Abstract

White-light scanning interferometry (WLSI) is a useful technique to measure surface profile when a test object contains discontinuous structures or microstructures. A black and white CCD camera is usually utilized to capture interferograms, and a series of corresponding algorithms is used to achieve the profile measurement. However, the color information in the interferograms is lost. A novel profile measurement method that uses phase information in different color channels (red–green–blue) of an interferogram obtained using a three-chip color CCD in WLSI is proposed. The phase values are extracted by a windowed Fourier transform algorithm. Simulation and experimental results are presented to demonstrate the validity of the proposed method.

© 2011 Optical Society of America

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  1. S. Mirza and C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44, 013601 (2005).
    [CrossRef]
  2. O. Sasaki and H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
    [CrossRef] [PubMed]
  3. T. Anna, S. K. Dubey, C. Shakher, A. Roy, and D. S. Mehta, “Sinusoidal fringe projection system based on compact and non-mechanical scanning low-coherence Michelson interferometer for three-dimensional shape measurement,” Opt. Commun. 282, 1237–1242 (2009).
    [CrossRef]
  4. J. C. Wyant, “White light interferometry,” Proc. SPIE 4737, 98–107 (2002).
    [CrossRef]
  5. J. Schmit and A. Olszak, “High-precision shape measurement by white-light interferometry with real-time scanner error correction,” Appl. Opt. 41, 5943–5950 (2002).
    [CrossRef] [PubMed]
  6. S. W. Kim and G. H. Kim, “Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry,” Appl. Opt. 38, 5968–5973 (1999).
    [CrossRef]
  7. J. C. Wyant and K. Creath, “Advances in interferometric optical profiling,” Int. J. Mach. Tools Manuf. 32, 5–10 (1992).
    [CrossRef]
  8. G. S. Kino and S. S. C. Chim, “Mirau correlation microscope,” Appl. Opt. 29, 3775–3783 (1990).
    [CrossRef] [PubMed]
  9. M. C. Park and S. W. Kim, “Direct quadratic polynomial fitting for fringe peak detection of white light scanning interferograms,” Opt. Eng. 39, 952–959 (2000).
    [CrossRef]
  10. S. Chen, A. W. Palmer, K. T. V. Grattan, and B. T. Meggitt, “Digital signal-processing techniques for electronically scanned optical-fiber white-light interferometry,” Appl. Opt. 31, 6003–6010 (1992).
    [CrossRef] [PubMed]
  11. K. G. Larkin, “Efficient nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Soc. Am. A 13, 832–843 (1996).
    [CrossRef]
  12. P. Sandoz, “An algorithm for profilometry by white-light phase-shifting interferometry,” J. Mod. Opt. 43, 1545–1554(1996).
  13. M. Li, C. Quan, and C. J. Tay, “Continuous wavelet transform for micro-component profile measurement using vertical scanning interferometry,” Opt. Laser Technol. 40, 920–929(2008).
    [CrossRef]
  14. P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
    [CrossRef]
  15. P. de Groot, X. C. D. Lega, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt. 41, 4571–4578 (2002).
    [CrossRef] [PubMed]
  16. Z. Zhang, D. P. Towers, and C. E. Towers, “Snapshot color fringe projection for absolute three-dimensional metrology of video sequences,” Appl. Opt. 49, 5947–5953 (2010).
    [CrossRef]
  17. J. M. Desse, F. Albe, and J. L. Tribillon, “Real-time color holographic interferometry,” Appl. Opt. 41, 5326–5333 (2002).
    [CrossRef] [PubMed]
  18. J. M. Dessel, P. Picart, and P. Tankam, “Digital three-color holographic interferometry for flow analysis,” Opt. Express 16, 5471–5480 (2008).
    [CrossRef]
  19. J. M. Desse, “Three-color differential interferometry,” Appl. Opt. 36, 7150–7156 (1997).
    [CrossRef]
  20. A. Pförtner and J. Schwider, “Red–Green–Blue interferometer for the metrology of discontinuous structures,” Appl. Opt. 42, 667–673 (2003).
    [CrossRef] [PubMed]
  21. H. C. Hsu, C. H. Tung, C. F. Kao, and C. C. Chang, “A white-light profiling algorithm adopting the multiwavelength interferometric technique,” Proc. SPIE 5531, 244–249 (2004).
    [CrossRef]
  22. M. Pawlowski, Y. Sakano, Y. Miyamoto, and M. Takeda, “Multi-spectral phase-crossing white-light interferometry,” Proc. SPIE 5776, 88–93 (2005).
    [CrossRef]
  23. M. Pawlowski, Y. Sakano, Y. Miyamoto, and M. Takeda, “Phase-crossing algorithm for white-light fringes analysis,” Opt. Commun. 260, 68–72 (2006).
    [CrossRef]
  24. Z. Buchta, P. Jedlička, M. Matějka, V. Kolařík, B. Mikel, J. Lazar, and O. Číp, “White-light interference fringe detection using color CCD camera,” in the Proceedings of IEEE AFRICON 2009 (IEEE, 2009), pp. 1–5.
    [CrossRef]
  25. M. Li, “Development of fringe analysis techniques in white light interferometry for micro-component measurement,” Ph.D. thesis (National University of Singapore, 2008).
  26. M. Born and E. Wolf, Principles of Optics, 6th ed.(Pergamon, 1980).
  27. K. Qian, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).
    [CrossRef]
  28. K. Qian, H. Wang, and W. Gao, “Windowed Fourier transform for fringe pattern analysis: theoretical analyses,” Appl. Opt. 47, 5408–5419 (2008).
    [CrossRef]
  29. C. Quan, H. Niu, and C. J. Tay, “An improved windowed Fourier transform for fringe demodulation,” Opt. Laser Technol. 42, 126–131 (2010).
    [CrossRef]
  30. L. Bruno, G. Felice, and A. Poggialini, “Design and calibration of a piezoelectric actuator for interferometric applications,” Opt. Lasers Eng. 45, 1148–1156 (2007).
    [CrossRef]
  31. S. Ma, C. Quan, R. Zhu, C. J. Tay, L. Chen, and Z. Gao, “Micro-profile measurement based on windowed Fourier transform in white-light scanning interferometry,” Opt. Commun. 284, 2488–2493 (2011).
    [CrossRef]

2011 (1)

S. Ma, C. Quan, R. Zhu, C. J. Tay, L. Chen, and Z. Gao, “Micro-profile measurement based on windowed Fourier transform in white-light scanning interferometry,” Opt. Commun. 284, 2488–2493 (2011).
[CrossRef]

2010 (2)

C. Quan, H. Niu, and C. J. Tay, “An improved windowed Fourier transform for fringe demodulation,” Opt. Laser Technol. 42, 126–131 (2010).
[CrossRef]

Z. Zhang, D. P. Towers, and C. E. Towers, “Snapshot color fringe projection for absolute three-dimensional metrology of video sequences,” Appl. Opt. 49, 5947–5953 (2010).
[CrossRef]

2009 (1)

T. Anna, S. K. Dubey, C. Shakher, A. Roy, and D. S. Mehta, “Sinusoidal fringe projection system based on compact and non-mechanical scanning low-coherence Michelson interferometer for three-dimensional shape measurement,” Opt. Commun. 282, 1237–1242 (2009).
[CrossRef]

2008 (3)

2007 (2)

L. Bruno, G. Felice, and A. Poggialini, “Design and calibration of a piezoelectric actuator for interferometric applications,” Opt. Lasers Eng. 45, 1148–1156 (2007).
[CrossRef]

K. Qian, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).
[CrossRef]

2006 (1)

M. Pawlowski, Y. Sakano, Y. Miyamoto, and M. Takeda, “Phase-crossing algorithm for white-light fringes analysis,” Opt. Commun. 260, 68–72 (2006).
[CrossRef]

2005 (2)

M. Pawlowski, Y. Sakano, Y. Miyamoto, and M. Takeda, “Multi-spectral phase-crossing white-light interferometry,” Proc. SPIE 5776, 88–93 (2005).
[CrossRef]

S. Mirza and C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44, 013601 (2005).
[CrossRef]

2004 (1)

H. C. Hsu, C. H. Tung, C. F. Kao, and C. C. Chang, “A white-light profiling algorithm adopting the multiwavelength interferometric technique,” Proc. SPIE 5531, 244–249 (2004).
[CrossRef]

2003 (1)

2002 (4)

2000 (1)

M. C. Park and S. W. Kim, “Direct quadratic polynomial fitting for fringe peak detection of white light scanning interferograms,” Opt. Eng. 39, 952–959 (2000).
[CrossRef]

1999 (1)

1997 (1)

1996 (2)

K. G. Larkin, “Efficient nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Soc. Am. A 13, 832–843 (1996).
[CrossRef]

P. Sandoz, “An algorithm for profilometry by white-light phase-shifting interferometry,” J. Mod. Opt. 43, 1545–1554(1996).

1995 (1)

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

1992 (2)

1990 (1)

1986 (1)

Albe, F.

Anna, T.

T. Anna, S. K. Dubey, C. Shakher, A. Roy, and D. S. Mehta, “Sinusoidal fringe projection system based on compact and non-mechanical scanning low-coherence Michelson interferometer for three-dimensional shape measurement,” Opt. Commun. 282, 1237–1242 (2009).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed.(Pergamon, 1980).

Bruno, L.

L. Bruno, G. Felice, and A. Poggialini, “Design and calibration of a piezoelectric actuator for interferometric applications,” Opt. Lasers Eng. 45, 1148–1156 (2007).
[CrossRef]

Buchta, Z.

Z. Buchta, P. Jedlička, M. Matějka, V. Kolařík, B. Mikel, J. Lazar, and O. Číp, “White-light interference fringe detection using color CCD camera,” in the Proceedings of IEEE AFRICON 2009 (IEEE, 2009), pp. 1–5.
[CrossRef]

Chang, C. C.

H. C. Hsu, C. H. Tung, C. F. Kao, and C. C. Chang, “A white-light profiling algorithm adopting the multiwavelength interferometric technique,” Proc. SPIE 5531, 244–249 (2004).
[CrossRef]

Chen, L.

S. Ma, C. Quan, R. Zhu, C. J. Tay, L. Chen, and Z. Gao, “Micro-profile measurement based on windowed Fourier transform in white-light scanning interferometry,” Opt. Commun. 284, 2488–2493 (2011).
[CrossRef]

Chen, S.

Chim, S. S. C.

Cíp, O.

Z. Buchta, P. Jedlička, M. Matějka, V. Kolařík, B. Mikel, J. Lazar, and O. Číp, “White-light interference fringe detection using color CCD camera,” in the Proceedings of IEEE AFRICON 2009 (IEEE, 2009), pp. 1–5.
[CrossRef]

Creath, K.

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

de Groot, P.

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

Deck, L.

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

Desse, J. M.

Dessel, J. M.

Dubey, S. K.

T. Anna, S. K. Dubey, C. Shakher, A. Roy, and D. S. Mehta, “Sinusoidal fringe projection system based on compact and non-mechanical scanning low-coherence Michelson interferometer for three-dimensional shape measurement,” Opt. Commun. 282, 1237–1242 (2009).
[CrossRef]

Felice, G.

L. Bruno, G. Felice, and A. Poggialini, “Design and calibration of a piezoelectric actuator for interferometric applications,” Opt. Lasers Eng. 45, 1148–1156 (2007).
[CrossRef]

Gao, W.

Gao, Z.

S. Ma, C. Quan, R. Zhu, C. J. Tay, L. Chen, and Z. Gao, “Micro-profile measurement based on windowed Fourier transform in white-light scanning interferometry,” Opt. Commun. 284, 2488–2493 (2011).
[CrossRef]

Grattan, K. T. V.

Hsu, H. C.

H. C. Hsu, C. H. Tung, C. F. Kao, and C. C. Chang, “A white-light profiling algorithm adopting the multiwavelength interferometric technique,” Proc. SPIE 5531, 244–249 (2004).
[CrossRef]

Jedlicka, P.

Z. Buchta, P. Jedlička, M. Matějka, V. Kolařík, B. Mikel, J. Lazar, and O. Číp, “White-light interference fringe detection using color CCD camera,” in the Proceedings of IEEE AFRICON 2009 (IEEE, 2009), pp. 1–5.
[CrossRef]

Kao, C. F.

H. C. Hsu, C. H. Tung, C. F. Kao, and C. C. Chang, “A white-light profiling algorithm adopting the multiwavelength interferometric technique,” Proc. SPIE 5531, 244–249 (2004).
[CrossRef]

Kim, G. H.

Kim, S. W.

M. C. Park and S. W. Kim, “Direct quadratic polynomial fitting for fringe peak detection of white light scanning interferograms,” Opt. Eng. 39, 952–959 (2000).
[CrossRef]

S. W. Kim and G. H. Kim, “Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry,” Appl. Opt. 38, 5968–5973 (1999).
[CrossRef]

Kino, G. S.

Kolarík, V.

Z. Buchta, P. Jedlička, M. Matějka, V. Kolařík, B. Mikel, J. Lazar, and O. Číp, “White-light interference fringe detection using color CCD camera,” in the Proceedings of IEEE AFRICON 2009 (IEEE, 2009), pp. 1–5.
[CrossRef]

Kramer, J.

Larkin, K. G.

Lazar, J.

Z. Buchta, P. Jedlička, M. Matějka, V. Kolařík, B. Mikel, J. Lazar, and O. Číp, “White-light interference fringe detection using color CCD camera,” in the Proceedings of IEEE AFRICON 2009 (IEEE, 2009), pp. 1–5.
[CrossRef]

Lega, X. C. D.

Li, M.

M. Li, C. Quan, and C. J. Tay, “Continuous wavelet transform for micro-component profile measurement using vertical scanning interferometry,” Opt. Laser Technol. 40, 920–929(2008).
[CrossRef]

M. Li, “Development of fringe analysis techniques in white light interferometry for micro-component measurement,” Ph.D. thesis (National University of Singapore, 2008).

Ma, S.

S. Ma, C. Quan, R. Zhu, C. J. Tay, L. Chen, and Z. Gao, “Micro-profile measurement based on windowed Fourier transform in white-light scanning interferometry,” Opt. Commun. 284, 2488–2493 (2011).
[CrossRef]

Matejka, M.

Z. Buchta, P. Jedlička, M. Matějka, V. Kolařík, B. Mikel, J. Lazar, and O. Číp, “White-light interference fringe detection using color CCD camera,” in the Proceedings of IEEE AFRICON 2009 (IEEE, 2009), pp. 1–5.
[CrossRef]

Meggitt, B. T.

Mehta, D. S.

T. Anna, S. K. Dubey, C. Shakher, A. Roy, and D. S. Mehta, “Sinusoidal fringe projection system based on compact and non-mechanical scanning low-coherence Michelson interferometer for three-dimensional shape measurement,” Opt. Commun. 282, 1237–1242 (2009).
[CrossRef]

Mikel, B.

Z. Buchta, P. Jedlička, M. Matějka, V. Kolařík, B. Mikel, J. Lazar, and O. Číp, “White-light interference fringe detection using color CCD camera,” in the Proceedings of IEEE AFRICON 2009 (IEEE, 2009), pp. 1–5.
[CrossRef]

Mirza, S.

S. Mirza and C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44, 013601 (2005).
[CrossRef]

Miyamoto, Y.

M. Pawlowski, Y. Sakano, Y. Miyamoto, and M. Takeda, “Phase-crossing algorithm for white-light fringes analysis,” Opt. Commun. 260, 68–72 (2006).
[CrossRef]

M. Pawlowski, Y. Sakano, Y. Miyamoto, and M. Takeda, “Multi-spectral phase-crossing white-light interferometry,” Proc. SPIE 5776, 88–93 (2005).
[CrossRef]

Niu, H.

C. Quan, H. Niu, and C. J. Tay, “An improved windowed Fourier transform for fringe demodulation,” Opt. Laser Technol. 42, 126–131 (2010).
[CrossRef]

Okazaki, H.

Olszak, A.

Palmer, A. W.

Park, M. C.

M. C. Park and S. W. Kim, “Direct quadratic polynomial fitting for fringe peak detection of white light scanning interferograms,” Opt. Eng. 39, 952–959 (2000).
[CrossRef]

Pawlowski, M.

M. Pawlowski, Y. Sakano, Y. Miyamoto, and M. Takeda, “Phase-crossing algorithm for white-light fringes analysis,” Opt. Commun. 260, 68–72 (2006).
[CrossRef]

M. Pawlowski, Y. Sakano, Y. Miyamoto, and M. Takeda, “Multi-spectral phase-crossing white-light interferometry,” Proc. SPIE 5776, 88–93 (2005).
[CrossRef]

Pförtner, A.

Picart, P.

Poggialini, A.

L. Bruno, G. Felice, and A. Poggialini, “Design and calibration of a piezoelectric actuator for interferometric applications,” Opt. Lasers Eng. 45, 1148–1156 (2007).
[CrossRef]

Qian, K.

K. Qian, H. Wang, and W. Gao, “Windowed Fourier transform for fringe pattern analysis: theoretical analyses,” Appl. Opt. 47, 5408–5419 (2008).
[CrossRef]

K. Qian, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).
[CrossRef]

Quan, C.

S. Ma, C. Quan, R. Zhu, C. J. Tay, L. Chen, and Z. Gao, “Micro-profile measurement based on windowed Fourier transform in white-light scanning interferometry,” Opt. Commun. 284, 2488–2493 (2011).
[CrossRef]

C. Quan, H. Niu, and C. J. Tay, “An improved windowed Fourier transform for fringe demodulation,” Opt. Laser Technol. 42, 126–131 (2010).
[CrossRef]

M. Li, C. Quan, and C. J. Tay, “Continuous wavelet transform for micro-component profile measurement using vertical scanning interferometry,” Opt. Laser Technol. 40, 920–929(2008).
[CrossRef]

Roy, A.

T. Anna, S. K. Dubey, C. Shakher, A. Roy, and D. S. Mehta, “Sinusoidal fringe projection system based on compact and non-mechanical scanning low-coherence Michelson interferometer for three-dimensional shape measurement,” Opt. Commun. 282, 1237–1242 (2009).
[CrossRef]

Sakano, Y.

M. Pawlowski, Y. Sakano, Y. Miyamoto, and M. Takeda, “Phase-crossing algorithm for white-light fringes analysis,” Opt. Commun. 260, 68–72 (2006).
[CrossRef]

M. Pawlowski, Y. Sakano, Y. Miyamoto, and M. Takeda, “Multi-spectral phase-crossing white-light interferometry,” Proc. SPIE 5776, 88–93 (2005).
[CrossRef]

Sandoz, P.

P. Sandoz, “An algorithm for profilometry by white-light phase-shifting interferometry,” J. Mod. Opt. 43, 1545–1554(1996).

Sasaki, O.

Schmit, J.

Schwider, J.

Shakher, C.

T. Anna, S. K. Dubey, C. Shakher, A. Roy, and D. S. Mehta, “Sinusoidal fringe projection system based on compact and non-mechanical scanning low-coherence Michelson interferometer for three-dimensional shape measurement,” Opt. Commun. 282, 1237–1242 (2009).
[CrossRef]

S. Mirza and C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44, 013601 (2005).
[CrossRef]

Takeda, M.

M. Pawlowski, Y. Sakano, Y. Miyamoto, and M. Takeda, “Phase-crossing algorithm for white-light fringes analysis,” Opt. Commun. 260, 68–72 (2006).
[CrossRef]

M. Pawlowski, Y. Sakano, Y. Miyamoto, and M. Takeda, “Multi-spectral phase-crossing white-light interferometry,” Proc. SPIE 5776, 88–93 (2005).
[CrossRef]

Tankam, P.

Tay, C. J.

S. Ma, C. Quan, R. Zhu, C. J. Tay, L. Chen, and Z. Gao, “Micro-profile measurement based on windowed Fourier transform in white-light scanning interferometry,” Opt. Commun. 284, 2488–2493 (2011).
[CrossRef]

C. Quan, H. Niu, and C. J. Tay, “An improved windowed Fourier transform for fringe demodulation,” Opt. Laser Technol. 42, 126–131 (2010).
[CrossRef]

M. Li, C. Quan, and C. J. Tay, “Continuous wavelet transform for micro-component profile measurement using vertical scanning interferometry,” Opt. Laser Technol. 40, 920–929(2008).
[CrossRef]

Towers, C. E.

Towers, D. P.

Tribillon, J. L.

Tung, C. H.

H. C. Hsu, C. H. Tung, C. F. Kao, and C. C. Chang, “A white-light profiling algorithm adopting the multiwavelength interferometric technique,” Proc. SPIE 5531, 244–249 (2004).
[CrossRef]

Turzhitsky, M.

Wang, H.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed.(Pergamon, 1980).

Wyant, J. C.

J. C. Wyant, “White light interferometry,” Proc. SPIE 4737, 98–107 (2002).
[CrossRef]

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

Zhang, Z.

Zhu, R.

S. Ma, C. Quan, R. Zhu, C. J. Tay, L. Chen, and Z. Gao, “Micro-profile measurement based on windowed Fourier transform in white-light scanning interferometry,” Opt. Commun. 284, 2488–2493 (2011).
[CrossRef]

Appl. Opt. (11)

O. Sasaki and H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
[CrossRef] [PubMed]

G. S. Kino and S. S. C. Chim, “Mirau correlation microscope,” Appl. Opt. 29, 3775–3783 (1990).
[CrossRef] [PubMed]

J. M. Desse, “Three-color differential interferometry,” Appl. Opt. 36, 7150–7156 (1997).
[CrossRef]

S. W. Kim and G. H. Kim, “Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry,” Appl. Opt. 38, 5968–5973 (1999).
[CrossRef]

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

J. M. Desse, F. Albe, and J. L. Tribillon, “Real-time color holographic interferometry,” Appl. Opt. 41, 5326–5333 (2002).
[CrossRef] [PubMed]

J. Schmit and A. Olszak, “High-precision shape measurement by white-light interferometry with real-time scanner error correction,” Appl. Opt. 41, 5943–5950 (2002).
[CrossRef] [PubMed]

A. Pförtner and J. Schwider, “Red–Green–Blue interferometer for the metrology of discontinuous structures,” Appl. Opt. 42, 667–673 (2003).
[CrossRef] [PubMed]

S. Chen, A. W. Palmer, K. T. V. Grattan, and B. T. Meggitt, “Digital signal-processing techniques for electronically scanned optical-fiber white-light interferometry,” Appl. Opt. 31, 6003–6010 (1992).
[CrossRef] [PubMed]

K. Qian, H. Wang, and W. Gao, “Windowed Fourier transform for fringe pattern analysis: theoretical analyses,” Appl. Opt. 47, 5408–5419 (2008).
[CrossRef]

Z. Zhang, D. P. Towers, and C. E. Towers, “Snapshot color fringe projection for absolute three-dimensional metrology of video sequences,” Appl. Opt. 49, 5947–5953 (2010).
[CrossRef]

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

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

J. Mod. Opt. (2)

P. Sandoz, “An algorithm for profilometry by white-light phase-shifting interferometry,” J. Mod. Opt. 43, 1545–1554(1996).

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

J. Opt. Soc. Am. A (1)

Opt. Commun. (3)

S. Ma, C. Quan, R. Zhu, C. J. Tay, L. Chen, and Z. Gao, “Micro-profile measurement based on windowed Fourier transform in white-light scanning interferometry,” Opt. Commun. 284, 2488–2493 (2011).
[CrossRef]

T. Anna, S. K. Dubey, C. Shakher, A. Roy, and D. S. Mehta, “Sinusoidal fringe projection system based on compact and non-mechanical scanning low-coherence Michelson interferometer for three-dimensional shape measurement,” Opt. Commun. 282, 1237–1242 (2009).
[CrossRef]

M. Pawlowski, Y. Sakano, Y. Miyamoto, and M. Takeda, “Phase-crossing algorithm for white-light fringes analysis,” Opt. Commun. 260, 68–72 (2006).
[CrossRef]

Opt. Eng. (2)

S. Mirza and C. Shakher, “Surface profiling using phase shifting Talbot interferometric technique,” Opt. Eng. 44, 013601 (2005).
[CrossRef]

M. C. Park and S. W. Kim, “Direct quadratic polynomial fitting for fringe peak detection of white light scanning interferograms,” Opt. Eng. 39, 952–959 (2000).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (2)

M. Li, C. Quan, and C. J. Tay, “Continuous wavelet transform for micro-component profile measurement using vertical scanning interferometry,” Opt. Laser Technol. 40, 920–929(2008).
[CrossRef]

C. Quan, H. Niu, and C. J. Tay, “An improved windowed Fourier transform for fringe demodulation,” Opt. Laser Technol. 42, 126–131 (2010).
[CrossRef]

Opt. Lasers Eng. (2)

L. Bruno, G. Felice, and A. Poggialini, “Design and calibration of a piezoelectric actuator for interferometric applications,” Opt. Lasers Eng. 45, 1148–1156 (2007).
[CrossRef]

K. Qian, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).
[CrossRef]

Proc. SPIE (3)

H. C. Hsu, C. H. Tung, C. F. Kao, and C. C. Chang, “A white-light profiling algorithm adopting the multiwavelength interferometric technique,” Proc. SPIE 5531, 244–249 (2004).
[CrossRef]

M. Pawlowski, Y. Sakano, Y. Miyamoto, and M. Takeda, “Multi-spectral phase-crossing white-light interferometry,” Proc. SPIE 5776, 88–93 (2005).
[CrossRef]

J. C. Wyant, “White light interferometry,” Proc. SPIE 4737, 98–107 (2002).
[CrossRef]

Other (3)

Z. Buchta, P. Jedlička, M. Matějka, V. Kolařík, B. Mikel, J. Lazar, and O. Číp, “White-light interference fringe detection using color CCD camera,” in the Proceedings of IEEE AFRICON 2009 (IEEE, 2009), pp. 1–5.
[CrossRef]

M. Li, “Development of fringe analysis techniques in white light interferometry for micro-component measurement,” Ph.D. thesis (National University of Singapore, 2008).

M. Born and E. Wolf, Principles of Optics, 6th ed.(Pergamon, 1980).

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Figures (7)

Fig. 1
Fig. 1

Schematic layout of a Michelson-type WLSI setup.

Fig. 2
Fig. 2

Simulated results of an object with steps of 0.013 and 0.028 μm for various random intensity noises. (a) Three- dimensional plot by the proposed method with a 20% random intensity noise; (b) 3-D plot by the phase-crossing method with a 20% random intensity noise; (c) RMS error of the profile obtained by the proposed and phase-crossing methods for different noise levels.

Fig. 3
Fig. 3

Simulated results of an object with steps of 0.013 and 0.028 μm for color coupling between channels and various random intensity noises. (a) RMS error of the profile obtained by the proposed method; (b) 3-D plot of the WFT spectrum of a test point in the G channel.

Fig. 4
Fig. 4

Measured results of a flat mirror. (a) Color white-light interferogram of a flat mirror; (b) microprofile of the mirror obtained by the proposed method.

Fig. 5
Fig. 5

Interferograms of a measured convex MEMS wafer. (a) Color white-light interferogram of a convex MEMS wafer; (b) corresponding gray interferogram of the R channel; (c) The corresponding gray interferogram of the G channel; (d) corresponding gray interferogram of the B channel.

Fig. 6
Fig. 6

Measured results of a convex MEMS wafer. (a) White-light interference signals of a test point in different channels; (b) center of a zero-order fringe of the corresponding point determined by the EF; (c) microprofile of an object obtained by the phase-crossing method; (d) microprofile of an object obtained by proposed method; (e) measurement along cross section A A in Fig. 4a.

Fig. 7
Fig. 7

Measured results of a microstructure MEMS wafer. (a) Color white-light interferogram of a microstructure MEMS wafer; (b) microprofile of an object obtained by the phase-crossing method; (c) microprofile of an object obtained by proposed method; (d) measurement along cross section A A in (a).

Tables (1)

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Table 1 Parameters of a Simulated White-Light Source

Equations (11)

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I m ( z ) = I 0 m + γ m I 0 m g m ( z z 0 ) cos [ 4 π ( z z 0 ) / λ 0 m + ϕ 0 m ] ,
φ m ( z ) = 4 π ( z z 0 ) / λ 0 m + ϕ 0 m ,
φ m = A m z + B m ,
S I m ( a , b ) = + I m ( z ) exp ( ( z b ) 2 / 2 σ 2 ) exp ( j a z ) d z ,
φ = m tan 1 { Im [ S f ( a 0 , b ) ] Re [ S f ( a 0 , b ) ] } .
d ( φ R 2 + φ G 2 + φ B 2 ) d z = 2 ( A R 2 + A G 2 + A B 2 ) z + 2 ( A R B R + A G B G + A B B B ) = 0 ,
h = z 0 = A R B R + A G B G + A B B B A R 2 + A G 2 + A B 2 .
E F = | φ R φ G | + | φ R φ B | + | φ G φ B | .
A m ( i = 1 n ( φ m i A m z i B m ) 2 ) = 0 , B m ( i = 1 n ( φ m i A m z i B m ) 2 ) = 0 ,
A m = n i = 1 n z i φ m i i = 1 n z i i = 1 n φ m i n i = 1 n z i 2 ( i = 1 n z i ) 2 , B m = i = 1 n z i i = 1 n z i φ m i i = 1 n z i 2 i = 1 n φ m i ( i = 1 n z i ) 2 n i = 1 n z i 2 .
M = [ 0.70 0.10 0.20 0.20 0.85 0.15 0.10 0.05 0.65 ] .

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