Abstract

An optical method has been developed to measure the deformation of a membrane in a microphone. A fringe projector that consists of an optical fiber and an optical wedge is described and analyzed by geometric optics. A three-step phase-shifting technique that involves the introduction of an arbitrary phase is discussed. The fine fringe patterns projected onto a small test surface are captured by a CCD camera mounted on a long-distance microscope. With the aid of a phase-shifting technique and signal-demodulating techniques, the proposed setup is capable of measuring deformation of the membrane of the order of as much as submicrometers.

© 2002 Optical Society of America

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References

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  1. G. M. Sessler, “Acoustic sensors,” Sens. Actuators A25–A27, 323–330 (1991.
    [CrossRef]
  2. P. R. Scheeper, A. G. H. van der Donk, W. Olthuis, P. Bergveld, “Review of silicon microphone,” Sens. Actuators A44, 1–11 (1994).
    [CrossRef]
  3. M. Idesawa, T. Yatagai, T. Soma, “Scanning moiré method and automatic measurement of 3-D shapes,” Appl. Opt. 16, 2152–2162 (1977).
    [CrossRef] [PubMed]
  4. Y. Z. Dai, F. P. Chiang, “Contouring by moiré interferometry,” Exp. Mech. 31, 76–81 (1991).
    [CrossRef]
  5. C. Quan, P. J. Bryanston-Cross, “Double-source holographic contouring using fibre optics,” Opt. Laser Technol. 22, 255–259 (1990).
    [CrossRef]
  6. P. Carelli, D. Paoletti, G. S. Spagnolo, “Holographic of surface defects in artwork,” Opt. Eng. 30, 1294–1298 (1991).
    [CrossRef]
  7. D. R. Burton, M. J. Lalor, “Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping,” Appl. Opt. 33, 2939–2947 (1994).
    [CrossRef] [PubMed]
  8. X. Y. Su, W. S. Zhou, G. Vonbally, D. Vukicevic, “Automated phase measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
    [CrossRef]
  9. W. S. Zhou, X. Y. Su, “A direct mapping algorithm for phase measuring profilometry,” J. Mod. Opt. 41, 89–94 (1994).
    [CrossRef]
  10. P. K. Piotr, “Polarization based fringe projection interferometer for phase stepping techniques,” in Optical Inspection and Micromeasurements, C. Goreki, ed., Proc. SPIE.2782, 250–257 (1996).
    [CrossRef]
  11. G. S. Spagnolo, D. Paoletti, D. Ambrosini, “Vibration monitoring by fiber optic fringe projection and Fourier tranaform analysis,” Opt. Commun. 139, 17–23 (1997).
    [CrossRef]
  12. P. S. Huang, Q. Hu, F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface,” Opt. Eng. 38, 1065–1071 (1999).
    [CrossRef]
  13. S. S. Helen, M. P. Kothiyal, R. S. Sirohi, “White-light interferometry with polarization phase-shifter at the input of the interferometer,” J. Mod. Opt. 47, 1137–1145 (2000).
    [CrossRef]
  14. K. Creath, “High resolution optical profile,” in Surface Characterization and Testing II, J. E. Greiven Kamp, M. Young, eds., Proc. SPIE1164, 142–147 (1989).
    [CrossRef]
  15. J. C. Wyant, K. Creath, “Advances in interferometric optical profiling,” Int. J. Mach. Tools Manuf. 32, 5–10 (1992).
    [CrossRef]
  16. J. Bergqvist, J. Gobet, “Capacitive microphone with a surface micromachined backplate using electroplating technology,” J. Microelectromech. Syst. 3, 69–75 (1994).
    [CrossRef]
  17. M. Pedersen, W. Olthuis, P. Bergveld, “Harmonic distortion in silicon condenser microphones,” J. Acoust. Soc. Am. 102, 1582–1587 (1997).
    [CrossRef]
  18. H. Eugene, A. Alfred, Optics (Addison-Wesley, London, 1979).
  19. J. H. Yi, S. H. Kim, Y. K. Kwak, “A nanometric displacement measurement method using the detection of fringe peak movement,” Meas. Sci. Technol. 11, 1353–1358 (2000).
    [CrossRef]
  20. S. H. Wang, C. J. Tay, C. G. Quan, H. M. Shang, “An optical fiber fringe projector for micro-component,” Optik (Stuttgart) 111, 419–422 (2000).
  21. K. Creath, “Phase-shifting speck interferometry,” Appl. Opt. 24, 3053–3058 (1985).
    [CrossRef]
  22. Z. Wang, M. S. Graca, P. J. Bryanston-Cross, D. J. Whitehouse, “Phase-shifted image matching algorithm for displacement measurement,” Opt. Eng. 35, 2327–2332 (1996).
    [CrossRef]
  23. C. Quan, C. J. Tay, H. M. Shang, P. J. Bryanston-Cross, “Contour measurement by fibre optics fringe projection and Fourier transform analysis,” Opt. Commun. 119, 479–483 (1995).
    [CrossRef]
  24. Y. Y. Hung, L. Lin, H. M. Shang, B. G. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39, 143–149 (2000).
    [CrossRef]

2000 (4)

S. S. Helen, M. P. Kothiyal, R. S. Sirohi, “White-light interferometry with polarization phase-shifter at the input of the interferometer,” J. Mod. Opt. 47, 1137–1145 (2000).
[CrossRef]

J. H. Yi, S. H. Kim, Y. K. Kwak, “A nanometric displacement measurement method using the detection of fringe peak movement,” Meas. Sci. Technol. 11, 1353–1358 (2000).
[CrossRef]

S. H. Wang, C. J. Tay, C. G. Quan, H. M. Shang, “An optical fiber fringe projector for micro-component,” Optik (Stuttgart) 111, 419–422 (2000).

Y. Y. Hung, L. Lin, H. M. Shang, B. G. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39, 143–149 (2000).
[CrossRef]

1999 (1)

P. S. Huang, Q. Hu, F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

1997 (2)

G. S. Spagnolo, D. Paoletti, D. Ambrosini, “Vibration monitoring by fiber optic fringe projection and Fourier tranaform analysis,” Opt. Commun. 139, 17–23 (1997).
[CrossRef]

M. Pedersen, W. Olthuis, P. Bergveld, “Harmonic distortion in silicon condenser microphones,” J. Acoust. Soc. Am. 102, 1582–1587 (1997).
[CrossRef]

1996 (1)

Z. Wang, M. S. Graca, P. J. Bryanston-Cross, D. J. Whitehouse, “Phase-shifted image matching algorithm for displacement measurement,” Opt. Eng. 35, 2327–2332 (1996).
[CrossRef]

1995 (1)

C. Quan, C. J. Tay, H. M. Shang, P. J. Bryanston-Cross, “Contour measurement by fibre optics fringe projection and Fourier transform analysis,” Opt. Commun. 119, 479–483 (1995).
[CrossRef]

1994 (4)

W. S. Zhou, X. Y. Su, “A direct mapping algorithm for phase measuring profilometry,” J. Mod. Opt. 41, 89–94 (1994).
[CrossRef]

J. Bergqvist, J. Gobet, “Capacitive microphone with a surface micromachined backplate using electroplating technology,” J. Microelectromech. Syst. 3, 69–75 (1994).
[CrossRef]

P. R. Scheeper, A. G. H. van der Donk, W. Olthuis, P. Bergveld, “Review of silicon microphone,” Sens. Actuators A44, 1–11 (1994).
[CrossRef]

D. R. Burton, M. J. Lalor, “Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping,” Appl. Opt. 33, 2939–2947 (1994).
[CrossRef] [PubMed]

1992 (2)

X. Y. Su, W. S. Zhou, G. Vonbally, D. Vukicevic, “Automated phase measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

J. C. Wyant, K. Creath, “Advances in interferometric optical profiling,” Int. J. Mach. Tools Manuf. 32, 5–10 (1992).
[CrossRef]

1991 (3)

G. M. Sessler, “Acoustic sensors,” Sens. Actuators A25–A27, 323–330 (1991.
[CrossRef]

P. Carelli, D. Paoletti, G. S. Spagnolo, “Holographic of surface defects in artwork,” Opt. Eng. 30, 1294–1298 (1991).
[CrossRef]

Y. Z. Dai, F. P. Chiang, “Contouring by moiré interferometry,” Exp. Mech. 31, 76–81 (1991).
[CrossRef]

1990 (1)

C. Quan, P. J. Bryanston-Cross, “Double-source holographic contouring using fibre optics,” Opt. Laser Technol. 22, 255–259 (1990).
[CrossRef]

1985 (1)

1977 (1)

Alfred, A.

H. Eugene, A. Alfred, Optics (Addison-Wesley, London, 1979).

Ambrosini, D.

G. S. Spagnolo, D. Paoletti, D. Ambrosini, “Vibration monitoring by fiber optic fringe projection and Fourier tranaform analysis,” Opt. Commun. 139, 17–23 (1997).
[CrossRef]

Bergqvist, J.

J. Bergqvist, J. Gobet, “Capacitive microphone with a surface micromachined backplate using electroplating technology,” J. Microelectromech. Syst. 3, 69–75 (1994).
[CrossRef]

Bergveld, P.

M. Pedersen, W. Olthuis, P. Bergveld, “Harmonic distortion in silicon condenser microphones,” J. Acoust. Soc. Am. 102, 1582–1587 (1997).
[CrossRef]

P. R. Scheeper, A. G. H. van der Donk, W. Olthuis, P. Bergveld, “Review of silicon microphone,” Sens. Actuators A44, 1–11 (1994).
[CrossRef]

Bryanston-Cross, P. J.

Z. Wang, M. S. Graca, P. J. Bryanston-Cross, D. J. Whitehouse, “Phase-shifted image matching algorithm for displacement measurement,” Opt. Eng. 35, 2327–2332 (1996).
[CrossRef]

C. Quan, C. J. Tay, H. M. Shang, P. J. Bryanston-Cross, “Contour measurement by fibre optics fringe projection and Fourier transform analysis,” Opt. Commun. 119, 479–483 (1995).
[CrossRef]

C. Quan, P. J. Bryanston-Cross, “Double-source holographic contouring using fibre optics,” Opt. Laser Technol. 22, 255–259 (1990).
[CrossRef]

Burton, D. R.

Carelli, P.

P. Carelli, D. Paoletti, G. S. Spagnolo, “Holographic of surface defects in artwork,” Opt. Eng. 30, 1294–1298 (1991).
[CrossRef]

Chiang, F. P.

P. S. Huang, Q. Hu, F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Y. Z. Dai, F. P. Chiang, “Contouring by moiré interferometry,” Exp. Mech. 31, 76–81 (1991).
[CrossRef]

Creath, K.

J. C. Wyant, K. Creath, “Advances in interferometric optical profiling,” Int. J. Mach. Tools Manuf. 32, 5–10 (1992).
[CrossRef]

K. Creath, “Phase-shifting speck interferometry,” Appl. Opt. 24, 3053–3058 (1985).
[CrossRef]

K. Creath, “High resolution optical profile,” in Surface Characterization and Testing II, J. E. Greiven Kamp, M. Young, eds., Proc. SPIE1164, 142–147 (1989).
[CrossRef]

Dai, Y. Z.

Y. Z. Dai, F. P. Chiang, “Contouring by moiré interferometry,” Exp. Mech. 31, 76–81 (1991).
[CrossRef]

Eugene, H.

H. Eugene, A. Alfred, Optics (Addison-Wesley, London, 1979).

Gobet, J.

J. Bergqvist, J. Gobet, “Capacitive microphone with a surface micromachined backplate using electroplating technology,” J. Microelectromech. Syst. 3, 69–75 (1994).
[CrossRef]

Graca, M. S.

Z. Wang, M. S. Graca, P. J. Bryanston-Cross, D. J. Whitehouse, “Phase-shifted image matching algorithm for displacement measurement,” Opt. Eng. 35, 2327–2332 (1996).
[CrossRef]

Helen, S. S.

S. S. Helen, M. P. Kothiyal, R. S. Sirohi, “White-light interferometry with polarization phase-shifter at the input of the interferometer,” J. Mod. Opt. 47, 1137–1145 (2000).
[CrossRef]

Hu, Q.

P. S. Huang, Q. Hu, F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Huang, P. S.

P. S. Huang, Q. Hu, F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Hung, Y. Y.

Y. Y. Hung, L. Lin, H. M. Shang, B. G. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39, 143–149 (2000).
[CrossRef]

Idesawa, M.

Kim, S. H.

J. H. Yi, S. H. Kim, Y. K. Kwak, “A nanometric displacement measurement method using the detection of fringe peak movement,” Meas. Sci. Technol. 11, 1353–1358 (2000).
[CrossRef]

Kothiyal, M. P.

S. S. Helen, M. P. Kothiyal, R. S. Sirohi, “White-light interferometry with polarization phase-shifter at the input of the interferometer,” J. Mod. Opt. 47, 1137–1145 (2000).
[CrossRef]

Kwak, Y. K.

J. H. Yi, S. H. Kim, Y. K. Kwak, “A nanometric displacement measurement method using the detection of fringe peak movement,” Meas. Sci. Technol. 11, 1353–1358 (2000).
[CrossRef]

Lalor, M. J.

Lin, L.

Y. Y. Hung, L. Lin, H. M. Shang, B. G. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39, 143–149 (2000).
[CrossRef]

Olthuis, W.

M. Pedersen, W. Olthuis, P. Bergveld, “Harmonic distortion in silicon condenser microphones,” J. Acoust. Soc. Am. 102, 1582–1587 (1997).
[CrossRef]

P. R. Scheeper, A. G. H. van der Donk, W. Olthuis, P. Bergveld, “Review of silicon microphone,” Sens. Actuators A44, 1–11 (1994).
[CrossRef]

Paoletti, D.

G. S. Spagnolo, D. Paoletti, D. Ambrosini, “Vibration monitoring by fiber optic fringe projection and Fourier tranaform analysis,” Opt. Commun. 139, 17–23 (1997).
[CrossRef]

P. Carelli, D. Paoletti, G. S. Spagnolo, “Holographic of surface defects in artwork,” Opt. Eng. 30, 1294–1298 (1991).
[CrossRef]

Park, B. G.

Y. Y. Hung, L. Lin, H. M. Shang, B. G. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39, 143–149 (2000).
[CrossRef]

Pedersen, M.

M. Pedersen, W. Olthuis, P. Bergveld, “Harmonic distortion in silicon condenser microphones,” J. Acoust. Soc. Am. 102, 1582–1587 (1997).
[CrossRef]

Piotr, P. K.

P. K. Piotr, “Polarization based fringe projection interferometer for phase stepping techniques,” in Optical Inspection and Micromeasurements, C. Goreki, ed., Proc. SPIE.2782, 250–257 (1996).
[CrossRef]

Quan, C.

C. Quan, C. J. Tay, H. M. Shang, P. J. Bryanston-Cross, “Contour measurement by fibre optics fringe projection and Fourier transform analysis,” Opt. Commun. 119, 479–483 (1995).
[CrossRef]

C. Quan, P. J. Bryanston-Cross, “Double-source holographic contouring using fibre optics,” Opt. Laser Technol. 22, 255–259 (1990).
[CrossRef]

Quan, C. G.

S. H. Wang, C. J. Tay, C. G. Quan, H. M. Shang, “An optical fiber fringe projector for micro-component,” Optik (Stuttgart) 111, 419–422 (2000).

Scheeper, P. R.

P. R. Scheeper, A. G. H. van der Donk, W. Olthuis, P. Bergveld, “Review of silicon microphone,” Sens. Actuators A44, 1–11 (1994).
[CrossRef]

Sessler, G. M.

G. M. Sessler, “Acoustic sensors,” Sens. Actuators A25–A27, 323–330 (1991.
[CrossRef]

Shang, H. M.

S. H. Wang, C. J. Tay, C. G. Quan, H. M. Shang, “An optical fiber fringe projector for micro-component,” Optik (Stuttgart) 111, 419–422 (2000).

Y. Y. Hung, L. Lin, H. M. Shang, B. G. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39, 143–149 (2000).
[CrossRef]

C. Quan, C. J. Tay, H. M. Shang, P. J. Bryanston-Cross, “Contour measurement by fibre optics fringe projection and Fourier transform analysis,” Opt. Commun. 119, 479–483 (1995).
[CrossRef]

Sirohi, R. S.

S. S. Helen, M. P. Kothiyal, R. S. Sirohi, “White-light interferometry with polarization phase-shifter at the input of the interferometer,” J. Mod. Opt. 47, 1137–1145 (2000).
[CrossRef]

Soma, T.

Spagnolo, G. S.

G. S. Spagnolo, D. Paoletti, D. Ambrosini, “Vibration monitoring by fiber optic fringe projection and Fourier tranaform analysis,” Opt. Commun. 139, 17–23 (1997).
[CrossRef]

P. Carelli, D. Paoletti, G. S. Spagnolo, “Holographic of surface defects in artwork,” Opt. Eng. 30, 1294–1298 (1991).
[CrossRef]

Su, X. Y.

W. S. Zhou, X. Y. Su, “A direct mapping algorithm for phase measuring profilometry,” J. Mod. Opt. 41, 89–94 (1994).
[CrossRef]

X. Y. Su, W. S. Zhou, G. Vonbally, D. Vukicevic, “Automated phase measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

Tay, C. J.

S. H. Wang, C. J. Tay, C. G. Quan, H. M. Shang, “An optical fiber fringe projector for micro-component,” Optik (Stuttgart) 111, 419–422 (2000).

C. Quan, C. J. Tay, H. M. Shang, P. J. Bryanston-Cross, “Contour measurement by fibre optics fringe projection and Fourier transform analysis,” Opt. Commun. 119, 479–483 (1995).
[CrossRef]

van der Donk, A. G. H.

P. R. Scheeper, A. G. H. van der Donk, W. Olthuis, P. Bergveld, “Review of silicon microphone,” Sens. Actuators A44, 1–11 (1994).
[CrossRef]

Vonbally, G.

X. Y. Su, W. S. Zhou, G. Vonbally, D. Vukicevic, “Automated phase measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

Vukicevic, D.

X. Y. Su, W. S. Zhou, G. Vonbally, D. Vukicevic, “Automated phase measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

Wang, S. H.

S. H. Wang, C. J. Tay, C. G. Quan, H. M. Shang, “An optical fiber fringe projector for micro-component,” Optik (Stuttgart) 111, 419–422 (2000).

Wang, Z.

Z. Wang, M. S. Graca, P. J. Bryanston-Cross, D. J. Whitehouse, “Phase-shifted image matching algorithm for displacement measurement,” Opt. Eng. 35, 2327–2332 (1996).
[CrossRef]

Whitehouse, D. J.

Z. Wang, M. S. Graca, P. J. Bryanston-Cross, D. J. Whitehouse, “Phase-shifted image matching algorithm for displacement measurement,” Opt. Eng. 35, 2327–2332 (1996).
[CrossRef]

Wyant, J. C.

J. C. Wyant, K. Creath, “Advances in interferometric optical profiling,” Int. J. Mach. Tools Manuf. 32, 5–10 (1992).
[CrossRef]

Yatagai, T.

Yi, J. H.

J. H. Yi, S. H. Kim, Y. K. Kwak, “A nanometric displacement measurement method using the detection of fringe peak movement,” Meas. Sci. Technol. 11, 1353–1358 (2000).
[CrossRef]

Zhou, W. S.

W. S. Zhou, X. Y. Su, “A direct mapping algorithm for phase measuring profilometry,” J. Mod. Opt. 41, 89–94 (1994).
[CrossRef]

X. Y. Su, W. S. Zhou, G. Vonbally, D. Vukicevic, “Automated phase measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

Appl. Opt. (3)

Exp. Mech. (1)

Y. Z. Dai, F. P. Chiang, “Contouring by moiré interferometry,” Exp. Mech. 31, 76–81 (1991).
[CrossRef]

Int. J. Mach. Tools Manuf. (1)

J. C. Wyant, K. Creath, “Advances in interferometric optical profiling,” Int. J. Mach. Tools Manuf. 32, 5–10 (1992).
[CrossRef]

J. Acoust. Soc. Am. (1)

M. Pedersen, W. Olthuis, P. Bergveld, “Harmonic distortion in silicon condenser microphones,” J. Acoust. Soc. Am. 102, 1582–1587 (1997).
[CrossRef]

J. Microelectromech. Syst. (1)

J. Bergqvist, J. Gobet, “Capacitive microphone with a surface micromachined backplate using electroplating technology,” J. Microelectromech. Syst. 3, 69–75 (1994).
[CrossRef]

J. Mod. Opt. (2)

S. S. Helen, M. P. Kothiyal, R. S. Sirohi, “White-light interferometry with polarization phase-shifter at the input of the interferometer,” J. Mod. Opt. 47, 1137–1145 (2000).
[CrossRef]

W. S. Zhou, X. Y. Su, “A direct mapping algorithm for phase measuring profilometry,” J. Mod. Opt. 41, 89–94 (1994).
[CrossRef]

Meas. Sci. Technol. (1)

J. H. Yi, S. H. Kim, Y. K. Kwak, “A nanometric displacement measurement method using the detection of fringe peak movement,” Meas. Sci. Technol. 11, 1353–1358 (2000).
[CrossRef]

Opt. Commun. (3)

C. Quan, C. J. Tay, H. M. Shang, P. J. Bryanston-Cross, “Contour measurement by fibre optics fringe projection and Fourier transform analysis,” Opt. Commun. 119, 479–483 (1995).
[CrossRef]

X. Y. Su, W. S. Zhou, G. Vonbally, D. Vukicevic, “Automated phase measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[CrossRef]

G. S. Spagnolo, D. Paoletti, D. Ambrosini, “Vibration monitoring by fiber optic fringe projection and Fourier tranaform analysis,” Opt. Commun. 139, 17–23 (1997).
[CrossRef]

Opt. Eng. (4)

P. S. Huang, Q. Hu, F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Y. Y. Hung, L. Lin, H. M. Shang, B. G. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39, 143–149 (2000).
[CrossRef]

P. Carelli, D. Paoletti, G. S. Spagnolo, “Holographic of surface defects in artwork,” Opt. Eng. 30, 1294–1298 (1991).
[CrossRef]

Z. Wang, M. S. Graca, P. J. Bryanston-Cross, D. J. Whitehouse, “Phase-shifted image matching algorithm for displacement measurement,” Opt. Eng. 35, 2327–2332 (1996).
[CrossRef]

Opt. Laser Technol. (1)

C. Quan, P. J. Bryanston-Cross, “Double-source holographic contouring using fibre optics,” Opt. Laser Technol. 22, 255–259 (1990).
[CrossRef]

Optik (Stuttgart) (1)

S. H. Wang, C. J. Tay, C. G. Quan, H. M. Shang, “An optical fiber fringe projector for micro-component,” Optik (Stuttgart) 111, 419–422 (2000).

Sens. Actuators (2)

G. M. Sessler, “Acoustic sensors,” Sens. Actuators A25–A27, 323–330 (1991.
[CrossRef]

P. R. Scheeper, A. G. H. van der Donk, W. Olthuis, P. Bergveld, “Review of silicon microphone,” Sens. Actuators A44, 1–11 (1994).
[CrossRef]

Other (3)

P. K. Piotr, “Polarization based fringe projection interferometer for phase stepping techniques,” in Optical Inspection and Micromeasurements, C. Goreki, ed., Proc. SPIE.2782, 250–257 (1996).
[CrossRef]

K. Creath, “High resolution optical profile,” in Surface Characterization and Testing II, J. E. Greiven Kamp, M. Young, eds., Proc. SPIE1164, 142–147 (1989).
[CrossRef]

H. Eugene, A. Alfred, Optics (Addison-Wesley, London, 1979).

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of two-point-light-source interferometry with an optical fiber and an optical wedge.

Fig. 2
Fig. 2

Optical geometry for analysis of fringe projection.

Fig. 3
Fig. 3

Experimental setup.

Fig. 4
Fig. 4

(a) Microphone chip. (b) Cross sectional view of the microphone. IC, integrated circuit.

Fig. 5
Fig. 5

Fringe pattern with phase shifts of (a) 0°, (b) 90°, (c) 180°, and (d) 270°.

Fig. 6
Fig. 6

Gray values of the fringe pattern.

Fig. 7
Fig. 7

Relation between phase shifting (∇φ) and fiber displacement (δ).

Fig. 8
Fig. 8

Newton’s rings without a linear fringe pattern.

Fig. 9
Fig. 9

(a) Initial unwrapped phase map of the membrane, (b) plot across the membrane profile in phase (radians), (c) plot of the profile’s height (nanometers) V, volts.

Fig. 10
Fig. 10

Membrane profile at three applied voltages. V, volts.

Fig. 11
Fig. 11

Three-dimensional perspective plot of the step etched upon the silicon substrate.

Fig. 12
Fig. 12

Comparison of cross-sectional profiles of the step measured by (a) the proposed method and (b) the stylus method.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

P0=D/dλ,
t=L tan θ,
d=2t tan β sin α,
sin α=n0 sin β,
d=L sin α tanarcsinn0 sin αtan θ.
d=K tan θ,
P0=DλK tan θ.
Δ=d/Dδ,
δφ=2πdDλδ.
I=a+b cosφ+δφ,
I1=a+b cos φ,
I2=a+b cosφ+δφ2,
I3=a+b cosφ+δφ3,
I4=a+b cosφ+δφ4,
tan φ=I3-I1cos δφ4-cos δφ2-I4-I2cos δφ3-1I3-I1sin δφ4-sin δφ2-I4-I2sin δφ3.
φ=arctanI4-I2I1-I3.
hx=Δxtan ϕ=NxP0tan ϕ,
hx=P0φx2π tan ϕ=Cφx,

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