Abstract

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

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  1. S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, J.P. Gilles, "3D measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope," Opt. Lasers Eng. 36, 77-101, (2001)
    [CrossRef]
  2. L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, T. Dean, "Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques," in Microsystems Engineering: Metrology and Inspection III, C. Gorecki, ed., Proc. SPIE 5145, 23-32, (2003)
    [CrossRef]
  3. H. J. Tiziani, J. Liesener, C. Pruss, S. Reichelt, L. Seifert, "Active wavefront shaping and analysis," in Eighth International Symposium on Laser Metrology, R. Rodriguez-Vera and F. Mendoza-Santoyo, eds., Proc. SPIE 5776, 1-9, (2005)
    [CrossRef]
  4. D. Dayton, S. Restaino, J. Gonglewski, "Novel spatial light modulators for active and adaptive optics," in High-Resolution Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, eds., Proc. SPIE 4124, 78-88, (2000)
    [CrossRef]
  5. X. Wang, B. Wang, J. Pouch et al., "Liquid Crystal On Silicon (LCoS) wavefront corrector and beam steerer," in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, eds., Proc. SPIE 5162, 139-146, (2003)
    [CrossRef]
  6. S. P. Kotovai in.,"Modal liquid crystal wavefront corrector," Opt. Express 10, 1258-1272, (2002)
    [PubMed]
  7. M. N. Horensteina, S. Pappasa, A. Fishov, T. G. Bifano, "Electrostatic micromirrors for subaperturing in an adaptive optics system," J. Electrost. 54, 321-332, (2002)
    [CrossRef]
  8. L. Salbut, J. Kacperski, A. Styk, M. Jozwik, H. Urey, C. Gorecki, A. Jacobelli, T. Dean, "Interferometric methods for static and dynamic characterizations of micromembranes designed for sensing functions," in Optical Micro- and Nanometrology in Manufacturing Technology, C. Gorecki and A. K. Asundi, eds., Proc. SPIE 5458, 287-298, (2004)
  9. X. Wang, B. Wang, J. Pouch, F. Miranda, J. E Anderson, P. J Bos, "Performance evaluation of a liquid-crystal-on-silicon spatial light modulator," Opt. Eng. 43, 2769-2774, (2004)
    [CrossRef]
  10. J. Kacperski, M. Kujawinska, "Multifunctional interferometric platform for static and dynamic MEMS measurement," in Advanced Characterization Techniques for Optics, Semiconductors, and Nanotechnologies II, A. Duparre, B. Singh, Zu-Han Gu, eds., Proc. SPIE 5878, 64-73, (2005)
  11. http://www.hanaoh.com
  12. M. (Xinghua) Wang, B. Wang, "Liquid Crystal On Silicon (LCoS) spatial light modulator data sheets and technical details," private communication of Liquid Crystal Institute, Kent State University, 2003
  13. X. Wang, B. Wang, P. J. Bos, J. E. Anderson, J. J. Pouch, and F. A. Miranda, "Finite-difference time-domain simulation of a liquid-crystal optical phased array," J. Opt. Soc. Am. A 22, 346-354, (2005)
    [CrossRef]
  14. J. Kacperski, M. Kujawinska, X. Wang, P. J. Bos, "Active microinterferometer with liquid crystal on silicon (LCoS) for extended range static and dynamic micromembrane measurement," in Interferometry XII: Applications, W. Osten and E. Novak, eds., Proc. SPIE 5532, 37-43, (2004)
    [CrossRef]
  15. A. Styk, K. Patorski, "Identification of nonlinear recording error in phase shifting interferometry," Opt. Lasers Eng. (to be published)
  16. A. Sabac, C. Gorecki, M. Jozwik, T. Dean, A. Jacobelli, "Design, testing, and calibration of an integrated Mach-Zehnder-based optical read-out architecture for MEMS characterization," in Optical Micro- and Nanometrology in Manufacturing Technology, C. Gorecki and A. K. Asundi, eds., Proc. SPIE 5458, 141-146, (2004)
    [CrossRef]
  17. J. Kacperski, M. Kujawinska, J. Krezel, "Modified linear and circular carrier frequency Fourier transform method applied for studies of vibrating microelements," in Optical Micro- and Nanometrology in Manufacturing Technology, C. Gorecki and A. K. Asundi, eds., Proc. SPIE 5458, 287-298, (2004)
    [CrossRef]
  18. S. Petitgrand, R. Yahiaoui, A. Bosseboeuf, K. Danaie, "Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization," in Microsystems Engineering: Metrology and Inspection, C. Gorecki, W. P. Jueptner, M. Kujawinska, eds., Proc. SPIE 4400, 51-60, (2001)
    [CrossRef]

2005

2004

X. Wang, B. Wang, J. Pouch, F. Miranda, J. E Anderson, P. J Bos, "Performance evaluation of a liquid-crystal-on-silicon spatial light modulator," Opt. Eng. 43, 2769-2774, (2004)
[CrossRef]

2002

S. P. Kotovai in.,"Modal liquid crystal wavefront corrector," Opt. Express 10, 1258-1272, (2002)
[PubMed]

M. N. Horensteina, S. Pappasa, A. Fishov, T. G. Bifano, "Electrostatic micromirrors for subaperturing in an adaptive optics system," J. Electrost. 54, 321-332, (2002)
[CrossRef]

2001

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, J.P. Gilles, "3D measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope," Opt. Lasers Eng. 36, 77-101, (2001)
[CrossRef]

Anderson, J. E

X. Wang, B. Wang, J. Pouch, F. Miranda, J. E Anderson, P. J Bos, "Performance evaluation of a liquid-crystal-on-silicon spatial light modulator," Opt. Eng. 43, 2769-2774, (2004)
[CrossRef]

Anderson, J. E.

Bifano, T. G.

M. N. Horensteina, S. Pappasa, A. Fishov, T. G. Bifano, "Electrostatic micromirrors for subaperturing in an adaptive optics system," J. Electrost. 54, 321-332, (2002)
[CrossRef]

Bos, P. J

X. Wang, B. Wang, J. Pouch, F. Miranda, J. E Anderson, P. J Bos, "Performance evaluation of a liquid-crystal-on-silicon spatial light modulator," Opt. Eng. 43, 2769-2774, (2004)
[CrossRef]

Bos, P. J.

Bosseboeuf, A.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, J.P. Gilles, "3D measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope," Opt. Lasers Eng. 36, 77-101, (2001)
[CrossRef]

Danaie, K.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, J.P. Gilles, "3D measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope," Opt. Lasers Eng. 36, 77-101, (2001)
[CrossRef]

Fishov, A.

M. N. Horensteina, S. Pappasa, A. Fishov, T. G. Bifano, "Electrostatic micromirrors for subaperturing in an adaptive optics system," J. Electrost. 54, 321-332, (2002)
[CrossRef]

Gilles, J.P.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, J.P. Gilles, "3D measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope," Opt. Lasers Eng. 36, 77-101, (2001)
[CrossRef]

Horensteina, M. N.

M. N. Horensteina, S. Pappasa, A. Fishov, T. G. Bifano, "Electrostatic micromirrors for subaperturing in an adaptive optics system," J. Electrost. 54, 321-332, (2002)
[CrossRef]

Kotova, S. P.

Miranda, F.

X. Wang, B. Wang, J. Pouch, F. Miranda, J. E Anderson, P. J Bos, "Performance evaluation of a liquid-crystal-on-silicon spatial light modulator," Opt. Eng. 43, 2769-2774, (2004)
[CrossRef]

Miranda, F. A.

Pappasa, S.

M. N. Horensteina, S. Pappasa, A. Fishov, T. G. Bifano, "Electrostatic micromirrors for subaperturing in an adaptive optics system," J. Electrost. 54, 321-332, (2002)
[CrossRef]

Patorski, K.

A. Styk, K. Patorski, "Identification of nonlinear recording error in phase shifting interferometry," Opt. Lasers Eng. (to be published)

Petitgrand, S.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, J.P. Gilles, "3D measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope," Opt. Lasers Eng. 36, 77-101, (2001)
[CrossRef]

Pouch, J.

X. Wang, B. Wang, J. Pouch, F. Miranda, J. E Anderson, P. J Bos, "Performance evaluation of a liquid-crystal-on-silicon spatial light modulator," Opt. Eng. 43, 2769-2774, (2004)
[CrossRef]

Pouch, J. J.

Styk, A.

A. Styk, K. Patorski, "Identification of nonlinear recording error in phase shifting interferometry," Opt. Lasers Eng. (to be published)

Wang, B.

X. Wang, B. Wang, P. J. Bos, J. E. Anderson, J. J. Pouch, and F. A. Miranda, "Finite-difference time-domain simulation of a liquid-crystal optical phased array," J. Opt. Soc. Am. A 22, 346-354, (2005)
[CrossRef]

X. Wang, B. Wang, J. Pouch, F. Miranda, J. E Anderson, P. J Bos, "Performance evaluation of a liquid-crystal-on-silicon spatial light modulator," Opt. Eng. 43, 2769-2774, (2004)
[CrossRef]

Wang, X.

X. Wang, B. Wang, P. J. Bos, J. E. Anderson, J. J. Pouch, and F. A. Miranda, "Finite-difference time-domain simulation of a liquid-crystal optical phased array," J. Opt. Soc. Am. A 22, 346-354, (2005)
[CrossRef]

X. Wang, B. Wang, J. Pouch, F. Miranda, J. E Anderson, P. J Bos, "Performance evaluation of a liquid-crystal-on-silicon spatial light modulator," Opt. Eng. 43, 2769-2774, (2004)
[CrossRef]

Yahiaoui, R.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, J.P. Gilles, "3D measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope," Opt. Lasers Eng. 36, 77-101, (2001)
[CrossRef]

J. Electrost.

M. N. Horensteina, S. Pappasa, A. Fishov, T. G. Bifano, "Electrostatic micromirrors for subaperturing in an adaptive optics system," J. Electrost. 54, 321-332, (2002)
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

X. Wang, B. Wang, J. Pouch, F. Miranda, J. E Anderson, P. J Bos, "Performance evaluation of a liquid-crystal-on-silicon spatial light modulator," Opt. Eng. 43, 2769-2774, (2004)
[CrossRef]

Opt. Express

Opt. Lasers Eng.

A. Styk, K. Patorski, "Identification of nonlinear recording error in phase shifting interferometry," Opt. Lasers Eng. (to be published)

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, J.P. Gilles, "3D measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope," Opt. Lasers Eng. 36, 77-101, (2001)
[CrossRef]

Other

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, T. Dean, "Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques," in Microsystems Engineering: Metrology and Inspection III, C. Gorecki, ed., Proc. SPIE 5145, 23-32, (2003)
[CrossRef]

H. J. Tiziani, J. Liesener, C. Pruss, S. Reichelt, L. Seifert, "Active wavefront shaping and analysis," in Eighth International Symposium on Laser Metrology, R. Rodriguez-Vera and F. Mendoza-Santoyo, eds., Proc. SPIE 5776, 1-9, (2005)
[CrossRef]

D. Dayton, S. Restaino, J. Gonglewski, "Novel spatial light modulators for active and adaptive optics," in High-Resolution Wavefront Control: Methods, Devices, and Applications II, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, eds., Proc. SPIE 4124, 78-88, (2000)
[CrossRef]

X. Wang, B. Wang, J. Pouch et al., "Liquid Crystal On Silicon (LCoS) wavefront corrector and beam steerer," in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, eds., Proc. SPIE 5162, 139-146, (2003)
[CrossRef]

J. Kacperski, M. Kujawinska, "Multifunctional interferometric platform for static and dynamic MEMS measurement," in Advanced Characterization Techniques for Optics, Semiconductors, and Nanotechnologies II, A. Duparre, B. Singh, Zu-Han Gu, eds., Proc. SPIE 5878, 64-73, (2005)

http://www.hanaoh.com

M. (Xinghua) Wang, B. Wang, "Liquid Crystal On Silicon (LCoS) spatial light modulator data sheets and technical details," private communication of Liquid Crystal Institute, Kent State University, 2003

J. Kacperski, M. Kujawinska, X. Wang, P. J. Bos, "Active microinterferometer with liquid crystal on silicon (LCoS) for extended range static and dynamic micromembrane measurement," in Interferometry XII: Applications, W. Osten and E. Novak, eds., Proc. SPIE 5532, 37-43, (2004)
[CrossRef]

A. Sabac, C. Gorecki, M. Jozwik, T. Dean, A. Jacobelli, "Design, testing, and calibration of an integrated Mach-Zehnder-based optical read-out architecture for MEMS characterization," in Optical Micro- and Nanometrology in Manufacturing Technology, C. Gorecki and A. K. Asundi, eds., Proc. SPIE 5458, 141-146, (2004)
[CrossRef]

J. Kacperski, M. Kujawinska, J. Krezel, "Modified linear and circular carrier frequency Fourier transform method applied for studies of vibrating microelements," in Optical Micro- and Nanometrology in Manufacturing Technology, C. Gorecki and A. K. Asundi, eds., Proc. SPIE 5458, 287-298, (2004)
[CrossRef]

S. Petitgrand, R. Yahiaoui, A. Bosseboeuf, K. Danaie, "Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization," in Microsystems Engineering: Metrology and Inspection, C. Gorecki, W. P. Jueptner, M. Kujawinska, eds., Proc. SPIE 4400, 51-60, (2001)
[CrossRef]

L. Salbut, J. Kacperski, A. Styk, M. Jozwik, H. Urey, C. Gorecki, A. Jacobelli, T. Dean, "Interferometric methods for static and dynamic characterizations of micromembranes designed for sensing functions," in Optical Micro- and Nanometrology in Manufacturing Technology, C. Gorecki and A. K. Asundi, eds., Proc. SPIE 5458, 287-298, (2004)

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Figures (14)

Fig. 1.
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

Fig. 2.
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

Fig. 3.
Fig. 3.

Estimated phase shift introduced by LCoS SLM (according to [13])

Fig. 4.
Fig. 4.

LCoS SLM E-O characteristic obtained for He-Ne laser (λ=632.8 nm)

Fig. 5.
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)

Fig. 6.
Fig. 6.

The schematic views (a) and photograph (b) of the micromembrane (0.45×0.45 mm2 with PZT layer [2,16]

Fig. 7.
Fig. 7.

Exemplary interferograms of a) 0.45×0.45 mm2, and b) 1.35×1.35 mm2 micromembrane

Fig. 8.
Fig. 8.

Block diagrams of the measurement procedures using LCoS SLM and applied to determination of different physical values characterizing an object under test.

Fig. 9.
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

Fig. 10.
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

Fig. 11.
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

Fig. 12.
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

Fig. 13.
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)

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

Tables (3)

Tables Icon

Table 1. The list of measurement problems and their possible solutions by means of LCoS SLM as an active reference mirror

Tables Icon

Table 2. Main technical parameters of the system

Tables Icon

Table 3. Device specification for phase only LCoS SLM [12]

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