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The modification of classical Twyman-Green interferometer by implementation of Liquid Crystal on Silicon (LCoS) spatial light modulator as the reference mirror allows introducing arbitrary phase in the reference wavefront. This special capability is applied to facilitate the measurements of shape and deformation of active microelements and extend the range of such measurement. This can be realized by introducing linear or circular spatial carrier frequency into interferogram or by compensating object wavefront deformation. Moreover LCoS display can be used as an accurate phase shifter if the proper calibration is introduced. The analysis of sources of measurement errors introduced by LCoS display is presented and the ways of their elimination are discussed. The possible application of LCoS based laser interferometer for initial microelement shape determination and transient deformation monitoring as well as active reference phase modification are shown and experimentally confirmed during silicon micromembranes studies.
©2006 Optical Society of America
1. Introduction
Micro-Electro-Mechanical Systems are nowadays frequently used in many fields of industry. The number of their applications increases and their functions became more and more responsible. Therefore precise knowledge about their static (shape, deformations, stresses) and dynamic (resonance frequencies, amplitude and phase of vibration) properties is necessary. Due to its fragility and small sizes non-contact and high sensitive measurement method is required. Two-beam laser interferometry is one of the most popular testing methods of microelements and Twyman-Green interferometer is the most frequent configuration for full-field shape determination and out-of-plane displacement measurement [1,2]. However the elements under test may bring additional challenges: their surfaces may have complicated shape and large shape gradients which restricts their testing by means of interferometer with flat reference mirror.
Table 1. The list of measurement problems and their possible solutions by means of LCoS SLM as an active reference mirror
Active wavefront correction in interferometry has been used for several years but it is still not common. Deformable mirror [3], liquid crystal matrix [4–6] or DMD [7] are reported as the useful devices for wavefront shaping, most often for measurement of relatively big elements (in the order of a few centimetres). However the increasing number of microelements with a complex shapes and functionalities also require active approach to their interferometric characterization and testing [8].
The aim of this work is to show great benefits given by using phase Liquid Crystal on Silicon (LCoS) Spatial Light Modulator (SLM) [9] as a reference element in Twyman-Green interferometer applied to MEMS/MOEMS elements studies [10]. LCoS display can work as an active mirror, which changes phase of reflected light according to the measurement requirements. Therefore it is possible to obtain extended measurement range and simplify some examinations through object wavefront compensation. Also LCoS SLM can work simultaneously as a phase shifter replacing PZT transducers used at present. Advantages and disadvantages of such ideas are discussed in this paper at the example of silicon micromembranes measurement.
The most common problems that are found during measurements by means of Twyman-Green interferometer and are considered to be solved using LCoS device as a reference mirror are listed in Table 1.
In the paper after presenting the system proposed (Section 2), the methods of its calibration (Section 3), the features of the investigated objects (Section 4) and general measurement methodology (Section 5) we provide several examples of successful implementation in measurements of static and vibrating silicon micromembranes (Section 6).
2. Measurement setup
The scheme of measurement platform is presented in Fig. 1. The main optical module consists of Twyman-Green interferometer and long working distance microscope (LDM). The interferometer is formed with a beam-splitter cube and exchangeable reference element (R). This element may be a mirror placed at piezoelectric transducer (to introduce phase shift in interferograms), or LCoS display. Depending on the reference element (R) used the system may work as:
• conventional two-beam interferometer (R: mirror) [8];
• active two-beam interferometer (R: LCoS display).
Fig. 1. Scheme of the interferometric platform: a) overall scheme of the system, b) scheme of the reference arm when LCoS display is used, c) mutual relationship between LCoS SLM active area and size/location of the reference beam; A, B – reference and object beams respectively
Beam expander should be placed into the reference arm of the interferometer when LCoS display is used (see Fig. 1(b)). It is applied to increase dimension of the reference beam and to image LCoS SLM surface in the object plane of the microscope. This is necessary to adjust size of the LCoS SLM active area (15×20 mm2) and size of its pixel (19 µm) to the field of view of the microscope and to CCD camera resolution. Simply, the size of LCoS matrix is too big in comparison with the field of view of the microscope and phase modification of the reference beam with high spatial resolution (comparable to CCD’s resolution) would not be possible without using additional optics. The beam expander applied has 15x magnification what allows using approximately 75% of LCoS SLM active area (Fig. 1(c)) when field-of-view of the microscope (LDM) equals 0.8 mm×1 mm.
Laser diode (λ=665 nm) or He-Ne laser (λ=632 nm) are used interchangeably as a light source. The laser diode can work in pulse mode with frequency up to 5 MHz (square signal). He-Ne laser, which coherence length is large (approx. 800 mm), is employed when LCoS display serves as a reference element. It is necessary in order to assure high contrast of the interference fringes in the presence of significant optical paths difference, caused by the presence of beam expander, in the interferometer.
An active microelement under test (e.g. silicon micromembrane or micromirror) may be loaded by voltage signal (optionally amplified) supplied from the generator. The other signal generator strobes the laser when stroboscopic interferometry is used. The computer with special software is utilized for interferogram processing and controlling of PZT and SLM elements.
Main technical parameters of the system are listed in table 2.
Table 2. Main technical parameters of the system
3. LCoS element and its calibration in the system
Spatial light modulator used in our system is an electrically addressed, reflective, phase modulator produced by Hana Microdisplay Technologies Inc. [11,12]. The control of the spatial light modulator is very similar to liquid crystal display; an XVGA static image or video signal is generated by computer and directly input to the LCoS display driver. 2-D phase information can be directly written to the phase-only device, at high accuracy with video speed. Wavefront modifications are obtained by introducing to the LCoS SLM driver Phase Correction Maps (PCM: 8 bit, grey-level bitmaps) representing computer generated or experimentally determined phase distribution in the form of phase modulo 2π. The amount of phase shift depends on the grey level in a given pixel of such map and the light wavelength applied in the system. Most often Phase Correction Maps are created on the basis of phase maps calculated from interferograms (see Section 5) which are delivered also as mod 2π maps. This allows creating PCM in a very simple way without necessity to perform any, time consuming phase unwrapping procedure.
The basic parameters of LCoS display used in our experiment are given in Table 3. It has high resolution and relatively small pixel size, as well as the ability to correct 1 wave magnitude with at least 8 pixels without loosing much efficiency. It means that using whole aperture of SLM, the device is capable of introducing up to 128 fringes of tilt and approximately 30 fringes of spherical wavefront peak-to-valley at high efficiency.
Table 3. Device specification for phase only LCoS SLM [12]
The performance of LCoS SLM in an interferometric system depends on:
• flatness of the SLM reflective surface;
• influence of flyback regions [13];
• proper calibration.
The reflective surface of the LCoS display is not flat. This is significant disadvantage in the case when such element is used as a reference surface in an interferometric system. Moreover the beam expander (see Fig. 1(b)) aberrations also affect wavefront shape of the reference beam. These two wavefront deformations add each other in the output of reference interferometric channel. The final systematic error introduced by both sources is shown in Fig. 2(b). To measure it, the certified mirror (flatness=λ/20) was used in object channel of the interferometer. This error may be actively corrected through introducing by LCoS SLM the Phase Correction Map (PCM) created on the basis of the measured wavefront deformation.
Fig. 2. The measured wavefront deformation of the reference beam caused by nonflatness of the LCoS SLM surface and aberrations of the beam expander: a) interferogram, b) wavefront shape
The other specific feature of LCoS device is that molecules of liquid crystal in neighbouring pixels cannot have drastically different orientation what means that violent phase change between next pixels of LCoS display is impossible. There are intermediate regions (so called: flyback regions, see Fig. 3) between neighbouring pixels and size of these regions depends on the value of phase difference introduced in the neighbouring pixels [13]. The biggest intermediate region occurs on the border of phase jump 0–2π. The width of such region may have the size of a few pixels which can significantly disturb the interferogram and consequently the phase values [14].
The use of LCoS SLM for proper phase correction of the reference beam in the interferometer is possible when we know the calibration curve of this element given by the relation between grey level in PCM and phase retardation introduced by SLM. Such relation is called Electro-Optical (E-O) characteristic. To determine such a characteristic a calibration process is necessary. In order to simplify calibration process we decided to perform it directly at the measurement setup (Twyman-Green interferometer). The process is controlled by the specially written software and it is performed in the following steps:
• flat specimen (i.e. mirror) is put in the object arm of the interferometer and it is tilted in order to introduce the linear, spatial carrier frequency into the interferogram;
• the program generates uniform bitmaps (PCMs), corresponding to the constant phase shift steps equal π/2, and sends them to LCoS display;
• for each PCM the intensity profile in the interferograms along certain, selected by the user, direction perpendicular to the interference fringes is registered;
• sine function (equation: A+B • sin(C • x+D)) is fitted to each profile and a set of initial mod 2π phase values (D) of sine is determined;
• unwrapping procedure creates smooth O-E characteristic of the SLM.
Total procedure lasts approximately 10 seconds. As the interferometer is very sensitive to air flows and vibration, small noise may be visible in the determined characteristic. Therefore several characteristics are registered (10 in our case) and the averaged values are used to create the final calibration curve. Such a relation obtained for He-Ne laser (λ=632.8 nm) is presented in Fig. 4.
The determined characteristic is strongly nonlinear and for grey levels above 170 no phase change occurs. The range of phase delay (for λ=632.8 nm) equals 4π. However for the lowest grey levels (from 0 to approx. 10) the contrast of observed interference fringes is significantly lower than for other part of the characteristic; therefore we decided to work within the range 10 ÷ 170 grey levels marked in Fig. 4 as the useful range. It reduces the working range of LCoS SLM but allows avoiding errors in the reconstructed phase maps caused by variable fringe contrast. We also analysed the spatial nonuniformity of phase shift introduced by LCoS display pixels. The simple analysis relied on introduction of uniform PCM equivalent to 2π phase shift (according to E-O characteristic) to the half of LCoS display domain. If the interferometric fringes along border between the two halves were continuous and the phase calculated did not suffer any phase jump we concluded that the spatial uniformity of phase shift introduced by SLM was acceptable. Those trials have been performed in horizontal and vertical directions of the LCoS matrix domain and we concluded that the nonuniformity is neglectable.
To check the correctness and accuracy of the calibration we have studied the LCoS SLM ability to work as the phase shifter for the interferogram analysis by the temporal phase shifting method. The lattice-site representation (L-SR) of phase shift angle histogram has been used. This method is precisely described in [15]. We have applied it for evaluation of the output accuracy of 5 frames (5f) algorithm (with π/2 phase shift) which is most often used in further interferogram analysis. In such a case the L-SR requires five, mutually phase shifted interferograms for creating histogram and its analysis allows assessing not only phase shift exactness but also linearity of the fringe detection i.e. departure of the interference pattern from a sinusoid. For the ideal experiment conditions and constant π/2 phase shift the straight horizontal segment passing through the origin should be visible in the histogram. The histogram calculated from the interferograms obtained by phase shifting introduced by LCoS SLM is presented in Fig. 5. It shows that the approximate phase shift realized by SLM is 92 ± 2 degrees instead 90 degrees. On the basis of this histogram we conclude that LCoS display is able to realize phase shifts accurately enough to be compensated by 5-frame TPS algorithm. It also indicates that the PCMs are obtained with the accuracy of a few degrees. Significant width of the segment is the result of considerable noise in the interferograms which is caused by speckle, parasitic fringes and local imperfections of the SLM. Besides of this it may be concluded that the interferogram detection is linear or small second order nonlinearity occurs.
Fig. 5. Lattice-site representation of phase shift angle histogram calculated from 5 interferograms mutually phase shifted by π/2 (expected value of the phase shift)
4. Objects under test
The measured object was fabricated by THALES Research & Technology and Institute FEMTO-ST Université de Franche-Comté within EU project OCMMM [16]. These are silicon micromembranes with dimensions 0.45×0.45 mm2 and 1.35×1.35 mm2 (Fig. 6). Due to the technological process, which includes introducing PZT layer at the top of microelement, the membrane suffers a concave departure from the flat shape. Additionally in the smaller membrane a waveguide channel had been introduced.
The exemplary interferograms of 0.45×0.45 mm2 and 1.35×1.35 mm2 micromembranes are shown in Fig. 7. The first membrane (Fig. 7(a)) has just a few fringes and it will be used in our experiment for measurement of out-of-plane displacement due to electric load. The bigger membrane introduces very dense fringes (Fig. 7(b)) due to high shape gradients and it is clearly seen that testing that membrane, even in static conditions, at any conventional interferometric stand may be complicated. Therefore this object will be used to show the possibility to expand the measurement range in the Twyman-Green interferometer with LCoS SLM.
Fig. 6. The schematic views (a) and photograph (b) of the micromembrane (0.45×0.45 mm2 with PZT layer [2,16]
5. Description of general methodology
Selected examples of the applicability of LCoS SLM for active silicon micromembranes testing are presented and discussed below. LCoS display has been fulfilling several tasks during the measurements including:
• phase shifter for Temporal Phase Shifting (TPS) interferogram analysis method;
• object’s shape compensator/corrector;
• required reference phase generator.
In the case when LCOS is not used for the reference wavefront shape change but for phase shift of an interferogram only, the best way to introduce the phase shift is to supply a set of uniform grey level maps (3, 4 or 5 maps depending on TPS algorithm used) corresponding to a phase change equalled π/2 according to the LCoS device O-E characteristic (Fig. 4). When LCoS SLM is supposed to act as a phase shifter and phase corrector simultaneously there are two approaches to shift the phase of an interferogram:
I. a set of uniform grey level maps described above is simply added to PCM used for wavefront shaping and then such a set of PCMs is supplied to LCoS display;
II. a set of PCMs is created on the basis of mod 2π phase map used for wavefront shaping by shifting phase fringes in such a map sequentially by i·π/2 (i=0, 1, 2, 3, 4).
First method requires LCoS SLM to have range of phase change equalled at least 3π (in order to use 3-frame TPS method) or 4π (for 5-frame TPS). This is because PCM for wavefront shaping utilizes 2π of the SLM phase range and at least 2 phase shifts by π/2 have to be performed. In our case phase change that LCoS display may introduce equals ~3π (see Fig. 4) therefore 3-frame TPS method of fringe pattern analysis may be used only. This may result in lower (in comparison with 4 phase steps (5-frames) TPS method) accuracy if the SLM calibration is not exact.
Fig. 8. Block diagrams of the measurement procedures using LCoS SLM and applied to determination of different physical values characterizing an object under test.
The second approach does not require LCoS SLM phase range bigger than this necessary for PCM i.e. 2π, independently of the number of phase shifts. Therefore the 5-frame TPS method can be used and some errors caused by phase shift inaccuracy are corrected. However the shift of phase fringes means that flyback regions are shifted also and it introduces additional errors into the interferograms and fringe pattern processing.
Besides performing interferogram phase shift, linear or circular spatial carrier frequency fringes may be also easily introduced to the interferogram through using LCoS display. This capability is applied when the Fourier Transform Method (FTM) of interferograms analysis is used.
Depending on the features of microelement under test and the physical value that should be determined different measurement procedure ought to be used. Some of them require additional calculation or measurements to be performed at first. The block diagrams of the procedures used in the studies reported in Section 6 are presented in Fig. 8.
6. Results of experiments
To confirm functionality of the system several tests have been performed. The exemplary experimental results are presented and discussed below.
6.1 Static shape determination
In order to determine accurately the shape of an object under test we have to get rid of the significant systematic error brought into the reference beam by LCoS SLM and beam expander imperfections (Fig. 2). The wavefront is corrected by introducing onto SLM the PCM calculated from the interferogram obtained in Twyman-Green arrangement with a reference flat mirror placed in the object arm of the interferometer. The exemplary mod (2π) PCM map used for wavefront correction is shown in Fig. 9(a). The proof-of-principle experiment was performed at 0.45 mm×0.45 mm micromembrane (Fig. 6). At first its shape was calculated by 5-frame TPS method from an interferogram without correction (Fig. 9(c)). Next the proper PCM was introduced at LCoS display, the modified interferogram was obtained and the phase (correct shape of micromembrane) was calculated (Fig. 9(e)).
To estimate accuracy of such measurement the result was compared with the one obtained in the optimized conditions i.e. for the case of flat reference mirror shifted by linear PZT transducer and using 5-frame TPS algorithm. The difference between these two results interpreted as the measurement uncertainty obtained in active interferometer is shown in Fig. 9(f). The biggest errors are caused by flyback regions and occur in the areas where phase of the interferogram changes rapidly. It refers to the edges of the layers deposited onto the membrane and places corresponding with phase “jumps” in PCM. However the overall accuracy of the shape measurement is high with RMS=16 nm.
Fig. 9. Interferograms and results obtained during micromembrane shape determination: a) one of three PCM for systematic error correction, b) initial interferogram, c) shape of the membrane with systematic error, d) corrected interferogram, e) shape of the membrane after correction, f) difference between height maps obtained in setups using alternatively a flat mirror and LCoS SLM as a reference element
The uncertainty we have determined by using the second method of phase shift (see Section 5) and 5-frame TPS was a little worse (RMS bigger by approx. 2 nm) than using first method and 3-frame TPS. This fact confirms good calibration of LCoS SLM, as 3 frame algorithm requires the very accurate phase shifts.
6.2 Out-of-plane displacement measurement
One of the most important advantages of using LCoS SLM as a reference element is the ability to measure directly out-of-plane deformation of an element under test. After phase correction performed by SLM in order to remove interference fringes from the interferogram of a specimen in initial state, out-of-plane deformation of this specimen may be directly measured on the basis of interference fringes that will appear in the interferogram. Interferograms and results of such experiment are presented in Fig. 10. On the basis of mod 2π phase map (calculated using 5-frame TPS algorithm) of the initial interferograms of unloaded 0.45×0.45 mm2 membrane a set of PCMs is created (one of such PCM is shown in Fig. 10(b)). Supplying such PCMs to the LCoS display when the object is loaded a set of phase shifted interferograms (for TPS algorithm) is obtained (Fig. 10(d)) and the out-of-plane deformation is calculated directly from them (Fig. 10(e)). In our experiment membrane was loaded by constant voltage equalled 35V.
Fig. 10. Interferograms and results obtained during micromembrane out-of-plane deformation measurement: a) initial interferogram, b) PCM for the phase of the object beam and systematic error compensation, c) corrected interferogram of unloaded and d) loaded membrane, e) calculated out-of-plane deformation
To enable phase calculation using FFT method the linear, mathematically designed spatial carrier frequency may be introduced into the interferogram. In such a case only one interferogram is required for a specimen height map measurement so this algorithm is more convenient for dynamic or instable object testing. Results of such trial are presented in Fig. 11. In our experiment the PCM applied included the sum of the phases due to spatial carrier frequency, systematic error of interferometer with LCoS SLM and the specimen initial shape. This PCM, supplied to LCoS display, is presented in Fig. 11(b). The effect of introducing this PCM into T-G interferometer is clearly seen in Fig. 11(c) at which the linear fringes are visible. The fringes and phase representing out-of-plane displacement of micromembrane due to the loading by constant voltage equalled 35V are given in Fig. 11(d) and 11(e). Visible edges of the layers deposited onto the membrane slightly disturb the interference pattern what is a source of some errors in calculated displacement. Also using FFT method which includes heavy filtering in frequency domain we may loose the detailed information about the steps or local high gradients in the object.
Fig. 11. Interferograms and results obtained during micromembrane out-of-plane deformation measurement using interferograms with linear spatial frequency: a) initial interferogram, b) PCM with the phase of the object beam, systematic phase error compensation and mathematically added linear phase (2πf0x), c) corrected interferogram of unloaded and d) loaded membrane with f0, e) calculated out-of-plane deformation
The difference between maximum values of the deformation (measured as the difference in height between corner of the membrane and centre of it) calculated using TPS and FFT methods (compare Fig. 10(e) and 11(e)) equals approximately 80 nm. Such a significant discrepancy between the results may be caused by the measurement uncertainty (±35 nm) and by hysteresis of the PZT layer.
6.3 Shape determination using circular, spatial carrier frequency technique
Some microelements have so complicated shape that introduction of linear, spatial frequency into their interferogram does not give the expected results (the fringes are closed or too dense for the camera). If then TPS algorithm cannot be used for any reason (unstable element; no phase shifter) the only solution may be introduction of circular spatial carrier frequency. Such procedure can be easily performed using LCoS SLM as a reference element in the interferometer. Conical wavefront needed can be created by mathematically designed PCM supplied to the SLM. Phase calculation of the interferogram with circular spatial frequency can be made using Coordinate Transform FFT or Direct Filtering FFT [17] methods. Because circular carrier is mathematically designed it is easy to subtract it from the calculated phase of the interferogram and to obtain proper height map of the specimen. The results of such procedure performed for 0.45×0.45 mm2 silicon micromembrane using Coordinate Transform FFT method are shown in Fig. 12.
Similarly as in Section 6.1 the accuracy of this measurement has been estimated by comparison with the result obtained in the setup with flat mirror as a reference, when 5-frame TPS algorithm was utilized for interferograms phase calculation. Output of such a comparison computed as a difference between these two results is shown in Fig. 12(d). Because of numerous edges of layers deposited onto the membrane that introduce significant errors during interferogram processing the uncertainty of such measurement is worse than in the previous case (Section 6.1) and it is estimated at ± 50 nm. It is seen that the biggest errors occurred near the edges of the layers (high spatial frequencies). The reason for this was the fact that some object high frequencies were cut out in the Fourier spectrum. Otherwise proper phase calculation of the interferogram would be impossible because of the presence of significant high frequency noise.
Fig. 12. Results obtained during micromembrane shape determination using circular spatial carrier frequency technique: a) PCM for the systematic error correction and for the introduction of circular carrier, b) corrected interferogram, c) calculated shape of the membrane, d) difference between height map obtained using described technique and height map obtained with 5-frames TPS algorithm and flat mirror as a reference
6.4 Increasing measurement range of the interferometer
Using LCoS SLM and mathematically designed PCM it is possible to decrease number of interference fringes when they are too dense for the camera. Thanks to this measurement range of an interferometer can be increased. The example of such operation is presented in Fig. 13. The central part of 1.35×1.35 mm2 membrane (Fig. 7(b)) was investigated. It can be seen at the interferogram (Fig. 13(a)) that fringes near right and left edge of the image are almost undistinguishable therefore it would be impossible or very complicated to calculate phase of such interferogram. Using LCoS display we can generate conical reference wavefront by mathematically designed PCM and thanks to this partially compensate deformation of the object wavefront. Phase of such corrected interferogram (Fig. 13(c)) can be easily calculated. The phase calculated from interferogram and the PCM applied are added and the total, correct shape of the element is obtained (Fig. 13(d)).
Fig. 13. Interferograms and result obtained during vastly deflected membrane shape determination: a) initial interferogram, b) PCM for the systematic error correction and for partly compensation of the object wavefront curvature, c) corrected interferogram, d) calculated height map of the membrane after addition of the compensated phase (final result)
6.5 Visualization of negative values of Bessel function
Another application of phase correction by LCoS SLM in two-beam interferometer is improvement of negative values of Bessel function visualization. The contrast of interference fringes in interferogram of sinusoidally vibrating object under test is modulated by Bessel function - J0 (0 order, 1st type) [18]. On the basis of such contrast modulation fringes (Bessel fringes) one can estimate amplitude of the specimen vibration and determine vibration mode. However the disadvantage of this method is low contrast of Bessel fringes (Fig. 14 I). In order to overcome this drawback the Enhanced Time Average Technique (ETAT) is most frequently used [2] (Fig. 14 II). It allows to visualize absolute value of Bessel function on the basis of 4 or 5 mutually phase shifted interferograms. We have found that using LCoS display for object wavefront compensation enable to visualize real profile of Bessel function. The quality of this visualization is worse than for ETAT but the biggest advantage of this active method is that the process is going in real time and no calculation is needed therefore it may be useful for precise resonance frequencies searching. The visualisation is most effective if such a phase correction is introduced to see dark fringe within the whole interferogram of static object (Fig. 14 III). Then positive values of Bessel function are visible as dark places while negative values are white (because in these places contrast of the interference fringes is inverted). Exemplary images obtained using time-average, enhanced time-average and object wavefront compensation techniques during 0.45×0.45 mm2 micromembrane testing for 1st and 2nd resonance modes of their vibration are presented in Fig. 14.
Fig. 14. The results of Bessel fringes visualization of 0.45×0.45 mm2 micromembrane vibrating at its a) first resonance mode (f=222 kHz, U=3 VPP) and b) second resonance mode (f=535 kHz, U=20 VPP) using different techniques
7. Conclusions
In the paper the modified Twyman-Green interferometer with liquid crystal spatial phase modulator serving as the reference element has been presented and its calibration process has been described. The vast benefits for characterization of microelements resulted from LCoS SLM application in Twyman-Green interferometer are clearly shown. Functionality of the interferometer and a class of microobjects possible to study has been extended by utilizing phase SLM for modifications of the reference wavefront. The techniques for LCoS SLM calibration and the methodology for measurement performed with temporal and spatial methods of interferogram analysis are introduced and proved to be efficient. Applicability of the system has been confirmed at the examples of shape and out-of-plane displacement measurements of the active, silicon micromembrane subjected to static and dynamic loading.
The use of spatial light modulators in two beam interferometry promises great advantages in measurement simplification and automation. Also the class of object possible to measure can be significantly increased. Therefore we plan to continue works with LCoS SLM in order to improve measurement accuracy and speed up measurement process. Future works will be concentrated on improving the SLM calibration procedure and phase correction process, as well as designing of special filter for errors reduction in interferograms which are caused by flyback regions.
In future the design of the Twyman-Green interferometer with LCoS display as a reference element may be simplified and the systematic errors may be significantly decreased when spatial light modulator with smaller pixel size (preferably 1 µm×1 µm) and less crosstalks between the neighbouring pixels appears on the market. Implementation of a new generation of LCoS spatial light modulators in the active interferometer will also increase the range of its applications.
Acknowledgments
The LCoS SLM was provided by Liquid Crystal Institute, Kent State University within the cooperation between SPIE Student Chapters at WUT and KSU.
The active micromembranes have been developed within 5th EU project OCMMM no. G1RD-CT-2000-00261 and provided for the experiments by CNRS-FEMTO-ST, Besançon, France.
The work is financially supported by Warsaw University of Technology within statutory grant and EU NoE NEMO, as well as by the Ministry of Education and Science within project no: KBN PB 3 T10C 016 29.
The authors thank Prof. K. Patorski and A. Styk for the fruitful discussion on the lattice-site representation histograms method.
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