XIPE optical module redefinition for a 4 m focal length

XIPE optical module redefinition for a 4 m focal length

INAF/OAB technical report 06/2015

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Issued by D. Spiga (INAF/OAB) Reviewed by G. Tagliaferri (INAF/OAB), P. Soffitta, E. Costa, S. Fabiani (INAF/IAPS)

Istituto Nazionale di Astrofisica (INAF) Via del Parco Mellini, 00100 Roma, Italy Osservatorio Astronomico di Brera (OAB) Via Brera 28, 20121 Milano, Italy Via E. Bianchi 46, 23807 Merate, Italy



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Contents 1. Scope of the document ................................................................................................3 2. New optical design: 30 shells, f = 4 m ........................................................................4 3. Performance verification and conclusions ................................................................5 3.1. Effective area .......................................................................................................... 5 3.2. Angular resolution ................................................................................................... 8 3.3. Conclusions ............................................................................................................ 9

Reference Documents [RD1]. Soffitta, P., Barcons, X., Bellazzini, R., et al, XIPE: the X-ray imaging polarimetry explorer, Experimental Astronomy, Vol. 36, Issue 3, pp.523-567 (2013) [RD2]. Spiga, D., Tagliaferri, G., Costa, E., Soffitta, P., Muleri, F., “Mirror module design for the XIPE Xray polarimeter”, INAF/OAB internal report 10/2014 [RD3]. Soffitta, P. et al., XIPE: the X-ray imaging polarimetry explorer, Call for a Medium-size mission opportunity in ESA‟s Science Programme for a launch in 2025 (M4) [RD4]. Spiga, D., Cotroneo, V., Basso, S., et al. Analytical computation of the off-axis effective area of grazing incidence X-ray mirrors, Astronomy and Astrophysics, Vol. 505, Issue 1, pp.373-384 (2009) [RD5]. Spiga, D., Optics for X-ray telescopes: analytical treatment of the off-axis effective area of mirrors in optical modules, Astronomy & Astrophysics, Vol. 529, id. A18 (2011) [RD6]. Fabiani, S., E. Costa, Del Monte, E., et al., The imaging properties of the Gas Pixel Detector as a focal plane polarimeter, ApJ Suppl. Series 212:25 (2014)

Acronyms EA FOV HEW IAPS INAF IP MLT MS OAB SXM XRR VF XIPE

Effective Area Field Of View Half-Energy Width Istituto di Astrofisica e Planetologia Spaziali/ Institute for Spatial Astrophysics and Planetology Istituto Nazionale di AstroFisica / Italian Institute for Astrophysics Intersection Plane Media-Lario Technologies Mirror Shell Osservatorio Astronomico di Brera / Brera Astronomical Observatory Soft X-ray Module X-ray Reflectivity Vignetting Function X-ray Imaging Polarimetry Explorer



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1. Scope of the document This brief note reports the reviewed design of the XIPE X-ray telescope optical module [RD1], initially conceived at INAF-OAB in collaboration with INAF-IAPS with a 3500 mm focal length and a maximum shell diameter at the IP of 380 mm. The SXT mirror module was meant to cover the soft X-ray band with an angular resolution of 20 arcsec HEW or better. Owing to the mirror size at play, the optical module design was based on the well-consolidated technique of Nickel electroforming, which is known to have the capabilities to reach this figure accuracy (such as for JET-X and XMM). The results were reported in detail in [RD2], showing that the requested effective area (larger than 300 cm2 at 3 keV) can be easily reached. The design was also included in the XIPE telescope proposed to ESA for the M4 call [RD3], and as of today pre-selected for a further assessment in view of the final selection in 2016. In this document, we modify the design of the XIPE optical module to increase the effective area in three ways: 1) increasing the focal length to 4 m: this entails a reflectivity improvement on the side of high energies, but it also reduces the single mirror cross-section, hence this sole change is insufficient; a possibility is however to re-modulate the diameters of the shells to improve the density of the nesting, keeping the same unobstructed field of view. This mitigates the geometric area reduction, while it improves the reflectivity at high energies. 2) increase of the shell number from 27 to 30, adding 2 more shells on the side of the outer diameters and one on the small diameter side. This is made possible by the large margins left on the mirror module mass (40 kg for the 3500 mm design vs. 100 kg allowed). 3) a combination of the 2 point above. This is the approach we adopt in Sect. 2. Even if in [RD2] we also designed a HXT, we hereafter limit ourselves to the SXT case, since it is the only one that was included in the proposal submitted to ESA. In Sect. 2 we expose the new optical design, studied following the same guidelines used for the 3500 mm focal length case, and we check the optical performances. In Sect. 3 we check the performances of the 4000 mm focal length configuration with 30 shells.



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2. New optical design: 30 shells, f = 4 m Excepting the focal length and the number of mirror shells, the optical design has been performed keeping exactly the same parameters adopted in the 3500 mm focal length one (thickness/radius ratio of 1.7×10-3, 10 arcmin diam. unobstructed FOV, 300 mm+300 mm mirror length, 10% structure vignetting, see [RD1]) and still assuming a 30% additional mass for the supporting structure (spider and case). Using the usual formulae to populate the mirror module with nested shells [RD4],[RD5], we obtain the diameters listed in Tab. 1. The new shells are highlighted in red. number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

φ max(mm) 407.49 397.75 388.21 378.88 369.76 360.83 352.09 343.54 335.18 326.99 318.98 311.15 303.48 295.98 288.65 281.47 274.44 267.57 260.85 254.27 247.83 241.53 235.37 229.34 223.44 217.65 211.98 206.42 200.97 195.62

φ med (mm) 400.00 390.43 381.07 371.92 362.96 354.19 345.62 337.23 329.01 320.98 313.12 305.43 297.90 290.54 283.34 276.29 269.39 262.65 256.05 249.59 243.27 237.09 231.04 225.12 219.32 213.64 208.08 202.62 197.27 192.03

φ min(mm) 377.51 368.48 359.65 351.01 342.55 334.28 326.18 318.26 310.51 302.93 295.51 288.25 281.15 274.20 267.40 260.75 254.25 247.88 241.65 235.56 229.59 223.76 218.05 212.46 206.99 201.63 196.38 191.23 186.18 181.23

τ (mm) 0.350 0.341 0.333 0.325 0.317 0.310 0.302 0.295 0.288 0.281 0.274 0.267 0.261 0.254 0.248 0.242 0.236 0.230 0.224 0.218 0.213 0.207 0.202 0.200 0.200 0.200 0.200 0.200 0.200 0.200

α 0 (arcmin) 42.94 41.91 40.91 39.93 38.97 38.03 37.11 36.21 35.33 34.46 33.62 32.80 31.99 31.20 30.43 29.67 28.93 28.21 27.50 26.80 26.13 25.46 24.81 24.18 23.56 22.95 22.35 21.76 21.19 20.63

Ageom (cm2) 42.78 40.75 38.83 36.98 35.23 33.55 31.94 30.41 28.95 27.55 26.22 24.95 23.73 22.58 21.47 20.42 19.41 18.45 17.54 16.66 15.83 15.04 14.28 13.56 12.87 12.21 11.58 10.98 10.41 9.86

mass (kg) 2.348 2.237 2.132 2.030 1.934 1.842 1.753 1.669 1.589 1.512 1.439 1.369 1.302 1.239 1.178 1.121 1.065 1.013 0.962 0.914 0.869 0.825 0.784 0.755 0.736 0.717 0.698 0.680 0.662 0.644

Tab. 1: characteristic parameters of the shells of the non-obstructed XIPE optical module with a 4 m focal length. The geometric area values are already reduced by 10% because of spider vignetting.



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3. Performance verification and conclusions 3.1.

Effective area

We have checked the effective area performances of the new design in two ways, the same adopted in [RD2]. One is the numerical integration of the equations reported in [RD4], [RD5], which assume a simple double-cone profile. This method has the advantage of not being affected by statistics problems, but is still very accurate for mirror shells with small ratios L/f. With a 3.5 m focal length and a 600 mm total shell length, the effect of the Wolter-I profile on the effective area are discussed in detail in [RD2], and turn out to be very small (in the order of 1%-2%). Increasing the focal length to 4 m (keeping the mirror length constant) actually mitigates the even small effects of departure from the Wolter-I profile in the adopted model.

Fig. 1: ray-tracing model, mirror module aperture. The ray origin positions are traced with different colours, assuming a source at infinity and (left) 5 arcmin off-axis or (right) 20 arcmin off-axis. Red locations correspond to rays reflected twice and focused. In green we have marked the regions where single reflections on the parabolae occur and exit the module as stray-light. Locations where single reflections on the hyperbolae occur and are obstructed at the exit are displayed in light blue. Yellow points denote positions where doubly reflected rays are obstructed on the backside of the hyperbolae. Only a very few rays (dim blue) exit after having a single reflection on the hyperbola.

We have anyway re-checked the correctness of the conclusions by running a ray-tracing routine on a 30-mirror Wolter-I module (Fig. 1). In order to reach a sufficient accuracy, 106 had to be launched, simulating the reflection on the surfaces and accounting for all possible ray obstructions. Using either method, we have computed the effective area in the 0.1-10 X-ray band assuming an equivalent mirror roughness of 4 Å and a reflective coating of a) a 30 nm thick layer of Iridium or b) a 30 nm Ir + 10 nm of amorphous Carbon. The results for the two kinds of coating are shown in Fig. 2 (left). As already noticed for the 3.5 m focal length design, the Ir+C design enables a much higher response in the vicinities of the target energy of 3 keV. In addition, the new design allows us reaching an on-axis effective area of 550 cm2 per single module at 3 keV. At the same energy, and



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off-axis by 5 arcmin, the effective area is of almost 500 cm2. In Fig. 2 (right) we also compare the results with the expectations from the previous design. The improvement is apparent. The analytically computed effective area trend is also confirmed by the outcomes of the detailed raytracing (Fig. 2, dots), on- and off-axis.

Fig. 2: new design: effective area for pure Ir and Ir+C coatings. The accuracy of the analytical computation is confirmed by the outcomes of the ray-tracing.

Fig. 3: the on-axis effective area achieved by modifying the baseline design. Increasing the focal length, remodulating the diameters and adding 3 shells entails a relevant effective area increase with a total mass increase of only 9 kg with respect to the baseline design.



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In Fig. 3 we show the effective area changes introduced by the individual changes in the design. We clearly see that bringing the focal length from 3.5 m to 4 m, after re-modulating the mirror diameters (which allows us to slightly increase them), enhances the effective area above 2.5 keV. The high-energy response is clearly enhanced by the focal length extended to 4 m. In order to obtain a significant improvement of effective area below 2.5 keV, however, we need to include 3 additional shells in the design (2 of them on the outer diameter side). We have finally compared the off-axis vignetting function of the module at 3 keV and 6 keV for the old and the new design. The calculation was performed analytically as described in [RD2] and [RD5], and the result is displayed in Fig. 4. We note that the design with a 4 m focal length has at 3 keV a higher effective area on-axis, but is slightly more affected by the off-axis vignetting. The vignetting function computed at 6 keV, in contrast (Fig. 5), shows better performances for a focal length of 4 m, using both solutions with 30 or 27 shells, as a result of the shallower incidence angles and the extended reflectivity bandwidth.

Fig. 4: the effective area of the 4 m focal length module at 3 keV, as a function of the off-axis angle.

Fig. 5: the effective area of the 4 m focal length module at 6 keV, as a function of the off-axis angle.



3.2.

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Angular resolution

We have also simulated the angular resolution expected from the XIPE optical module with 30 shells and a 4 m focal length. We have considered the cases of a perfect optic and of a mirror module with a 20 arcsec HEW, on-axis and 5 arcmin off-axis. The ray-tracing simulations in the 0.1- 10 keV band are shown in Fig. 6: we have also considered the degradation introduced by the GPD caused by the inclined penetration of rays, which may interact within 1 cm of range throughout the gas cell. In line with the tests performed at PANTER [RD6], most of the imaging resolution degradation is caused by mirror imperfections. The effect of the GPD thickness is also visible, but only to a minor extent: it amounts to only 9 arcsec, in agreement with the formula HEWincl = 2 !

5mm ! tan(4 ! 0.5deg) = 9arcsec 2 ! 4000mm

where 0.5 deg is the average incidence angle on the shells and 5 mm is the half-thickness of the GPD. The factor of 2 in the denominator arises from the half-power specification and the same factor in the numerator accounts for the diameter.

Fig. 6: simulated in-focus images on the XIPE focal plane, 4 m focal length, 30 shell mirror module. (upper line) from perfect optic: (left) on a CCD, on-axis, HEW = 0 arcsec. (center) on the GPD, onaxis, HEW = 9 arcsec (right), on the GPD, 5 arcmin off-axis, HEW = 9.2 arcsec. (bottom line) from a 20 arcsec HEW optic: (left) on a CCD, on-axis, HEW = 20 arcsec. (center) on the GPD, on-axis, HEW =22 arcsec (right), on the GPD, 5 arcmin off-axis, HEW = 22 arcsec.



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The off-axis aberration is negligible up to a 5 arcmin off-axis angle, completely flooded by the PSF related to profile errors and roughness of the reflecting surfaces. We note that the GPD HEW and the one from the optics add up in quadrature to a very good approximation. 3.3.

Conclusions

In this document we have computed an alternative design for the XIPE optical module, bringing the focal length to 4 m and adding some shells to increase the on-axis effective area to 550 cm2 at 3 keV. We have shown that this can be done at the cost of adding only 9 kg of module mass, including the structures. As a consequence of the smaller incidence angles, the field of view at 3 keV is a bit smaller than in the design with a 3500 mm focal length, but still much larger than 10 arcmin. At 6 keV, the field of view is larger for the 4 m design, regardless of whether 27 or 30 shells are used. For the 27 shell design, for example, the computed grasp at 6 keV for a focal length of 3.5 m is 45.6 cm2 deg2 versus a 55.7 cm2 deg2 for the 4 m design.