Abstract

We describe a LED-based stroboscopic white-light interferometer and a data analysis method that allow mapping out-of-plane surface vibration fields in electrically excited microstructures with sub-nm amplitude resolution for vibration frequencies ranging up to tens of MHz. The data analysis, which is performed entirely in the frequency domain, makes use of the high resolution available in the measured interferometric phase data. For demonstration, we image the surface vibration fields in a square-plate silicon MEMS resonator for three vibration modes ranging in frequency between 3 and 14 MHz. The minimum detectable vibration amplitude in this case was less than 100 pm.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. A. Bosseboeuf and S. Petitgrand, “Characterization of the static and dynamic behaviour of M(O)EMS by optical techniques: status and trends,” J. Micromech. Microeng.13, S23–S33 (2003).
    [CrossRef]
  4. J. Schmit, J. Reed, E. Novak, and J. K. Gimzewski, “Performance advances in interferometric optical profilers for imaging and testing,”J. Opt. A: Pure Appl. Opt.10, 064001 (2008).
    [CrossRef]
  5. S. Donati, Electro-Optical Instrumentation: Sensing and Measuring with Lasers (Prentice Hall, Upper Saddle River, NJ, 2004).
  6. K. Kokkonen, “Laser interferometers in physical acoustics,” in “Ultrasonics Symposium (IUS), 2009 IEEE International,” (2009), pp. 1036–1043.
    [CrossRef]
  7. W. Osten, Optical Inspection of Microsystems, Optical Science and Engineering (CRC/Taylor & Francis, Boca Raton, FL, 2007).
  8. G. G. Fattinger and P. T. Tikka, “Modified Mach–Zender laser interferometer for probing bulk acoustic waves,” Appl. Phys. Lett.79, 290–292 (2001).
    [CrossRef]
  9. J. E. Graebner, B. P. Barber, P. L. Gammel, D. S. Greywall, and S. Gopani, “Dynamic visualization of sub-angstrom high-frequency surface vibrations,” Appl. Phys. Lett.78, 159–161 (2001).
    [CrossRef]
  10. K. Kokkonen and M. Kaivola, “Scanning heterodyne laser interferometer for phase-sensitive absolute-amplitude measurements of surface vibrations,” Appl. Phys. Lett.92, 063502 (2008).
    [CrossRef]
  11. M. Hart, R. Conant, K. Lau, and R. Muller, “Stroboscopic interferometer system for dynamic MEMS characterization,” J. Microelectromech. Syst.9, 409–418 (2000).
    [CrossRef]
  12. S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. Gilles, “3D measurement of micromechanical devices vibration mode shapes with a stroboscopic interferometric microscope,” Opt. Laser. Eng.36, 77–101 (2001).
    [CrossRef]
  13. S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of phase and amplitude of MEMS vibrations by microscopic interferometry with stroboscopic illumination,” Proc. SPIE5145, 33–44 (2003).
    [CrossRef]
  14. I. Kassamakov, K. Hanhijärvi, I. Abbadi, J. Aaltonen, H. Ludvigsen, and E. Hæggström, “Scanning white-light interferometry with a supercontinuum source,” Opt. Lett.34, 1582–1584 (2009).
    [CrossRef] [PubMed]
  15. V. Heikkinen, I. Kassamakov, T. Paulin, A. Nolvi, and E. Hæggström, “Stroboscopic scanning white light interferometry at 2.7 MHz with 1.6 μm coherence length using a non-phosphor LED source,” Opt. Express21, 5247–5254 (2013).
    [CrossRef] [PubMed]
  16. P. de Groot and L. L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt.42, 389–401 (1995).
    [CrossRef]
  17. A. Harasaki, J. Schmit, and J. C. Wyant, “Improved vertical-scanning interferometry,” Appl. Opt.39, 2107–2115 (2000).
    [CrossRef]
  18. M. Fleischer, R. Windecker, and H. J. Tiziani, “Theoretical limits of scanning white-light interferometry signal evaluation algorithms,” Appl. Opt.40, 2815–2820 (2001).
    [CrossRef]
  19. P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt.41, 4571–4578 (2002).
    [CrossRef] [PubMed]
  20. A. Jaakkola, P. Rosenberg, S. Asmala, A. Nurmela, T. Pensala, T. Riekkinen, J. Dekker, T. Mattila, A. Alastalo, O. Holmgren, and K. Kokkonen, “Piezoelectrically transduced single-crystal-silicon plate resonators,” in “Proceedings of the IEEE Ultrasonics Symposium,” (IEEE, New York, 2008, Beijing, China, 2008), pp. 717–720.
  21. A. Jaakkola, J. Lamy, J. Dekker, T. Pensala, L. Lipiäinen, and K. Kokkonen, “Experimental study of the effects of size variations on piezoelectrically transduced MEMS resonators,” in “Proceedings of the IEEE International Frequency Control Symposium,” (IEEE, New York, 2010, Newport Beach, California, USA, 2010), pp. 410–414.
  22. K. Telschow, V. Deason, D. Cottle, and I. Larson, J.D., “Full-field imaging of gigahertz film bulk acoustic resonator motion,”IEEE Trans. Ultrason., Ferroelectr., Freq. Control50, 1279–1285 (2003).
    [CrossRef]
  23. S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of out-of-plane and in-plane vibrations of MEMS with (sub)nanometer resolution,” J. Micromech. Microeng.14, S97–S101 (2004).
    [CrossRef]
  24. L.-C. Chen, Y.-T. Huang, X.-L. Nguyen, J.-L. Chen, and C.-C. Chang, “Dynamic out-of-plane profilometry for nano-scale full-field characterization of MEMS using stroboscopic interferometry with novel signal deconvolution algorithm,” Opt. Laser. Eng.47, 237–251 (2009).
    [CrossRef]

2013

2009

I. Kassamakov, K. Hanhijärvi, I. Abbadi, J. Aaltonen, H. Ludvigsen, and E. Hæggström, “Scanning white-light interferometry with a supercontinuum source,” Opt. Lett.34, 1582–1584 (2009).
[CrossRef] [PubMed]

K. Kokkonen, “Laser interferometers in physical acoustics,” in “Ultrasonics Symposium (IUS), 2009 IEEE International,” (2009), pp. 1036–1043.
[CrossRef]

L.-C. Chen, Y.-T. Huang, X.-L. Nguyen, J.-L. Chen, and C.-C. Chang, “Dynamic out-of-plane profilometry for nano-scale full-field characterization of MEMS using stroboscopic interferometry with novel signal deconvolution algorithm,” Opt. Laser. Eng.47, 237–251 (2009).
[CrossRef]

2008

K. Kokkonen and M. Kaivola, “Scanning heterodyne laser interferometer for phase-sensitive absolute-amplitude measurements of surface vibrations,” Appl. Phys. Lett.92, 063502 (2008).
[CrossRef]

J. Schmit, J. Reed, E. Novak, and J. K. Gimzewski, “Performance advances in interferometric optical profilers for imaging and testing,”J. Opt. A: Pure Appl. Opt.10, 064001 (2008).
[CrossRef]

2004

S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of out-of-plane and in-plane vibrations of MEMS with (sub)nanometer resolution,” J. Micromech. Microeng.14, S97–S101 (2004).
[CrossRef]

2003

K. Telschow, V. Deason, D. Cottle, and I. Larson, J.D., “Full-field imaging of gigahertz film bulk acoustic resonator motion,”IEEE Trans. Ultrason., Ferroelectr., Freq. Control50, 1279–1285 (2003).
[CrossRef]

S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of phase and amplitude of MEMS vibrations by microscopic interferometry with stroboscopic illumination,” Proc. SPIE5145, 33–44 (2003).
[CrossRef]

A. Bosseboeuf and S. Petitgrand, “Characterization of the static and dynamic behaviour of M(O)EMS by optical techniques: status and trends,” J. Micromech. Microeng.13, S23–S33 (2003).
[CrossRef]

2002

2001

G. G. Fattinger and P. T. Tikka, “Modified Mach–Zender laser interferometer for probing bulk acoustic waves,” Appl. Phys. Lett.79, 290–292 (2001).
[CrossRef]

J. E. Graebner, B. P. Barber, P. L. Gammel, D. S. Greywall, and S. Gopani, “Dynamic visualization of sub-angstrom high-frequency surface vibrations,” Appl. Phys. Lett.78, 159–161 (2001).
[CrossRef]

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

M. Fleischer, R. Windecker, and H. J. Tiziani, “Theoretical limits of scanning white-light interferometry signal evaluation algorithms,” Appl. Opt.40, 2815–2820 (2001).
[CrossRef]

2000

A. Harasaki, J. Schmit, and J. C. Wyant, “Improved vertical-scanning interferometry,” Appl. Opt.39, 2107–2115 (2000).
[CrossRef]

M. Hart, R. Conant, K. Lau, and R. Muller, “Stroboscopic interferometer system for dynamic MEMS characterization,” J. Microelectromech. Syst.9, 409–418 (2000).
[CrossRef]

1995

P. de Groot and L. L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt.42, 389–401 (1995).
[CrossRef]

1986

J.-P. Monchalin, “Optical detection of ultrasound,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control33, 485–499 (1986).
[CrossRef]

1969

Aaltonen, J.

Abbadi, I.

Alastalo, A.

A. Jaakkola, P. Rosenberg, S. Asmala, A. Nurmela, T. Pensala, T. Riekkinen, J. Dekker, T. Mattila, A. Alastalo, O. Holmgren, and K. Kokkonen, “Piezoelectrically transduced single-crystal-silicon plate resonators,” in “Proceedings of the IEEE Ultrasonics Symposium,” (IEEE, New York, 2008, Beijing, China, 2008), pp. 717–720.

Asmala, S.

A. Jaakkola, P. Rosenberg, S. Asmala, A. Nurmela, T. Pensala, T. Riekkinen, J. Dekker, T. Mattila, A. Alastalo, O. Holmgren, and K. Kokkonen, “Piezoelectrically transduced single-crystal-silicon plate resonators,” in “Proceedings of the IEEE Ultrasonics Symposium,” (IEEE, New York, 2008, Beijing, China, 2008), pp. 717–720.

Barber, B. P.

J. E. Graebner, B. P. Barber, P. L. Gammel, D. S. Greywall, and S. Gopani, “Dynamic visualization of sub-angstrom high-frequency surface vibrations,” Appl. Phys. Lett.78, 159–161 (2001).
[CrossRef]

Bosseboeuf, A.

S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of out-of-plane and in-plane vibrations of MEMS with (sub)nanometer resolution,” J. Micromech. Microeng.14, S97–S101 (2004).
[CrossRef]

A. Bosseboeuf and S. Petitgrand, “Characterization of the static and dynamic behaviour of M(O)EMS by optical techniques: status and trends,” J. Micromech. Microeng.13, S23–S33 (2003).
[CrossRef]

S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of phase and amplitude of MEMS vibrations by microscopic interferometry with stroboscopic illumination,” Proc. SPIE5145, 33–44 (2003).
[CrossRef]

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

Chang, C.-C.

L.-C. Chen, Y.-T. Huang, X.-L. Nguyen, J.-L. Chen, and C.-C. Chang, “Dynamic out-of-plane profilometry for nano-scale full-field characterization of MEMS using stroboscopic interferometry with novel signal deconvolution algorithm,” Opt. Laser. Eng.47, 237–251 (2009).
[CrossRef]

Chen, J.-L.

L.-C. Chen, Y.-T. Huang, X.-L. Nguyen, J.-L. Chen, and C.-C. Chang, “Dynamic out-of-plane profilometry for nano-scale full-field characterization of MEMS using stroboscopic interferometry with novel signal deconvolution algorithm,” Opt. Laser. Eng.47, 237–251 (2009).
[CrossRef]

Chen, L.-C.

L.-C. Chen, Y.-T. Huang, X.-L. Nguyen, J.-L. Chen, and C.-C. Chang, “Dynamic out-of-plane profilometry for nano-scale full-field characterization of MEMS using stroboscopic interferometry with novel signal deconvolution algorithm,” Opt. Laser. Eng.47, 237–251 (2009).
[CrossRef]

Conant, R.

M. Hart, R. Conant, K. Lau, and R. Muller, “Stroboscopic interferometer system for dynamic MEMS characterization,” J. Microelectromech. Syst.9, 409–418 (2000).
[CrossRef]

Cottle, D.

K. Telschow, V. Deason, D. Cottle, and I. Larson, J.D., “Full-field imaging of gigahertz film bulk acoustic resonator motion,”IEEE Trans. Ultrason., Ferroelectr., Freq. Control50, 1279–1285 (2003).
[CrossRef]

Danaie, K.

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

de Groot, P.

P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt.41, 4571–4578 (2002).
[CrossRef] [PubMed]

P. de Groot and L. L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt.42, 389–401 (1995).
[CrossRef]

de Lega, X. C.

Deason, V.

K. Telschow, V. Deason, D. Cottle, and I. Larson, J.D., “Full-field imaging of gigahertz film bulk acoustic resonator motion,”IEEE Trans. Ultrason., Ferroelectr., Freq. Control50, 1279–1285 (2003).
[CrossRef]

Deck, L. L.

P. de Groot and L. L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt.42, 389–401 (1995).
[CrossRef]

Dekker, J.

A. Jaakkola, J. Lamy, J. Dekker, T. Pensala, L. Lipiäinen, and K. Kokkonen, “Experimental study of the effects of size variations on piezoelectrically transduced MEMS resonators,” in “Proceedings of the IEEE International Frequency Control Symposium,” (IEEE, New York, 2010, Newport Beach, California, USA, 2010), pp. 410–414.

A. Jaakkola, P. Rosenberg, S. Asmala, A. Nurmela, T. Pensala, T. Riekkinen, J. Dekker, T. Mattila, A. Alastalo, O. Holmgren, and K. Kokkonen, “Piezoelectrically transduced single-crystal-silicon plate resonators,” in “Proceedings of the IEEE Ultrasonics Symposium,” (IEEE, New York, 2008, Beijing, China, 2008), pp. 717–720.

Donati, S.

S. Donati, Electro-Optical Instrumentation: Sensing and Measuring with Lasers (Prentice Hall, Upper Saddle River, NJ, 2004).

Fattinger, G. G.

G. G. Fattinger and P. T. Tikka, “Modified Mach–Zender laser interferometer for probing bulk acoustic waves,” Appl. Phys. Lett.79, 290–292 (2001).
[CrossRef]

Fleischer, M.

Gammel, P. L.

J. E. Graebner, B. P. Barber, P. L. Gammel, D. S. Greywall, and S. Gopani, “Dynamic visualization of sub-angstrom high-frequency surface vibrations,” Appl. Phys. Lett.78, 159–161 (2001).
[CrossRef]

Gilles, J.

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

Gimzewski, J. K.

J. Schmit, J. Reed, E. Novak, and J. K. Gimzewski, “Performance advances in interferometric optical profilers for imaging and testing,”J. Opt. A: Pure Appl. Opt.10, 064001 (2008).
[CrossRef]

Gopani, S.

J. E. Graebner, B. P. Barber, P. L. Gammel, D. S. Greywall, and S. Gopani, “Dynamic visualization of sub-angstrom high-frequency surface vibrations,” Appl. Phys. Lett.78, 159–161 (2001).
[CrossRef]

Graebner, J. E.

J. E. Graebner, B. P. Barber, P. L. Gammel, D. S. Greywall, and S. Gopani, “Dynamic visualization of sub-angstrom high-frequency surface vibrations,” Appl. Phys. Lett.78, 159–161 (2001).
[CrossRef]

Greywall, D. S.

J. E. Graebner, B. P. Barber, P. L. Gammel, D. S. Greywall, and S. Gopani, “Dynamic visualization of sub-angstrom high-frequency surface vibrations,” Appl. Phys. Lett.78, 159–161 (2001).
[CrossRef]

Hæggström, E.

Hanhijärvi, K.

Harasaki, A.

Hart, M.

M. Hart, R. Conant, K. Lau, and R. Muller, “Stroboscopic interferometer system for dynamic MEMS characterization,” J. Microelectromech. Syst.9, 409–418 (2000).
[CrossRef]

Heikkinen, V.

Holmgren, O.

A. Jaakkola, P. Rosenberg, S. Asmala, A. Nurmela, T. Pensala, T. Riekkinen, J. Dekker, T. Mattila, A. Alastalo, O. Holmgren, and K. Kokkonen, “Piezoelectrically transduced single-crystal-silicon plate resonators,” in “Proceedings of the IEEE Ultrasonics Symposium,” (IEEE, New York, 2008, Beijing, China, 2008), pp. 717–720.

Huang, Y.-T.

L.-C. Chen, Y.-T. Huang, X.-L. Nguyen, J.-L. Chen, and C.-C. Chang, “Dynamic out-of-plane profilometry for nano-scale full-field characterization of MEMS using stroboscopic interferometry with novel signal deconvolution algorithm,” Opt. Laser. Eng.47, 237–251 (2009).
[CrossRef]

Jaakkola, A.

A. Jaakkola, J. Lamy, J. Dekker, T. Pensala, L. Lipiäinen, and K. Kokkonen, “Experimental study of the effects of size variations on piezoelectrically transduced MEMS resonators,” in “Proceedings of the IEEE International Frequency Control Symposium,” (IEEE, New York, 2010, Newport Beach, California, USA, 2010), pp. 410–414.

A. Jaakkola, P. Rosenberg, S. Asmala, A. Nurmela, T. Pensala, T. Riekkinen, J. Dekker, T. Mattila, A. Alastalo, O. Holmgren, and K. Kokkonen, “Piezoelectrically transduced single-crystal-silicon plate resonators,” in “Proceedings of the IEEE Ultrasonics Symposium,” (IEEE, New York, 2008, Beijing, China, 2008), pp. 717–720.

Kaivola, M.

K. Kokkonen and M. Kaivola, “Scanning heterodyne laser interferometer for phase-sensitive absolute-amplitude measurements of surface vibrations,” Appl. Phys. Lett.92, 063502 (2008).
[CrossRef]

Kassamakov, I.

Kokkonen, K.

K. Kokkonen, “Laser interferometers in physical acoustics,” in “Ultrasonics Symposium (IUS), 2009 IEEE International,” (2009), pp. 1036–1043.
[CrossRef]

K. Kokkonen and M. Kaivola, “Scanning heterodyne laser interferometer for phase-sensitive absolute-amplitude measurements of surface vibrations,” Appl. Phys. Lett.92, 063502 (2008).
[CrossRef]

A. Jaakkola, P. Rosenberg, S. Asmala, A. Nurmela, T. Pensala, T. Riekkinen, J. Dekker, T. Mattila, A. Alastalo, O. Holmgren, and K. Kokkonen, “Piezoelectrically transduced single-crystal-silicon plate resonators,” in “Proceedings of the IEEE Ultrasonics Symposium,” (IEEE, New York, 2008, Beijing, China, 2008), pp. 717–720.

A. Jaakkola, J. Lamy, J. Dekker, T. Pensala, L. Lipiäinen, and K. Kokkonen, “Experimental study of the effects of size variations on piezoelectrically transduced MEMS resonators,” in “Proceedings of the IEEE International Frequency Control Symposium,” (IEEE, New York, 2010, Newport Beach, California, USA, 2010), pp. 410–414.

Korpel, A.

Kramer, J.

Lamy, J.

A. Jaakkola, J. Lamy, J. Dekker, T. Pensala, L. Lipiäinen, and K. Kokkonen, “Experimental study of the effects of size variations on piezoelectrically transduced MEMS resonators,” in “Proceedings of the IEEE International Frequency Control Symposium,” (IEEE, New York, 2010, Newport Beach, California, USA, 2010), pp. 410–414.

Larson, I.

K. Telschow, V. Deason, D. Cottle, and I. Larson, J.D., “Full-field imaging of gigahertz film bulk acoustic resonator motion,”IEEE Trans. Ultrason., Ferroelectr., Freq. Control50, 1279–1285 (2003).
[CrossRef]

Lau, K.

M. Hart, R. Conant, K. Lau, and R. Muller, “Stroboscopic interferometer system for dynamic MEMS characterization,” J. Microelectromech. Syst.9, 409–418 (2000).
[CrossRef]

Lipiäinen, L.

A. Jaakkola, J. Lamy, J. Dekker, T. Pensala, L. Lipiäinen, and K. Kokkonen, “Experimental study of the effects of size variations on piezoelectrically transduced MEMS resonators,” in “Proceedings of the IEEE International Frequency Control Symposium,” (IEEE, New York, 2010, Newport Beach, California, USA, 2010), pp. 410–414.

Ludvigsen, H.

Mattila, T.

A. Jaakkola, P. Rosenberg, S. Asmala, A. Nurmela, T. Pensala, T. Riekkinen, J. Dekker, T. Mattila, A. Alastalo, O. Holmgren, and K. Kokkonen, “Piezoelectrically transduced single-crystal-silicon plate resonators,” in “Proceedings of the IEEE Ultrasonics Symposium,” (IEEE, New York, 2008, Beijing, China, 2008), pp. 717–720.

Monchalin, J.-P.

J.-P. Monchalin, “Optical detection of ultrasound,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control33, 485–499 (1986).
[CrossRef]

Muller, R.

M. Hart, R. Conant, K. Lau, and R. Muller, “Stroboscopic interferometer system for dynamic MEMS characterization,” J. Microelectromech. Syst.9, 409–418 (2000).
[CrossRef]

Nguyen, X.-L.

L.-C. Chen, Y.-T. Huang, X.-L. Nguyen, J.-L. Chen, and C.-C. Chang, “Dynamic out-of-plane profilometry for nano-scale full-field characterization of MEMS using stroboscopic interferometry with novel signal deconvolution algorithm,” Opt. Laser. Eng.47, 237–251 (2009).
[CrossRef]

Nolvi, A.

Novak, E.

J. Schmit, J. Reed, E. Novak, and J. K. Gimzewski, “Performance advances in interferometric optical profilers for imaging and testing,”J. Opt. A: Pure Appl. Opt.10, 064001 (2008).
[CrossRef]

Nurmela, A.

A. Jaakkola, P. Rosenberg, S. Asmala, A. Nurmela, T. Pensala, T. Riekkinen, J. Dekker, T. Mattila, A. Alastalo, O. Holmgren, and K. Kokkonen, “Piezoelectrically transduced single-crystal-silicon plate resonators,” in “Proceedings of the IEEE Ultrasonics Symposium,” (IEEE, New York, 2008, Beijing, China, 2008), pp. 717–720.

Osten, W.

W. Osten, Optical Inspection of Microsystems, Optical Science and Engineering (CRC/Taylor & Francis, Boca Raton, FL, 2007).

Paulin, T.

Pensala, T.

A. Jaakkola, P. Rosenberg, S. Asmala, A. Nurmela, T. Pensala, T. Riekkinen, J. Dekker, T. Mattila, A. Alastalo, O. Holmgren, and K. Kokkonen, “Piezoelectrically transduced single-crystal-silicon plate resonators,” in “Proceedings of the IEEE Ultrasonics Symposium,” (IEEE, New York, 2008, Beijing, China, 2008), pp. 717–720.

A. Jaakkola, J. Lamy, J. Dekker, T. Pensala, L. Lipiäinen, and K. Kokkonen, “Experimental study of the effects of size variations on piezoelectrically transduced MEMS resonators,” in “Proceedings of the IEEE International Frequency Control Symposium,” (IEEE, New York, 2010, Newport Beach, California, USA, 2010), pp. 410–414.

Petitgrand, S.

S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of out-of-plane and in-plane vibrations of MEMS with (sub)nanometer resolution,” J. Micromech. Microeng.14, S97–S101 (2004).
[CrossRef]

S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of phase and amplitude of MEMS vibrations by microscopic interferometry with stroboscopic illumination,” Proc. SPIE5145, 33–44 (2003).
[CrossRef]

A. Bosseboeuf and S. Petitgrand, “Characterization of the static and dynamic behaviour of M(O)EMS by optical techniques: status and trends,” J. Micromech. Microeng.13, S23–S33 (2003).
[CrossRef]

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

Reed, J.

J. Schmit, J. Reed, E. Novak, and J. K. Gimzewski, “Performance advances in interferometric optical profilers for imaging and testing,”J. Opt. A: Pure Appl. Opt.10, 064001 (2008).
[CrossRef]

Riekkinen, T.

A. Jaakkola, P. Rosenberg, S. Asmala, A. Nurmela, T. Pensala, T. Riekkinen, J. Dekker, T. Mattila, A. Alastalo, O. Holmgren, and K. Kokkonen, “Piezoelectrically transduced single-crystal-silicon plate resonators,” in “Proceedings of the IEEE Ultrasonics Symposium,” (IEEE, New York, 2008, Beijing, China, 2008), pp. 717–720.

Rosenberg, P.

A. Jaakkola, P. Rosenberg, S. Asmala, A. Nurmela, T. Pensala, T. Riekkinen, J. Dekker, T. Mattila, A. Alastalo, O. Holmgren, and K. Kokkonen, “Piezoelectrically transduced single-crystal-silicon plate resonators,” in “Proceedings of the IEEE Ultrasonics Symposium,” (IEEE, New York, 2008, Beijing, China, 2008), pp. 717–720.

Schmit, J.

J. Schmit, J. Reed, E. Novak, and J. K. Gimzewski, “Performance advances in interferometric optical profilers for imaging and testing,”J. Opt. A: Pure Appl. Opt.10, 064001 (2008).
[CrossRef]

A. Harasaki, J. Schmit, and J. C. Wyant, “Improved vertical-scanning interferometry,” Appl. Opt.39, 2107–2115 (2000).
[CrossRef]

Telschow, K.

K. Telschow, V. Deason, D. Cottle, and I. Larson, J.D., “Full-field imaging of gigahertz film bulk acoustic resonator motion,”IEEE Trans. Ultrason., Ferroelectr., Freq. Control50, 1279–1285 (2003).
[CrossRef]

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Supplementary Material (3)

» Media 1: MP4 (665 KB)     
» Media 2: MP4 (2523 KB)     
» Media 3: MP4 (2799 KB)     

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Figures (3)

Fig. 1
Fig. 1

Schematic presentation of the experimental setup, with the insets showing (a) the measured source spectrum and (b) the optical pulses (green line) tuned to phase δ with respect to the sample excitation waveform (blue line). A collimated LED beam is split into the sample and reference beams of a Michelson interferometer by a non-polarizing beam splitter. The returning beams are combined and imaged onto a camera (The Imaging Source DMK 21BU04) equipped with a lens for microscopic imaging (Volpi AS11/50).

Fig. 2
Fig. 2

Schematic presentation of the FDA approach for processing stroboscopic PSWLI data and illustration of the vibration analysis concept. (a) During the measurement, a stack of images is acquired as a function of the varied OPLD (z-scan). For each OPLD value, an image is recorded for each driving phase delay value δ. When examining the light intensity data from a particular camera pixel through the stack, Ixyδ(z), (b) a typical WLI interferogram with localized fringes is observed. (c) Applying a Fourier transform (FT) to the interferogram, the spectral amplitude content (A(k)) of this signal peaks at the spatial frequency k0, in the vicinity of which the spectral phase (Φ(k)) is linear. (d) The FDA analysis utilizes the spectral phase linearity to obtain a high-resolution height map for each measured driving phase value δ (covering exactly one vibration period). (e) The surface deformation at a single spatial point as a function of δ, hxy(δ), is a sinusoid with a DC-offset σxy. (f) Applying a second Fourier transform, independently for each spatial point on the set of height maps, yields the sample surface topography (σxy) and both the absolute amplitude (Axy) and phase (θxy) of the surface vibration.

Fig. 3
Fig. 3

A set of measured vibration amplitude (first row) and phase (second row) data for the 3.37 MHz, 7.18 MHz and 13.72 MHz vibration modes. The vibration amplitude and phase data for the 3.37 MHz mode are shown also for the reduced input drive powers of P0 −20 dB and P0 −40 dB. At the nominal input drive power (P0), the amplitude data feature more than 40 dB of dynamic range, and the nodal line of the vibration mode is seen as a thin and deep minimum, with the corresponding phase data showing a sharp transition. Decreasing the input drive power, and hence the vibration amplitude, serves to illustrate that the setup is capable of resolving vibration modes with a maximum amplitude of less than 300 pm, and features a minimum detectable amplitude limit of less than 100 pm. The amplitude and phase data can also be combined to create a 3D view of the instantaneous surface deformation at an arbitrary phase of the vibration (a,d,e), also demontrated by animating the surface vibration ( Media 1, Media 2, Media 3). The extremes of the colormaps for the 3D views correspond to the limits shown on each of the z-axes in (a,d,e). A schematic view (b) and photograph (c) of the square-plate silicon MEMS resonator is also included.

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