Dec 1, 2001 - 1873. Sinusoidally phase-modulated interference microscope for high-speed high-resolution topographic imagery. A. Dubois, L. Vabre, and ...
December 1, 2001 / Vol. 26, No. 23 / OPTICS LETTERS
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Sinusoidally phase-modulated interference microscope for high-speed high-resolution topographic imagery A. Dubois, L. Vabre, and A. C. Boccara Laboratoire d’Optique Physique, Ecole Supérieure de Physique et Chimie Industrielles, Centre National de la Recherche Scientifique, Unité Propre de Recherche A0005, 10 Rue Vauquelin, F-75231 Paris Cedex 5, France
Received July 16, 2001 We describe an interference microscope that produces topographic images with a minimum acquisition time of 20 ms. The system is based on phase-shifting interferometry with sinusoidal phase modulation induced by the oscillation of an interferometric objective (Michelson or Mirau). A CCD camera captures four images per oscillation period to produce a phase map in real time. The system is installed on a commercial microscope. © 2001 Optical Society of America OCIS codes: 180.3170, 180.6900, 120.6650, 120.6660, 120.3940.
Interference microscopy based on phase-shifting interferometry (PSI), associated with large detector arrays and powerful low-cost computers, is a highly effective method for obtaining high-resolution threedimensional topographic images of relatively smooth surfaces.1 – 3 Moreover, it has the advantage of being a noncontact and nondestructive method. However, it is generally limited to the study of static objects in a mechanically stable environment because it entails long measurement times. PSI requires the acquisition of several frames of interferograms for calculation of a phase map.4 Then a topographic image can be obtained after the 2p phase jumps are removed by a process known as phase unwrapping.5 In PSI techniques, the phase is usually shifted step by step between subsequent measurements. When the phase shift is induced by mechanical displacements, inertia limits the operation speed. The phase can also be shifted continuously while the interference signal is being integrated. In this so-called integrating-bucket technique, the phase is usually shifted linearly in a sawtoothlike manner.6,7 Compared with phase stepping, this technique permits faster operation. Achievement of PSI with sinusoidal phase modulation in a Michelson interferometer by making the reference mirror oscillate was proposed.8 Whereas a sawtoothlike oscillation becomes distorted at high frequency, a sinusoidal oscillation remains steady, permitting higher operation speed. However, this technique has seen little development. To the best of our knowledge, it has never been applied to interference microscopy. We have developed an interference microscope based on PSI in which the phase shift is induced by the oscillation of an interferometric objective to create sinusoidal phase modulation. In this Letter we describe the experimental setup and report on the measured performance. Application examples are also shown. The experimental setup is depicted in Fig. 1. It is based on a commercial microscope (from Leica) with an interferometric objective (Michelson or Mirau). The objective is mounted upon a piezoelectric transducer 0146-9592/01/231873-03$15.00/0
(PZT; Model PIFOC P721 from Polytec PI) to make it oscillate at the frequency f 苷 50 Hz. The interference signal can be written as I 共t兲 苷 I¯ 1 A cos关f 1 c sin共2pft 1 u兲兴 ,
(1)
where I¯ is the average intensity, A is the amplitude of the interference fringes, and f is the phase to be measured. The phase is modulated in a sinusoidal manner with period T 苷 1兾f , amplitude c 苷 2.45, and phase u 苷 0.96. The values of parameters c and u are those for which the inf luence of the additive noise is minimized.9 Signal I 共t兲 is integrated successively over the four quarters of modulation period T in a parallel manner by all the pixels of a CCD camera (DALSA CAD1; 256 3 256 pixels, 8 bits) operating at 4f 苷 200 Hz. The four frames obtained are
Fig. 1. Experimental setup. The illumination source is a filtered tungsten halogen lamp. The PZT makes the interferometric objective oscillate. The CCD camera records four images per oscillation period. Phase maps are calculated and displayed in real time. © 2001 Optical Society of America
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OPTICS LETTERS / Vol. 26, No. 23 / December 1, 2001
Ep 苷
Z
pT 兾4
共 p21兲T /4
I 共t兲dt,
p 苷 1, 2, 3, 4 .
(2)
One uses each series of four frames to calculate and produce a phase map in real time, using the following formula9: tan f 苷
E1 2 E2 2 E3 1 E4 . E1 2 E2 1 E3 2 E4
(3)
The PZT oscillation is controlled by an amplif ier – position servo controller by use of an internal sine function at 50 Hz. The peak-to-peak amplitude of the PZT oscillation is adjusted to the optimum value 共c兾2p兲l 苷 0.39l, where l is the optical wavelength. The accuracy of this adjustment is 61 nm. The CCD camera is triggered by another power generator, which delivers a transistor– transistor logic (TTL) signal at 200 Hz. The two generators are synchronized with an adjustable phase to adjust the parameter u to the optimum value of 0.96. This adjustment can be achieved with an accuracy of 60.01 rad. According to Ref. 9, the uncertainties on c and u lead to an uncertainty in height measurements of ⬃l兾800. The microscope uses Köhler illumination with a 100-W dc-supplied quartz tungsten halogen lamp. Interference f ilters are used to reduce the spectral bandwidth of the source to a few nanometers and to center the mean wavelength as desired. With a red filter centered at l 苷 645 nm, the peak-to-peak amplitude of the sinusoidal PZT displacement is 252 nm. One can accumulate the series of four frames before calculating the phase map to improve the signal-to-noise ratio. The phase map is unwrapped by the Goldstein algorithm5 based on the so-called branch-cut technique.5 The relative height prof ile h of the object, which corresponds to the height difference between the surface of the object and the surface of the reference mirror, is related to measured phase f by the formula f 苷 4ph兾lb ,
(4)
where b is a factor that depends on the numerical aperture (NA) of the system, which is equal to 1 for NA 苷 0 and decreases as NA increases.10 – 14 The factor b can be calculated by various approaches.10 – 14 For better precision, we prefer a measurement of the factor b because the actual NA of the objective is not well known.11 Moreover, the effective NA of the system can be modif ied by the aperture’s iris diaphragm opening. We determine factor b for a given microscope objective and a given aperture’s diaphragm iris opening by measuring the actual fringe spacing, which is lb兾2. The interference signal’s intensity is recorded on 5 pixels (at the four corners and in the center of the CCD array) by scanning a mirror through focus with the high-resolution PZT. The resultant plots, which consist of interference fringes, are then interpolated, and the average fringe spacing is calculated. Then we average the values obtained at the f ive points of
the image. The effective fringe spacing is measured with an accuracy better than 1 nm. When we take into account the effect of the NA and the uncertainties on the modulation parameters, the absolute accuracy for height calculations from Eq. (4) is ⬃1 nm. We verified this degree of accuracy by measuring the height of a calibrated step (VLSI standards). By taking a large number of independent measurements of this step height (modulation parameters and focus readjusted each time) we estimated their repeatability to be of the order of 1 nm. The measured height prof iles correspond to the difference between the object and the reference surfaces. To determine the surface prof ile of the object accurately requires that the reference surface be sufficiently f lat and smooth. Otherwise, the reference surface prof ile must be measured and subtracted. This measurement can be done with an ultrasmooth mirror. Another technique involves averaging a number of measurements of a smooth mirror.15 Between subsequent measurements, the mirror is moved by a distance greater than the correlation length of the surface. The generated reference surface prof ile can then be subtracted from subsequent measurements such that the measurements will not contain errors caused by the reference surface.15 All the calculations are carried out with an 800-MHz Pentium III computer with a Visual C++ compiled interface to control the image acquisition, display the phase map in real time, and unwrap it. Threedimensional images of reliefs are produced by Matlab software. A topographic image of a 500 mm 3 500 mm region on the surface of a mask for manufacture of integrated circuits is shown in Fig. 2. To illustrate the acquisition speed of our system, we reconstructed the surface topography of a moving object as a function of time. We placed an oil drop upon a f lat mount and acquired images of the surface as the drop spread. The results are presented in Fig. 3. We measured the noise by taking the difference of two phase maps acquired successively. The standard deviation of this difference yields the rms total noise. At the maximal frequency of 50 Hz, the noise was ⬃230 pm. As expected, accumulating several frames reduced the noise. At 1 Hz (50 frame series accumulated), a noise level of ⬃34 pm was
Fig. 2. Topographic image of a mask for the manufacture of integrated circuits with a 103, 0.3-NA Mirau objective (Nikon). Field of view, 500 mm 3 500 mm. Average height of the structures, 70 nm.
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where g is the fringe contrast, k is the number of accumulated images, and N is the average well-charge storage of the CCD pixels. With N 苷 100, 000 and g 苷 0.7 (according to measurements), the theory accords with the experiments for exposure times that are typically ,1 s. For longer exposure times, the experimental results deviate from the shot-noise limit because of instabilities from diverse sources (mechanical vibrations, thermal drifts, etc.) that begins to occur. Smoothing the images with a Sobel f ilter can reduce the noise by a factor of 2 without significant loss of lateral resolution. The surface topography of a polished silicon wafer is shown in Fig. 4. With a 1-s acquisition time, the noise is not visible. In conclusion, we have developed an interference microscope that is capable of producing topographic images with a minimum acquisition time of 20 ms. The surfaces of moving objects can be reconstructed. No special care for stability of the environment is required. Reliefs of a few tens of picometers in height can be detected. The system can easily be installed on a commercial microscope. Using a faster camera could even shorten the acquisition time. Operation was demonstrated with an 800-Hz camera (pixel number reduced to 128 3 128), which resulted in an acquisition time for a phase map of 5 ms. A. Dubois’s e-mail address is dubois@optique. espci.fr. Fig. 3. Phase maps from the surface of a spreading oil drop. Time between successive images, 100 ms; acquisition time for each image, 20 ms; field of view, 500 mm 3 500 mm.
Fig. 4. Topographic image of a polished silicon wafer (103, 0.3-NA Mirau objective; Nikon). Field of view, 500 mm 3 500 mm.
reached. Assuming that the system is purely limited by the shot noise, the rms noise Dz is approximately given by9 Dz 0.08 , 苷 p l g kN
(5)
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