

FWHM / Delta_T

D=62cm, U=0.2 m/s D=62cm, U=0.5 m/s D=62cm, U=1.0 m/s D=25cm, U=0.1 m/s D=25cm, U=1.0 m/s

0.1

0.01 0.1

1

10 Froude number

100

Figure 5.38: θ/∆T as a function of the Froude number for a ventilated mirror. The line represents the function θ/∆T = 0.18 F r−0.3 .

5-61

5.3. MIRROR SEEING

5.3.3.3

Active correction of mirror seeing

We have in this work regarded mirror seeing only with respect to its global effect on image quality. It would however be of great interest to understand the mirror seeing effect also in terms of the mirror aberration modes, particularly in view of the further development of extended active and adaptive optics systems. Some limited information is provided by Iye’s 62-cm experiment in which it is verified that a large part of the image aberration appears as originated from wavefront tilt and defocus errors. The data, however, do not allow us to derive the spectral density of the fluctuations with respect to temporal frequency. An estimation of the order of magnitude of the peak frequency of these fluctuations may nonetheless be tried on the base of mirror seeing geometry and physics. Noting that the FWHM value of free convection mirror seeing corresponds in the diagram of fig. 5.38 to a Froude number of about 0.1, one can evaluate a reference flow speed from expression (5.48): s ∆T gD U = (F r) T Assuming that the spectral density follows the Von Karman model, which is generally the case for spectra in turbulent flow phenomena, we would obtain: nmax ' 0.15

U z0

where z0 is the height of the viscous conductive layer where the turbulence is strongest. A numerical application with ∆T = 1K and z0 = 3 mm gives for an 8-meter mirror a frequency of about 8.3 Hz. While all caution should be taken concerning the absolute accuracy of this result, it appears that the order of magnitude of the required bandpass for active correction is likely in the range 5 to 15 Hz, that is quite outside the bandpass of active optics systems but well within the range aimed for advanced adaptive optics systems.

5-62

5.3.4


Synthesis

Mirror seeing is caused by natural or weakly mixed convection over a mirror warmer than ambient air. The seeing effect is generated in a thin region just above the viscous-conductive layer where the temperature fluctuations are largest and most intermittent. If its cause could be visualized, seeing would appear to come from a thin but very turbulent layer ”floating” a few millimeters above the surface. On the base of this physical description we have expressed the hypothesis that the average amplitude of the seeing would be essentially a function of the surface heat flux. The profile of CT2 can then be described by a similarity equation (5.45), valid down to the interface with the tiny viscous-conductive layer. Computations of mirror seeing with this similarity model show a good agreement with experimental results. The results of several experiments performed by various researchers, have been processed to get a homogeneous database. In absence of forced air flow, mirror seeing appears not to depend on the mirror size. The effect of inclination is more controversial: it is reported to be large for a small 25-cm mirror but does not appear in our analysis of the 3.6-m CFHT telescope. For the purpose of engineering parametric studies the following relationship is proposed: θ = 0.38 ∆T 1.2 with a possible spread of 25%. In the case of a ventilated mirror, the seeing decreases showing a dependency on the Froude number. The relationship derived from the experiments is: θ/∆T = 0.18 F r−0.3 The dependency on the Froude number suggests the influence of the mirror size. Thus larger mirrors should produce more seeing in the same conditions of ventilation.

5-63

5.4. NUMERICAL MODELS

5.4

Numerical models

Numerical computational fluid dynamic (CFD) models are widely used in the simulation of atmospheric flow and turbulence. Therefore it is of interest to investigate also their potential for predicting atmospheric seeing, since, in principle, an accurate computation of the mean seeing effect along a given line of sight is possible if all statistical turbulent quantities of the flow field are known with sufficient accuracy and spatial resolution.

5.4.1

Seeing computation by means of a fluid flow numerical model

We recall that the seeing FWHM angle is an integral function of the temperature structure coefficient CT2 which in turn can be defined in terms of the two dissipation quantities (momentum) and θ (temperature) - see equation (2.8) at page 2-7. If a k- scheme is used in the model the dissipation rate and the eddy diffusivities KM and KH are readily available in the program output. One can then compute numerically the temperature dissipation θ at any node by computing numerically its definition over the model grid: θ = K H

∆Tk ∆xk

2

(5.52)

Thus CT2 can be evaluated at each node of the model and integrated according to (2.15) to obtain the FWHM angle. This general procedure is summarized in fig. 5.39 below. One such model has been developed under an ESO contract by the Risø National Laboratory (Denmark) with the purpose of computing theoretical seeing profile through the atmospheric surface layer in mountain terrain [de Baas]. The outcome of this work outlined some problems associated with the use of CFD models for seeing evaluation: • In order to give reliable results, a CFD model should well represent all significant characteristics of the solid-fluid interface, from friction effects to shear flow and heat transfer. However, the structures surrounding a telescope are generally very complex, which makes the development of a model grid a long effort and adds greatly to its size. • The conditions, both aerodynamic and thermal of the local atmospheric environment are often not known with the detail and extent that would be required for an accurate and comprehensive model. Also those conditions are very variable, which also adds to the effort involved and makes experimental verifications objectively difficult.

5-64


Figure 5.39: General procedure for evaluating seeing from a CFD model In the cited case, the CFD model included several simplifications, such as an adiabatic air-ground interface and the inability to compute separated shear flows which reduced the reliability of the results. More recently a simulation aiming at predicting seeing through the entire atmosphere was attempted at Meteo-France by means of the mesoscale numerical weather prediction model PERIDOT [Bourgeault]. The model was quite comprehensive in incorporating accurate representations of radiative and friction transfer and of turbulence in general, being used operatively for meteorologic predictions. A favorable comparisons of model output and seeing measurements is reported, although some reserves on the effective usefulness of the results were expressed because the model low resolution (respectively 10 km and 3 km in the two cases studied).

5.4.2

CFD for evaluating mirror seeing

We have pointed out in several instances in this work that mirror seeing is a real outstanding issue for the performance of new generation telescopes. It is therefore of particular interest to investigate how CFD models may be used in this context. The parameterizations derived in the previous sections for the mirror seeing effects both with and without ventilation should be adequate for most practical design cases of

5-65


a telescope/enclosure systems. There will occur, however, special cases in which the airflow on the mirror has particular characteristics which are not well represented by the theoretical and experimental assumptions taken in described above. We have seen that the source of the mirror seeing effect is ”concentrated” in a very thin layer close to the surface of the mirror. Therefore a comprehensive CFD model would require a very tiny resolution of the grid model near the surface, while keeping a good representation of all the larger structures surrounding the mirror and the telescope which determine the general flow characteristics. Such models would be costly and in fact unpractical, at least with the present state of the art. We will therefore propose a simplified approach. The small height of the turbulent layer responsible of mirror seeing also means that the turbulence profile is essentially a function of surface flux and that conditions may be assumed to be horizontally homogeneous. This suggests to propose a numerical parameterization of the CT2 profile as a function only of surface flux and flow characteristics computed at one height from the surface. The purpose of the CFD model can then be limited to the computation of the general flow conditions above the mirror. From the main parameters of the flow computed at, say, 1 cm from the surface (mean velocity, turbulent kinetic energy, mean temperature and surface flux, the local CT2 profiles are evaluated by a similarity model adapted from the expressions (5.8) and (5.9), in which the friction velocity u∗ is replaced by an equivalent velocity scale uL evaluated from the turbulent kinetic energy e: √ uL = k 2e The CT2 profile is then computed as: zkgq CT2 = 4.9 1 − 7 uL T

!

q uL

2

2

z− 3

(5.53)

Following the interpretation of mirror seeing in conditions of mixed/forced convection illustrated in fig. 5.24 (page 5-41), the maximum of the CT2 profile is set at the interface between the viscous-conductive layer and the fully turbulent flow. This interface may be defined as the height at which the kinematic viscosity of air ν and the eddy diffusivity for momentum KM have the same value. Recalling expression (5.13) we obtain: ν zo = kuL For z < zo , CT2 is linearly interpolated to a zero value at the surface.

5-66

5.4.3


Application to a 1.25-m telescope project

The astronomical observatory of the University of Geneva is presently developing a new 1.25-m telescope. This telescope is provided with a closed tube as this design solution was deemed best to prevent temperature fluctuations arising in the dome from affecting the quality of the light beam. Still, a ventilation of the mirror surface is planned by mean of active fans mounted around the contour of the tube. The purpose of this preliminary investigation was to quantify at least approximatively the flow conditions in the tube, then to evaluate the mirror seeing of the telescope and the influence of the fans. The computation was performed with the ASTEC program available at EPFL. In order to save time for this pilot evaluation, the telescope tube has been modeled simply with a square cross-section 1200×1200 mm (fig. 5.40). The last fluid nodeplane before the mirror surface was set at 1 cm from the interface. The initial temperature was set at 283K with the mirror at 285K (∆Tm = 2K). The effect of the fans was simulated by setting outlet velocities at 6 locations roughly corresponding to the positions of fans in the telescope (fig. 5.42). Different fan flow rates were given as input. Fig. 5.43 below presents the main results at three locations 1 cm above the mirror, the height of the first fluid node-plane. The ASTEC output provides the node values for mean velocity, temperature and turbulent kinetic energy, from which the heat flux and turbulence intensity are derived. The local profiles of CT2 and the integrated seeing FWHM θ are computed by means of off-line post-processing according to Inlet flow

Fans

Outlet flow

Mirror

Figure 5.40: The CFD ”square” model with respect to the actual telescope shape


Figure 5.41: The grid of the CFD model

Figure 5.42: Mean speed plot

5-67

5-68


equations (5.53) and (2.15). The seeing FWHM averaged over the whole surface is then plotted in fig. 5.44. The seeing computed for the free convection case at the ”boxed” mirror is lower than for an open configuration. This result is due to the well known fact that the free convection heat transfer rate from a warmer horizontal surface is quite lower when this is enclosed (see for instance [Incoprera], page 517 ff.). However the seeing is not improved by the active flow caused by the fans. In fact the planned fans cannot provide a sufficient mean flow speed to obtain a significant flushing of the mirror surface, while they create large turbulence intensities. One may recall here that turbulence intensity values larger than 0.40 are generally associated to instantaneous flow reversals. If the fans are maintained, they should then only be used in conjunction with the daytime air/conditioning system, to enhance the heat exchange between mirror and air in order to eliminate or decrease the occurrence of mirror-air ∆T when observation begin.

5.4.4

Synthesis

Fluid flow numerical models have been used in at least two previous occasions with the aim of predicting seeing. It appears that, while the method is applicable in principle, there are also practical difficulties linked to the size of the model, the definition of the initial and boundary conditions, and the possibility to validate the computation by means of representative tests. We have attempted here an application to the problem of mirror seeing in which we have parameterized the local CT2 profile by means of a similarity relationship. The case of a mirror within a closed tube and ventilated by fans was simulated with interesting results. The conclusions that can be drawn from this study are that a simulation with a similarity parameterization of the CT2 profile is feasible and appears to give realistic results. The limitations of this approach are however intrinsic to the utilization of a CFD model. Indeed the main advantage of CFD models is in the possibility to simulate particular cases and conditions which cannot be represented by simple relationships or for which there are no experimental data. On the other hand the CT2 parameterization refers to a well characterized steady state condition and may not be as accurate in the actual model conditions.

5-69


0.8 0.7

(e) (m) (i)

0.6

U (m/s)

0.5

(e) (m) (i)

0.4 0.3 0.2 0.1 0 0

500

1000 1500 Total fan flow rate (m3/hr)

2000

2500

10

1 (e) (m) (i)

(e) (m) (i)

0.8 Turbulence intensity

Q (W/m2)

8

6

4

2

0.6

0.4

0.2

0

0 0

500


2000

2500

0

500


2000

2500

Figure 5.43: Mean speed, surface heat flux and turbulence intensity at three points located 1 cm above the mirror surface, versus the total airflow rate of the fans.

0.6


0.5

0.4

0.3

0.2

0.1

0 0

500


2000

2500

Figure 5.44: Average seeing FWHM computed over the mirror aperture versus the total airflow rate of the fans. The temperature difference between the mirror surface and ambient air is here 2K.

5-70

5.5


Surface layer seeing

The effect of the atmospheric surface layer (the first 30 ∼ 50 m) on the local seeing has been for a long time a main preoccupation of astronomers. Therefore the preferred sites for astronomical observatories are mountain summits which rise steeply in the free atmosphere and where the prevailing winds hardly flow up the mountain slope. In fact many infrastructural, operational and logistics requirements conflict often with this ideal. An observatory site must be on a reasonably accessible location. Often, for reasons of scale economy, several telescopes share the best astronomical sites and not all can be located on the highest and best exposed locations. Also, once the facility is completed with roads, buildings, parking lots, etc., the site itself has only a vague resemblance to its virgin appearance. As a consequence a telescope seldom stands in an atmospheric environment which is not affected by the proximity of the ground and other artificial structures. The general issue of seeing in the atmospheric surface and boundary layers has been discussed extensively in [Sarazin 92], a PhD dissertation which also includes several papers published on the subject. Therefore we will limit the scope of this work to two aspects which are particularly relevant to the civil engineering design of an astronomical observatory: 1. The criteria for choosing an optimum height of a telescope base. 2. The feasibility of wind tunnel simulations for modeling the seeing effects at a reduced scale, which would give a powerful tool for studying and improving the layout of an astronomical observatory.

5.5. SURFACE LAYER SEEING

5.5.1

5-71

The optimum height of a telescope base

The problem of deciding the height of the telescope pier is frequently one of the most controversial in the design of the observatory facility. On the one hand one would like to set the telescope out of the possibly negative effects of the ground proximity. On the other hand the cost of the building increases rapidly for every additional meter of height: first the cost of concrete, steel and handling equipment needed for a higher building, and later the additional time and effort required for every handling operation, from the initial assembly of telescope and dome to the regular maintenance handling of mirrors and instruments. When ample funds were available, the opinion of designers tended to be quite prudent and conservative with regard to the danger of seeing from the near-ground layer and the telescope support was set as high as practical (which in many cases was about 30 meters). When budgets were limited, telescopes were set at more modest heights and eventually the feared consequences on seeing quality did not materialize or anyway were not quantified. The case of the ESO 2.2-m telescope mentioned earlier in section 3.2.1 is quite typical in this respect. In reality the optimal height for a telescope from the standpoint of seeing quality will depend on the overall optical performance aimed for the telescope as well as of the particular phenomena in the near ground atmospheric layer, which may vary at different sites and also within particular locations of a same mountain site. For a modern technology large telescope which aims at an overall FWHM quality of the order of 0.5 arcsec, it will generally be desirable that the mean seeing contribution of the near-ground layer does not exceed about 0.1 ∼ 0.15 arcsec. A less ambitious telescope will accept easily 0.2 ∼ 0.3 arcsec from the near-ground layer without significant loss of performance7 . The local conditions of the surface layer on astronomical sites during night-time will of course vary but generally share two important characteristics: the turbulence intensity is low and the ground surface experiences a strong radiative cooling. Therefore the temperature gradient in the local surface layer is generally stable and we have seen (see page 5-3) that in those conditions the seeing will increase when the turbulence is augmented. The seeing in the surface layer can be evaluated by means of measurements of the CT2 coefficient at a few points along the vertical of the site. From the interpolated profile CT2 (z) the equivalent seeing FWHM can then be computed by equation (2.15). Fig. 5.45 shows some averaged profile reported from different sites.

7

We recall that seeing contributions along the line of sight add up with the power 5/3, while all other contributions add quadratically to the total seeing (see equations (2.16) and (2.26)).

5-72


0.1 Mauna Kea [Ando 89] Mauna Kea [Merril 87] La Palma (LEST-A)

CT2

0.01

La Palma (LEST-B)

0.001

0.0001

0

5

10

15 20 Height (m)

25

30

35

Figure 5.45: Some CT2 profiles reported from various observatories4 . All these profiles were measured on ”virgin” locations, during the site selection studies of new telescope projects. It may therefore be interesting to analyze the profiles on an already built observatory. Systematic recordings of the temperature structure coefficient CT2 at the La Silla observatory were taken by the author during 11 consecutive nights from Nov 20th 1986. The CT2 measurements were taken by special micro-thermal sensors developed at ESO and described in [Sarazin 92], located at three heights (10, 20 and 30 meters) on the La Silla main meteo tower (see fig. 3.3, on the left hand). The tower is located on the leeward edge of a roughly flattened ridge about 50 m wide, well exposed to the prevailing north winds of La Silla and not directly in the wake of the other domes built nearby on the ridge. There is also an asphalted road just upstream of the tower and therefore the test location may be taken as a reasonable example of a built site. The wind was about 5 ∼ 6 m/s during the measurement nights, which also corresponds to the yearly night-time average at La Silla. The CT2 data were averaged over periods of one hour and cover 70 hours of astronomically useful night-time. Short periods of cloudiness which occurred during some of the nights were taken out of the data set. The values recorded at the height of 10 m are generally greater than 4

The data from La Palma are from the site survey study for the LEST solar telescope [Ortolani 91].

5-73


height (m) 10 20 30

CT2 mean

(K2 /m2/3 ) rms max

0.0068 0.0063 0.0304 0.0014 0.0011 0.0062 0.0012 0.0010 0.0060

Table 5.2: Statistical summary of night-time CT2 data. those at 20 meters, which are very similar to the values for 30 meters as can be seen by the statistical summary shown in table 5.2. A further analysis suggested that the difference 10-20 meters was linked to the wind velocity. This is well shown in fig. 5.46, showing a plot of the ratios CT2 10 /CT2 20 and CT2 20 /CT2 30 versus the mean wind velocity. One can may recognize two ranges of wind velocity: a range of low winds up to about 10 m/s where the means of CT2 10 and CT2 20 are respectively about 10−2 and 10−3 K2 m−2/3 and the range beyond 12 m/s where CT2 is about 10−3 K2 m−2/3 at all heights. Thus strong winds mix the surface layer such that CT2 does not depend on the height from the ground. Fig. 5.47 shows the values evaluated for each set of measurements of the integral R 30 2 z1 CT dz with z1 as respectively 10, 15 and 20 meters, assuming a linear variation of CT2 . The equivalent seeing values are given in the table below. hR

i3/5

z1 θ = 0.94 z301 CT2 dz (m) mean rms max 10 15 20

0.163 0.107 0.069

0.144 0.092 0.063

0.379 0.236 0.165

Table 5.3: Statistical summary of integrated FWHM (arcsec) from height z1 It appears that the CT2 values measured in this case are significantly greater than those of fig. 5.45, although they are by no means alarming in absolute terms: a typical requirement that the mean seeing contribution of the near-ground layer does not exceed about 0.15 arcsec, would place the height of the opening (slit) of the telescope enclosure at about 11 m.

5-74


C2

C2

Figure 5.46: Ratios log CT2 10 (+) and log CT2 20 (4) versus wind speed. T 20

Integral values Silla:

R 30 z

T 30

Figure 5.47: CT2 dz in the ground layer computed from the measurements at La +=

R 30 10

CT2 dz,

2=

R 30 15

CT2 dz,

4=

R 30 20

CT2 dz.


5.5.2

5-75

Reduced scale simulation of near-ground seeing

It would obviously be of great advantage for the layout planning and the general design of an astronomical observatory to be able to perform reduced scale simulations in wind tunnels, including the direct measurements of thermal turbulence and seeing parameters. The purpose of the present section is to analyze the possibilities offered by wind tunnel testing of the surface layer turbulence with respect to the seeing issue and to determine the similarity rules which may allow the measurement of seeing parameters on reduced scale models. 5.5.2.1

Similarity rules for near-ground flow

The night-time surface layer is affected the radiative cooling of the ground which creates a thermally stable turbulent air layer. Simulation of turbulent flows at reduced scales must be based on strict similarity rules. The analysis of turbulent flow parameters allows the deductions of non-dimensional numbers which have to be respected in order that the flow in the wind tunnel correctly represents the real turbulent flow. For an isothermal flow, the following three rules are sufficient to ensure similarity between two turbulent flows: • Geometrical similarity, i.e. the three geometrical dimensions must respect the same scale. • The intensity of turbulence σu /U has to be the same in model and reality. • The turbulence length scales shall respect the geometrical scale. Therefore the frequency scale of the energy density spectra shall be reduced as the geometrical scale. These conditions also imply similarity of Reynolds number and surface roughness and are at best respected in typical boundary layer wind tunnels when the geometrical scale is ≈ 1/200 and the flow speed ≈ 10 m/s. When the turbulence is influenced by the thermal stratification, similarity of the flow requires additional conditions. If the flow speed is weak, the flow interacts with the thermal stratification and the likely outcome is a slope wind. In this case, similarity of a suitable stability parameter (such as the Richardson number or the Monin-Obukhov length) as well as of thermal air expansion are required. The analysis of similarity of such thermal winds is quite complex (see for instance [Hertig 86]) and leads to the requirements of a scale of about 1/2000 to 1/5000 depending on surface roughness ([Hertig 91]). Since this scale does not allow the

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correct simulation of turbulence spectra, it will not be possible to simulate seeing effects in these conditions. In stronger winds the thermal stratification does no longer drive the flow but still affects the turbulence. The similarity of thermal air expansion can be relaxed and the flow is only characterized by the thermal stability conditions. These can conveniently be represented by the Richardson number: g dT Ri = T dz

dU dz

!−2

Therefore for a correct simulation the scales (ratios of quantities between model and full scale conditions) of geometry, speed and temperature deviations shall be in the following relationship: λ∆T = λ2U λ−1 (5.54) z The graph in fig. 5.48 gives the temperature scale λ∆T as a function of the speed scale λU for different geometric scales λz . With a geometric scale of 1/200 and a speed reduction by a factor 2 or 4, sufficient to maintain a turbulent flow, the scale of temperature deviations in the wind tunnel with respect to full scale will be respectively 50 and 12.5 . For the expected full scale temperature deviations of 1 to 3K, these distorted temperature scales are indeed feasible in the wind tunnel. It is therefore possible to simulate in the wind tunnel both mechanical and thermal parameters of turbulence. The corresponding scaling of seeing can be conveniently derived from equation (5.7) which parameterizes thermal turbulence in the near-ground layer: CT2

dT = f (Ri) dz

!2

4

z3

(5.55)

which gives the scaling factor for CT2 between model and full scale conditions: λCT2 = λ2∆T λ−2/3 z

(5.56)

We can assume further that the temperature profiles are self-preserving for a same Richardson number, e.g.: T (z) = ∆Ts g(z) where ∆Ts is the bulk air-surface temperature difference and g(z) the normalized temperature profile for a unit ∆Ts . Recalling equations (2.13) and (2.10), we obtain for the seeing FWHM along a vertical direction: θ=B

Z

H

CT2 (z)dz

3/5

= B f (Ri)3/5 ∆Ts6/5

Z

H

4

g02 (z)z 3 dz

3/5

(5.57)

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where B is defined as: B = 2.591 · 10

−5

λ

−1/5

77.6 · 10

−6

1 + 7.52 10 λ

−3 −2

P 6/5

(5.58)

T2

f (Ri) shall be identical in both full and test scales, while the integral in equation (5.57) is proportional to the vertical geometrical scale to the power 1/5. The scaling factor for seeing between model and full scale conditions is then: 6/5

λθ = λB λ∆T λ1/5 z

(5.59)

Summarizing, this scaling relationship will be valid and applicable to reduce scale tests provided that: 1. The usual similarity conditions for the atmospheric boundary layer apply: geometrical similarity, same turbulence intensity, turbulence length scales respecting the geometry reduction. 2. The wind is sufficiently strong to exclude that local thermal conditions affect its mean speed and direction (no slope breezes). 3. The thermal stability parameter (i.e. the Richardson number or the MoninObukhov length) are the same in both model and full scale.

Scale of temperature deviations

100

80

60

40

20

Geometrical scale 1/100 1/200 1/300

0 0

0.2

0.4

0.6 Velocity scale

0.8

1

Figure 5.48: Required scale of temperature deviations λ∆T as a function of the speed scale λU for different geometric scales λz .

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5.5.2.2


Pilot test for direct measurement of seeing

A pilot test was run in the EPFL/LASEN biphase wind tunnel, which consists of a 12-m long channel with a variable cross-section ranging from 0.75 to 1 m2 . The first eight meters of floor fetch are equipped with cooling/heating elements. The flow speed may vary from 0.1 to 25 m/s. No artificial turbulence was created for the pilot test and the boundary layer is simply developed along the eight meters of refrigerated floor. The ambient air temperature was about 23◦ C and the wind tunnel lower surface was chilled to about -10◦ C. The similarity rules analyzed above result in the following scaling factors between model and full scale conditions: Geometrical scale λz Velocity scale λU Temperature scale λ∆T Scale8 of B factor - see (5.58) λB Scale of seeing λθ Velocity Temperature ∆Ts

Full scale 10 m/s -2.6 K

1/200 1/4 12.5/1 1.37/1 9.8/1

Model scale 2.5 m/s -33 K

The profiles of speed and temperature obtained in the wind tunnel are shown in fig. 5.49. The diagrams for mean speed and temperature show a favorable comparison with the theoretical surface layer profiles evaluated assuming a friction velocity u∗ of 0.07 m/s and a roughness length zo of 0.0002 m (0.04 m full-scale). Only the profile of turbulence intensity is somewhat lower than the corresponding theoretical one. Two measurement methods were attempted to evaluate the seeing through the boundary layer. The first method consisted in measuring the temperature spectrum with a micro-thermocouple. Recalling equation (2.7), CT2 can be evaluated in principle from any point of the inertial domain of the temperature spectrum: CT2 = 4

Φ(κw ) −5/3

κw

However, actual measurement of temperature spectra in this case presented several problems and no useful results were obtained. The bandwidth of the microthermocouple used was about 25 Hz, too low for the reduced wind tunnel scale9 . Furthermore, because of the small signal amplitude it was impossible to avoid signal pollution by the 50 Hz mains. 8

The scaling of the B factor takes account of the lower atmospheric pressure of an astronomical mountain site: here 770 mb with respect to 1000 mb for the wind tunnel. 9 One may recall that turbulence frequencies are increased inversely to the geometrical scale: as a comparison the velocity spectra are generally measured up to 200 Hz.

5-79

200

200

150

150 Height (mm)

Height (mm)


100

100

50

50

0

0 0

0.5

1

1.5 Speed (m/s)

2

2.5

3

0

5

10 15 Turbulence intensity (%)

20

200

Height (mm)

150

100

50

0 -16

-14

-12

-10 -8 -6 -4 Delta Temperature

-2

0

2

Figure 5.49: Wind tunnel profiles of mean speed, turbulence intensity and temperature compared with a theoretical profile computed assuming u∗ = 0.07 m/s and zo = 0.0002 m.

LASER DIODE

PSD f = 30 cm

BOUNDARY LAYER WIND TUNNEL

Beam D = 3 cm

REFRIGERATED SECTION ~ 8 meters

20 cm

MIRROR

Figure 5.50: Schematic of optical measurements in the wind tunnel.

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The second method consisted of a direct measurement of the seeing through the boundary layer by means of the same system used for the 4-cm mirror seeing test, in which the seeing is evaluated from the image motion of 3-cm diameter laser beam. The system and the procedure for obtaining seeing values are described in section 5.3.2.1 above. The frequency range of the position sensing detector (PSD) which measures the image motion is 1 kHz, and therefore covers amply the inertial range of the wind tunnel turbulence. The mirror was placed inside a 6-cm diameter hole located 20 cm downstream of the refrigerated section. The mirror surface was about 2 cm underneath the tunnel floor. The optical equipment was located above the wind tunnel as shown in fig. 5.50. Most test runs were performed at the speed of 2.5 m/s, still sufficient to generate a turbulent boundary layer, in order to minimize the disturbance to the optical measurements caused by vibrations of the wind tunnel. The main results obtained are summarized in table 5.4 below. Test No. 1 2 3 4 5 6 7 8

Speed U (m/s) 2.5 2.5 2.5 2.5 9.0 2.5 2.5 2.5

Air-surf. ∆T (K) -33 -33 -33 -33 -33 -11.2 -6.8 -3

Image motion 2 (µm2 ) σxy 5.04 5.04 5.00 5.10 23.4 2.53 1.34 1.29

Seeing image motion 2 (µm2 ) σxy 3.75 3.75 3.71 3.81 N.A. 1.24 0.05 0

Fried param. ro (m) 0.1 0.1 0.1 0.1 0.19 1.33 -

FWHM θtest (arcsec) 1.37 1.37 1.37 1.37 0.71 0.10 -

FWHM θfull−scale (arcsec) 0.14 0.14 0.14 0.14 0.07 0.01 -

Table 5.4: Summary of test results. The baseline test is No. 1, performed in the empty wind tunnel. Test No. 2 was a repetition, showing that the measurements are reproduceable. In test No. 3, which shows a very small amplitude decrease, there was a small wood block of size (l×w×h) 20×6×8 cm located about 40 cm in front of the light beam. In test No. 4 the block is made of aluminum and cooled to -10◦ C: only a tiny amplitude increase is recorded. Increasing the flow speed (test No. 5), the seeing should increase but so do also the vibrations, so that the measurement is hardly significant. Tests No. 6 and 7 were done when the wind tunnel was reheating, and show as expected a decrease of amplitude. In test No. 8 almost no cooling is in effect and the value measured must be considered as the signal background noise: it was therefore subtracted quadratically before the evaluation of the seeing angle. Some problems were outlined during the tests: • It would have been necessary to decouple the optical system and the mirror from the wind tunnel to eliminate the effect of vibrations.


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• The resolution of the PSD used is 3 µm , which is marginal with respect to the effects investigated and a more accurate system should be used for a further development of this test method. Nonetheless the conclusion that can be drawn from these simple experiments is positive and promising: wind tunnel simulations with thermal stratification and the optical method proposed are essentially feasible and can be applied, with some further development work, to a site and layout study for an astronomical observatory.

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Chapter 6 Systems Engineering In the previous chapter we have analyzed a number of issues in which atmospheric turbulence influences the performance of an optical telescope. In particular we have characterized and quantified: • the flow turbulence acting on the upper part of the telescope which is the main cause of guiding error • the optical aberrations of the primary mirror due to dynamic deformations caused by pressure fluctuations • the local seeing effects generated inside the enclosure • the mirror seeing effect and its dependency on temperature and flow speed The table at the next page summarizes the main results and the parameterizations relating the various local atmosphere effects to the telescope performance that have been obtained in this work. The purpose of this chapter will be to illustrate how the knowledge acquired on those different effects can be used and combined within a global evaluation of telescope performance and eventually integrated into a concurrent design process for both the enclosure and the telescope.

6-1

6-2

Problem Guiding error caused by wind buffeting

Optical aberrations caused by wind loading on the primary mirror (M1) Dome seeing: free convection from the floor

CHAPTER 6. SYSTEMS ENGINEERING

Main results and parameterizations High turbulence on the telescope upper part: large σp for 10◦ < α < 40◦ associated with low Lu and high frequency vortices

Method of derivation Wind tunnel tests

Wavefront rms error: D4 σw ' 2.17 · 105 Et 3 σp image size: D3 θw ' 306 Et 3 σp

Model & full-scale measurements

Either: • limit through-flow mean speed by a windscreen (or by a conventional dome) • leave telescope upper part in the free wind flow Limit pressure fluctuations on M1

Theoretical proximation

ap-

Enclosure thermal control, chilled floor

−1/5 4/3 qs

θd ' 20.9 Dd

Engineering action

Seeing from heat dissipation of the secondary mirror

θM 2 = 0.018 Q4/5 D−9/5

Experimental measurements and similarity relationship

Heat removal by a cooling circuit

Mirror seeing

Without ventilation: θm ' 0.38 ∆Tm with ventilation: θm ' 0.18 ∆Tm F r−0.3

Experimental and theoretical models

Either: • maintain ∆Tm ≤ 0 • ventilate the mirror surface

Surface layer seeing

Scaling relationship for similarity between different stable turbulent layers: λ∆T = λ2U λ−1 z Seeing scale: 6/5 1/5 λθ = λB λ∆T λz

Similarity analysis and pilot test

Consider reduced scale simulation in a wind tunnel

Table 6.1: Summary of main results and parameterizations of image quality with respect to local atmospheric effects.

6-3

6.1. ENGINEERING CRITERIA AND GUIDELINES

6.1

Engineering criteria and guidelines

We will here describe and discuss from the standpoint of telescope and enclosure engineering some main conclusions that can be drawn from the scientific/technical results derived in the previous chapters.

6.1.1

Wind turbulence on the telescope

2 ) Fig. 6.1 shows a comparison of the amplitude of of rms pressure fluctuations (σp /U∞ acting on the upper part of an 8-meter telescope in various enclosure configurations. The additional turbulence created by the slit is significant only for azimuth angles < 40◦ . In principle, the presence of a 50% permeability windscreen across the slit can provide conditions on the telescope in which the overall rms amplitude of pressure fluctuations is below the typical free flow situation.

0.5 VLT-cyl open VLT-cyl 50% ws NTT-type open NTT-type 50% ws retractable enclosure


0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0

20


80

Figure 6.1: Comparison of the amplitude of normalized rms pressure fluctuations 2 (σp /U∞ ) acting on the telescope top ring in different enclosure configurations. The advantage of the open air enclosure is more evident if one compares the amplitude of pressure fluctuations with frequency larger than 1 Hz, which is a typical bandwidth of the closed loop control system of the telescope drives (fig. 6.2). The free flow wind contains very little turbulent energy at high frequencies, while a slit produces most of the flow turbulence right in that frequency range: only a 20% permeability wind screen can reduce the pressure fluctuations to the free flow level, by dramatically cutting the mean flow speed.

6-4



0.25 VLT-cyl open VLT-cyl 20% ws NTT-type open NTT-type 20% ws retractable enclosure.

0.2

0.15

0.1

0.05

0 0

20


80

Figure 6.2: Amplitude of rms pressure fluctuations with frequency > 1 Hz, acting on the telescope top ring in different enclosures.

6.1.2

Wind buffeting on the primary mirror

The surface figure of the relatively thin primary mirrors of the new 8-m generation are quite sensitive to the turbulent pressure fluctuations caused by wind buffeting. For instance in the case of the VLT, the relationship (4.2) leads to specify, for a wavefront error of 200 nanometers, a threshold for the admissible pressure fluctuation at 1.3 Pa. This is a very low value that will generally be reached with a wind speed close to the mirror of about 3 m/s. From the practical engineering standpoint there are in principle three possible technical solutions to this problem: 1. Passive solution through wind shielding. Here the enclosure must be capable of shielding the mirror from nearly all wind loading. This is the approach taken by the VLT project, where the relationships (4.4) and (4.4) will allow the designers to relate the airflow speed near the mirror with the pressure fluctuations, thereby providing the quantitative data for evaluating the optical performance of the mirror under wind loads and then for determining the best operating strategy for the venting devices (windscreen, louvers) of the enclosure. This topic will be further discussed in section 6.2 below. The other alternatives require the upgrading of ”active optics” mirror support systems in order to provide a reaction capability of the mirror to fluctuating

6.1. ENGINEERING CRITERIA AND GUIDELINES

6-5

wind loads. 2. Increasing the number of virtual fix-points. This approach has been taken in particular by the Gemini project (see page 1-3), where it is planned to provide the mirror with six fix-points instead of three. This will reduce the mirror deflections, hence the optical aberrations by a factor of about four. 3. Increasing the bandwidth of the active optics control loop. We have seen that the peak frequency of the pressure fluctuations on a 8-m mirror is below 1 Hz in all the configurations tested. Therefore an extension of the active optics control loop up to at least 1 Hz, which appears technically feasible [Wilson 93], would achieve a sufficient dynamic correction of the effect of wind buffeting. Clearly, while the first alternative is completely within the design domain of the enclosure engineer, the other two will require a concurrent approach, in which the development of improved active optics systems is driven by a parametric analysis of the amplitude and frequencies of pressure fluctuations on the mirror, performed along the lines illustrated in section 4.2.

6.1.3

Dome seeing

Dome seeing, defined here as excluding the mirror contribution which is treated separately, is due to free or weakly mixed convection inside the entire volume of the telescope enclosure. The applicable similarity relationships (equation (5.29)) show that the occurrence of dome seeing requires significant surface heat fluxes, of the order of 10 W/m2 for θ = 0.25 arcsec. In a conventional dome where no ventilation occurs or is desired, the best technical solution to prevent dome seeing is the provision of a chilled floor. This will create a stable thermal inversion which will also ”damp” any free convection air motions that may arise from localized heat sources. As a ”second best” solution, probably less expensive, one can provide an internal insulation of the floor and of the walls, which will reduce the heat exchange between the building structure, with its large thermal inertia, and the air volume, the temperature of which varies more rapidly. In a ventilated enclosure such as the NTT, dome seeing is eliminated by the wind flushing through the telescope. Therefore no particular thermal control of the enclosure interior during observations needs to be planned. Suitable operating procedures should be established for the case when the enclosure is operated at a more shielded configuration (windshield up, louvers closed, side walls facing the wind). Then an occasional occurrence of dome seeing can be corrected by the operator ”flushing” the enclosure during an interruption of the observations.

6-6


A particular issue is set by heat generation at the secondary mirror unit. Seeing from this source was quite feared during the development of most recent telescopes and therefore heat extraction circuits were implemented. These circuits can be quite complex, also because they must reach the M2 unit through the spiders. In fact we have shown that the seeing effect (see equation (5.38)) is smaller than it was feared, even in low wind conditions. If the top ring of the telescope is reasonably exposed to the wind, the designer should consider trading-off the complications of a heat extracting circuit against a minor and occasional loss of image quality.

6.1.4

Mirror seeing

A positive temperature difference between the mirror and ambient air creates seeing with a rate between 0.3 to 0.4 arcsec per degree K in calm air. A forced air flow decreases this effect quite rapidly, but the pressure fluctuations may cause mirror deformations, as discussed above. The combined error analysis of seeing + wind buffeting and its consequences on the design and operation strategy of the telescope enclosure are treated in section 6.3.1.1 below. Here we will outline the possible technical means demanded by the problem. Considering the constraints given by the technology of the mirror and its support system, at the time of writing the only certain technical solution requires the active cooling of the mirror. Two methods, and their combination, are basically available. The first method requires that the entire telescope is kept very cold during the day in the closed enclosure. The second method involves providing a cooling disk under the primary mirror. All the available data indicate that over-cooling the mirror does not create seeing, at least down to -3K with respect to ambient air. Therefore daytime cooling may be considered sufficient for those sites where the air temperature does not drop exceedingly during the night. A detail analysis on the basis of the site meteo data will be required to assess the suitability of this solution. Direct cooling of the mirror is potentially more reliable and flexible, although one should still consider its large heat capacity. Because of this thermal inertia, a temperature control of the mirror will likely present limits with respect to the seeing effect. This leads us to forecast that ultimately the solution to the mirror seeing problem will consist of the unhindered ventilation of the mirror by the wind. This design approach will be made possible by the expected progress in extended active systems which will maintain an acceptable mirror figure with an airflow up to at least 7-8 m/s.

6.2. RANDOM CONDITIONS AND OPERATIONAL ASPECTS

6.2

6-7

Random conditions and operational aspects

We have already noted in section 2.4 the special random nature of the telescope error components due the effect of atmospheric turbulence, in opposition to the essentially deterministic or stable nature of the figuring and alignment errors . There are two aspects contributing to this random nature. The first one is the great variability of atmospheric external conditions on the site of the observatory. The second aspect is due to the operation of the telescope and its enclosure: the performance will be affected by the (statistically random) pointing direction of the telescope and by the operation of the windscreen and louvers of the enclosure. So far there has been hardly any attempt to take the random aspect of these effects in a concurrent engineering approach to the design of a telescope enclosure. For instance, engineering computations relative to wind loading on telescopes (computations concerning local seeing have been practically inexistent) generally consider either ”worst cases” or ”average cases” and fix somehow the input conditions. The results of these studies are then indicative of the general behavior and performance of the systems analyzed but can hardly claim to be a realistic prediction of a performance which can be later verified. For instance, suppose that conditions of strong winds are statistically associated to high values of natural seeing1 . Then errors caused by wind buffeting will be to some extent masked by the high seeing and therefore less critical to the telescope quality than if wind and natural seeing were statistically unrelated. There are numerous possible relationships of this kind which may have an impact on the design choices. Also the operational aspects of the enclosure with the use of louvers, venting openings and windscreens have never been the object of engineering studies. Even in the best observatories, the criteria for operating the venting devices come in the best case from empirical experience if not simply from a longtime unquestioned routine. As a contribution to these issues we will here introduce a system engineering approach based on the evaluation of statistical distributions of error components due to local seeing and guiding.

1

This is the case at the Paranal site of the VLT ([Sarazin 90]).

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6.3


A statistical model of telescope image quality

Because of the variability of atmospheric conditions and the great number of possible observing configurations a realistic and reliable assessment of the effect of the local atmosphere on the telescope performance can only be done by a statistical model. Such a model will also allow us to study in a realistic manner the effect of operational criteria for the venting devices of the enclosure. The model comprises the following elements: 1. The starting point is a large set of continuous night-time wind and natural seeing data measured on the site. Typically the set will have a record with the mean values for each period of 10 or 20 minutes. 2. A random zenithal distance between 0 and 60◦ and a random azimuth (±180◦ ) with respect to the mean wind direction are associated to each data record. This assumption is confirmed by actual statistical data of telescope operations. 3. The parameterizations for seeing and dynamic deformations of the mirror and for the guiding error. 4. The characteristics of the air flow inside the enclosure at all its different orientations configurations. 5. The criteria driving the operation of the wind screen, louvers and the other venting devices. 6. A performance assessment criterion that relates the effect of a disturbing influence to the overall best performance that is achievable in the actual conditions. The notion of Central Intensity Ratio presented in section 2.4 fulfills this condition as it assess the loss of image quality with respect to the limiting natural seeing. In the next pages we will illustrate the use of this statistical model using the VLT case as an example.

6.3. A STATISTICAL MODEL OF TELESCOPE IMAGE QUALITY

6.3.1

Parameterization of seeing and guiding effects

6.3.1.1

Wind versus seeing for the primary mirror

6-9

On the 8-m primary mirror of the VLT, wind will have both a negative effect as it will deform dynamically the surface shape and a positive effect as it will decrease the mirror seeing when the mirror is warmer than ambient air. To analyze this combination we need to parameterize both effects in the same terms. Dynamic deformations due to wind buffeting Combining equations (4.3) and (4.4) the rms slope error of the optical aberration θw is given by the expression D3 θw ' 45.9 ρU 2 3 Et

(6.1)

where U is the mean wind flow speed about 60 cm above the mirror. Inputing the data of the VLT 8.2-m mirror (see page 4-26) at the pressure height of ≈ 2500 m (ρ ' 1) equation (6.1) becomes θw ' 3.877 10−3 U 2

(6.2)

Mirror seeing The mirror seeing FWHM angle θm is parameterized from equations (5.49) and (5.50) as gD 0.3 (6.3) θm = 0.18 ∆T 1.3 T U2 obtaining for the particular case of the VLT mirror and an average temperature T = 10◦ C θm = 0.12 ∆T 1.3 U −0.6 (6.4) For small speed values of (U ≤ 0.2 m/s), approaching the free convection condition, θm is parameterized by equation (5.44): θm = 0.38 ∆T 1.2 The quadratic sum of θm and θw are plotted in fig. 6.3 for different positive mirror-air temperature differences. 6.3.1.2

Guiding errors

The parameterization of guiding errors is largely a control engineering task the details of which are beyond the scope of this report. Briefly, equation (2.24) is

6-10


0.3 Delta_T