Abstract

We describe an improved implementation of our previously reported common-path, phase shifting, and shearing interferometer. Using a time-multiplexed phase shifting scheme, we demonstrate higher sampling resolution, better light sensitivity, and use of arbitrary phase shifting algorithms. We describe microscopic imaging of the surface profile of a copper-plated silicon wafer and demonstrate that the system is vibration insensitive with λ/100 repeatability. In a more general discussion of our method, we describe the different functional elements and suggest alternative designs and improvements. Possible uses include full-field coherent imaging and high dynamic range wavefront sensing, which we briefly discuss.

© 2008 Optical Society of America

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  1. A. V. Oppenheim and J. S. Lim, "The importance of phase in signals," Proc. IEEE 69, 529 (1981).
    [CrossRef]
  2. J. Curlander and R. McDonough, Synthetic Aperture Radar, Systems and Signal Processing (Wiley, 1991).
  3. G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
    [CrossRef]
  4. T. Colomb, E. Cuche, P. Dahgren, A. M. Marian, F. Montfort, C. D. Depeursinge, P. Marquet, and P. J. Magistretti, "3D imaging of surfaces and cells by numerical reconstruction of wavefronts in digital holography applied to transmission and reflection microscopy," in Proceedings of 2002 IEEE International Symposium on Biomedical Imaging (IEEE, 2002), pp. 773-776.
  5. C. D. Depeursinge, E. Cuche, P. Marquet, T. Colomb, P. Dahlgren, A. M. Marian, F. Montfort, and P. J. Magistretti, "Digital holography applied to microscopy," Proc. SPIE 4659, 30-34 (2002).
    [CrossRef]
  6. R. Tumbar and D. J. Brady, "Sampling field sensor with anisotropic fan-out," Appl. Opt. 41, 6621-6636 (2002).
    [CrossRef] [PubMed]
  7. R. Tumbar and D. J. Brady, " Interferometric sensor and method to detect optical fields," U.S. patent 6,639,683 (28 October 2003).
  8. J. E. Greivenkamp and A. E. Lowman, "Modulation transfer function measurement of sparse-array sensors using a self-calibrating fringe pattern," Appl. Opt. 33, 5029-5036 (1994).
    [CrossRef] [PubMed]
  9. G. Toraldo di Francia, "Resolving power and information," J. Opt. Soc. Am. 45, 497-501 (1955).
    [CrossRef]
  10. K. Creath, "Phase-measurement interferometry techniques," in Progress in Optics, E.Wolf, ed. (North-Holland, 1988), Vol. 26, pp. 349-393.
    [CrossRef]
  11. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  12. D. C. Ghiglia and L. A. Romero, "Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods," J. Opt. Soc. Am. A 11, 107-117 (1994).
    [CrossRef]
  13. K. Itoh, "Analysis of the phase unwrapping algorithm," Appl. Opt. 21, 2470 (1982).
    [CrossRef] [PubMed]
  14. M. Unser, "Sampling--50 years after Shannon," Proc. IEEE 88, 569-589 (2000).
    [CrossRef]
  15. Kodak KAI-4021 Image Sensor, Eastman Kodak Company (2006).
  16. DALSA IA-G3 CMOS Area Array Sensor, Dalsa Corp. (2006).
  17. A. Papoulis, Signal Analysis (McGraw-Hill, 1977).
  18. H. E. Bennett and J. M. Bennett, "Polarization," in Handbook of Optics, W.G.Driscoll and W.Vaughan, eds. (McGraw-Hill, 1978).
  19. M. Francon, "Polarization interference microscopes," Appl. Opt. 3, 1033-1036 (1964).
    [CrossRef]
  20. D. S. Kliger, J. W. Lewis, and C. Einterz Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).
  21. M. Laikin, Lens Design, 3rd ed. (Marcel Dekker, 2001).
  22. J. D. Barchers, D. L. Fried, and D. J. Link, "Evaluation of the performance of a shearing interferometer in strong scintillation in the absence of additive measurement noise," Appl. Opt. 41, 3674-3684 (2002).
    [CrossRef] [PubMed]
  23. J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Fugate, "The performance of wavefront sensors in strong scintillation," Proc. SPIE 4839, 217-227 (2003).
    [CrossRef]
  24. D. G. Sandler, L. Cuellar, M. Lefebvre, T. Barrett, R. Arnold, P. Johnson, A. Rego, G. Smith, G. Taylor, and B. Spivey, "Shearing interferometry for laser-guide-star atmospheric correction at large D/r00," J. Opt. Soc. Am. A 11, 858-873 (1994).
    [CrossRef]

2004 (1)

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

2003 (1)

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Fugate, "The performance of wavefront sensors in strong scintillation," Proc. SPIE 4839, 217-227 (2003).
[CrossRef]

2002 (3)

J. D. Barchers, D. L. Fried, and D. J. Link, "Evaluation of the performance of a shearing interferometer in strong scintillation in the absence of additive measurement noise," Appl. Opt. 41, 3674-3684 (2002).
[CrossRef] [PubMed]

C. D. Depeursinge, E. Cuche, P. Marquet, T. Colomb, P. Dahlgren, A. M. Marian, F. Montfort, and P. J. Magistretti, "Digital holography applied to microscopy," Proc. SPIE 4659, 30-34 (2002).
[CrossRef]

R. Tumbar and D. J. Brady, "Sampling field sensor with anisotropic fan-out," Appl. Opt. 41, 6621-6636 (2002).
[CrossRef] [PubMed]

2000 (1)

M. Unser, "Sampling--50 years after Shannon," Proc. IEEE 88, 569-589 (2000).
[CrossRef]

1994 (3)

1982 (1)

K. Itoh, "Analysis of the phase unwrapping algorithm," Appl. Opt. 21, 2470 (1982).
[CrossRef] [PubMed]

1981 (1)

A. V. Oppenheim and J. S. Lim, "The importance of phase in signals," Proc. IEEE 69, 529 (1981).
[CrossRef]

1964 (1)

M. Francon, "Polarization interference microscopes," Appl. Opt. 3, 1033-1036 (1964).
[CrossRef]

1955 (1)

G. Toraldo di Francia, "Resolving power and information," J. Opt. Soc. Am. 45, 497-501 (1955).
[CrossRef]

Arnold, R.

D. G. Sandler, L. Cuellar, M. Lefebvre, T. Barrett, R. Arnold, P. Johnson, A. Rego, G. Smith, G. Taylor, and B. Spivey, "Shearing interferometry for laser-guide-star atmospheric correction at large D/r00," J. Opt. Soc. Am. A 11, 858-873 (1994).
[CrossRef]

Barchers, J. D.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Fugate, "The performance of wavefront sensors in strong scintillation," Proc. SPIE 4839, 217-227 (2003).
[CrossRef]

J. D. Barchers, D. L. Fried, and D. J. Link, "Evaluation of the performance of a shearing interferometer in strong scintillation in the absence of additive measurement noise," Appl. Opt. 41, 3674-3684 (2002).
[CrossRef] [PubMed]

Barrett, T.

D. G. Sandler, L. Cuellar, M. Lefebvre, T. Barrett, R. Arnold, P. Johnson, A. Rego, G. Smith, G. Taylor, and B. Spivey, "Shearing interferometry for laser-guide-star atmospheric correction at large D/r00," J. Opt. Soc. Am. A 11, 858-873 (1994).
[CrossRef]

Bennett, H. E.

H. E. Bennett and J. M. Bennett, "Polarization," in Handbook of Optics, W.G.Driscoll and W.Vaughan, eds. (McGraw-Hill, 1978).

Bennett, J. M.

H. E. Bennett and J. M. Bennett, "Polarization," in Handbook of Optics, W.G.Driscoll and W.Vaughan, eds. (McGraw-Hill, 1978).

Brady, D. J.

R. Tumbar and D. J. Brady, "Sampling field sensor with anisotropic fan-out," Appl. Opt. 41, 6621-6636 (2002).
[CrossRef] [PubMed]

R. Tumbar and D. J. Brady, " Interferometric sensor and method to detect optical fields," U.S. patent 6,639,683 (28 October 2003).

Brennan, T. J.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Fugate, "The performance of wavefront sensors in strong scintillation," Proc. SPIE 4839, 217-227 (2003).
[CrossRef]

Colomb, T.

C. D. Depeursinge, E. Cuche, P. Marquet, T. Colomb, P. Dahlgren, A. M. Marian, F. Montfort, and P. J. Magistretti, "Digital holography applied to microscopy," Proc. SPIE 4659, 30-34 (2002).
[CrossRef]

T. Colomb, E. Cuche, P. Dahgren, A. M. Marian, F. Montfort, C. D. Depeursinge, P. Marquet, and P. J. Magistretti, "3D imaging of surfaces and cells by numerical reconstruction of wavefronts in digital holography applied to transmission and reflection microscopy," in Proceedings of 2002 IEEE International Symposium on Biomedical Imaging (IEEE, 2002), pp. 773-776.

Coppola, G.

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

Creath, K.

K. Creath, "Phase-measurement interferometry techniques," in Progress in Optics, E.Wolf, ed. (North-Holland, 1988), Vol. 26, pp. 349-393.
[CrossRef]

Cuche, E.

C. D. Depeursinge, E. Cuche, P. Marquet, T. Colomb, P. Dahlgren, A. M. Marian, F. Montfort, and P. J. Magistretti, "Digital holography applied to microscopy," Proc. SPIE 4659, 30-34 (2002).
[CrossRef]

T. Colomb, E. Cuche, P. Dahgren, A. M. Marian, F. Montfort, C. D. Depeursinge, P. Marquet, and P. J. Magistretti, "3D imaging of surfaces and cells by numerical reconstruction of wavefronts in digital holography applied to transmission and reflection microscopy," in Proceedings of 2002 IEEE International Symposium on Biomedical Imaging (IEEE, 2002), pp. 773-776.

Cuellar, L.

D. G. Sandler, L. Cuellar, M. Lefebvre, T. Barrett, R. Arnold, P. Johnson, A. Rego, G. Smith, G. Taylor, and B. Spivey, "Shearing interferometry for laser-guide-star atmospheric correction at large D/r00," J. Opt. Soc. Am. A 11, 858-873 (1994).
[CrossRef]

Curlander, J.

J. Curlander and R. McDonough, Synthetic Aperture Radar, Systems and Signal Processing (Wiley, 1991).

Dahgren, P.

T. Colomb, E. Cuche, P. Dahgren, A. M. Marian, F. Montfort, C. D. Depeursinge, P. Marquet, and P. J. Magistretti, "3D imaging of surfaces and cells by numerical reconstruction of wavefronts in digital holography applied to transmission and reflection microscopy," in Proceedings of 2002 IEEE International Symposium on Biomedical Imaging (IEEE, 2002), pp. 773-776.

Dahlgren, P.

C. D. Depeursinge, E. Cuche, P. Marquet, T. Colomb, P. Dahlgren, A. M. Marian, F. Montfort, and P. J. Magistretti, "Digital holography applied to microscopy," Proc. SPIE 4659, 30-34 (2002).
[CrossRef]

De Nicola, S.

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

Depeursinge, C. D.

C. D. Depeursinge, E. Cuche, P. Marquet, T. Colomb, P. Dahlgren, A. M. Marian, F. Montfort, and P. J. Magistretti, "Digital holography applied to microscopy," Proc. SPIE 4659, 30-34 (2002).
[CrossRef]

T. Colomb, E. Cuche, P. Dahgren, A. M. Marian, F. Montfort, C. D. Depeursinge, P. Marquet, and P. J. Magistretti, "3D imaging of surfaces and cells by numerical reconstruction of wavefronts in digital holography applied to transmission and reflection microscopy," in Proceedings of 2002 IEEE International Symposium on Biomedical Imaging (IEEE, 2002), pp. 773-776.

Einterz Randall, C.

D. S. Kliger, J. W. Lewis, and C. Einterz Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

Ferraro, P.

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

Finizio, A.

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

Francon, M.

M. Francon, "Polarization interference microscopes," Appl. Opt. 3, 1033-1036 (1964).
[CrossRef]

Fried, D. L.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Fugate, "The performance of wavefront sensors in strong scintillation," Proc. SPIE 4839, 217-227 (2003).
[CrossRef]

J. D. Barchers, D. L. Fried, and D. J. Link, "Evaluation of the performance of a shearing interferometer in strong scintillation in the absence of additive measurement noise," Appl. Opt. 41, 3674-3684 (2002).
[CrossRef] [PubMed]

Fugate, R.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Fugate, "The performance of wavefront sensors in strong scintillation," Proc. SPIE 4839, 217-227 (2003).
[CrossRef]

Ghiglia, D. C.

Greivenkamp, J. E.

Grilli, S.

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

Iodice, M.

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

Itoh, K.

K. Itoh, "Analysis of the phase unwrapping algorithm," Appl. Opt. 21, 2470 (1982).
[CrossRef] [PubMed]

Johnson, P.

D. G. Sandler, L. Cuellar, M. Lefebvre, T. Barrett, R. Arnold, P. Johnson, A. Rego, G. Smith, G. Taylor, and B. Spivey, "Shearing interferometry for laser-guide-star atmospheric correction at large D/r00," J. Opt. Soc. Am. A 11, 858-873 (1994).
[CrossRef]

Kliger, D. S.

D. S. Kliger, J. W. Lewis, and C. Einterz Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

Laikin, M.

M. Laikin, Lens Design, 3rd ed. (Marcel Dekker, 2001).

Lefebvre, M.

D. G. Sandler, L. Cuellar, M. Lefebvre, T. Barrett, R. Arnold, P. Johnson, A. Rego, G. Smith, G. Taylor, and B. Spivey, "Shearing interferometry for laser-guide-star atmospheric correction at large D/r00," J. Opt. Soc. Am. A 11, 858-873 (1994).
[CrossRef]

Lewis, J. W.

D. S. Kliger, J. W. Lewis, and C. Einterz Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

Lim, J. S.

A. V. Oppenheim and J. S. Lim, "The importance of phase in signals," Proc. IEEE 69, 529 (1981).
[CrossRef]

Link, D. J.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Fugate, "The performance of wavefront sensors in strong scintillation," Proc. SPIE 4839, 217-227 (2003).
[CrossRef]

J. D. Barchers, D. L. Fried, and D. J. Link, "Evaluation of the performance of a shearing interferometer in strong scintillation in the absence of additive measurement noise," Appl. Opt. 41, 3674-3684 (2002).
[CrossRef] [PubMed]

Lowman, A. E.

Magistretti, P. J.

C. D. Depeursinge, E. Cuche, P. Marquet, T. Colomb, P. Dahlgren, A. M. Marian, F. Montfort, and P. J. Magistretti, "Digital holography applied to microscopy," Proc. SPIE 4659, 30-34 (2002).
[CrossRef]

T. Colomb, E. Cuche, P. Dahgren, A. M. Marian, F. Montfort, C. D. Depeursinge, P. Marquet, and P. J. Magistretti, "3D imaging of surfaces and cells by numerical reconstruction of wavefronts in digital holography applied to transmission and reflection microscopy," in Proceedings of 2002 IEEE International Symposium on Biomedical Imaging (IEEE, 2002), pp. 773-776.

Marian, A. M.

C. D. Depeursinge, E. Cuche, P. Marquet, T. Colomb, P. Dahlgren, A. M. Marian, F. Montfort, and P. J. Magistretti, "Digital holography applied to microscopy," Proc. SPIE 4659, 30-34 (2002).
[CrossRef]

T. Colomb, E. Cuche, P. Dahgren, A. M. Marian, F. Montfort, C. D. Depeursinge, P. Marquet, and P. J. Magistretti, "3D imaging of surfaces and cells by numerical reconstruction of wavefronts in digital holography applied to transmission and reflection microscopy," in Proceedings of 2002 IEEE International Symposium on Biomedical Imaging (IEEE, 2002), pp. 773-776.

Marquet, P.

C. D. Depeursinge, E. Cuche, P. Marquet, T. Colomb, P. Dahlgren, A. M. Marian, F. Montfort, and P. J. Magistretti, "Digital holography applied to microscopy," Proc. SPIE 4659, 30-34 (2002).
[CrossRef]

T. Colomb, E. Cuche, P. Dahgren, A. M. Marian, F. Montfort, C. D. Depeursinge, P. Marquet, and P. J. Magistretti, "3D imaging of surfaces and cells by numerical reconstruction of wavefronts in digital holography applied to transmission and reflection microscopy," in Proceedings of 2002 IEEE International Symposium on Biomedical Imaging (IEEE, 2002), pp. 773-776.

McDonough, R.

J. Curlander and R. McDonough, Synthetic Aperture Radar, Systems and Signal Processing (Wiley, 1991).

Montfort, F.

C. D. Depeursinge, E. Cuche, P. Marquet, T. Colomb, P. Dahlgren, A. M. Marian, F. Montfort, and P. J. Magistretti, "Digital holography applied to microscopy," Proc. SPIE 4659, 30-34 (2002).
[CrossRef]

T. Colomb, E. Cuche, P. Dahgren, A. M. Marian, F. Montfort, C. D. Depeursinge, P. Marquet, and P. J. Magistretti, "3D imaging of surfaces and cells by numerical reconstruction of wavefronts in digital holography applied to transmission and reflection microscopy," in Proceedings of 2002 IEEE International Symposium on Biomedical Imaging (IEEE, 2002), pp. 773-776.

Moretti, W.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Fugate, "The performance of wavefront sensors in strong scintillation," Proc. SPIE 4839, 217-227 (2003).
[CrossRef]

Oppenheim, A. V.

A. V. Oppenheim and J. S. Lim, "The importance of phase in signals," Proc. IEEE 69, 529 (1981).
[CrossRef]

Papoulis, A.

A. Papoulis, Signal Analysis (McGraw-Hill, 1977).

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Rego, A.

D. G. Sandler, L. Cuellar, M. Lefebvre, T. Barrett, R. Arnold, P. Johnson, A. Rego, G. Smith, G. Taylor, and B. Spivey, "Shearing interferometry for laser-guide-star atmospheric correction at large D/r00," J. Opt. Soc. Am. A 11, 858-873 (1994).
[CrossRef]

Romero, L. A.

Sandler, D. G.

D. G. Sandler, L. Cuellar, M. Lefebvre, T. Barrett, R. Arnold, P. Johnson, A. Rego, G. Smith, G. Taylor, and B. Spivey, "Shearing interferometry for laser-guide-star atmospheric correction at large D/r00," J. Opt. Soc. Am. A 11, 858-873 (1994).
[CrossRef]

Smith, G.

D. G. Sandler, L. Cuellar, M. Lefebvre, T. Barrett, R. Arnold, P. Johnson, A. Rego, G. Smith, G. Taylor, and B. Spivey, "Shearing interferometry for laser-guide-star atmospheric correction at large D/r00," J. Opt. Soc. Am. A 11, 858-873 (1994).
[CrossRef]

Spivey, B.

D. G. Sandler, L. Cuellar, M. Lefebvre, T. Barrett, R. Arnold, P. Johnson, A. Rego, G. Smith, G. Taylor, and B. Spivey, "Shearing interferometry for laser-guide-star atmospheric correction at large D/r00," J. Opt. Soc. Am. A 11, 858-873 (1994).
[CrossRef]

Taylor, G.

D. G. Sandler, L. Cuellar, M. Lefebvre, T. Barrett, R. Arnold, P. Johnson, A. Rego, G. Smith, G. Taylor, and B. Spivey, "Shearing interferometry for laser-guide-star atmospheric correction at large D/r00," J. Opt. Soc. Am. A 11, 858-873 (1994).
[CrossRef]

Toraldo di Francia, G.

G. Toraldo di Francia, "Resolving power and information," J. Opt. Soc. Am. 45, 497-501 (1955).
[CrossRef]

Tumbar, R.

R. Tumbar and D. J. Brady, "Sampling field sensor with anisotropic fan-out," Appl. Opt. 41, 6621-6636 (2002).
[CrossRef] [PubMed]

R. Tumbar and D. J. Brady, " Interferometric sensor and method to detect optical fields," U.S. patent 6,639,683 (28 October 2003).

Tyler, G. A.

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Fugate, "The performance of wavefront sensors in strong scintillation," Proc. SPIE 4839, 217-227 (2003).
[CrossRef]

Unser, M.

M. Unser, "Sampling--50 years after Shannon," Proc. IEEE 88, 569-589 (2000).
[CrossRef]

Appl. Opt. (3)

K. Itoh, "Analysis of the phase unwrapping algorithm," Appl. Opt. 21, 2470 (1982).
[CrossRef] [PubMed]

M. Francon, "Polarization interference microscopes," Appl. Opt. 3, 1033-1036 (1964).
[CrossRef]

J. D. Barchers, D. L. Fried, and D. J. Link, "Evaluation of the performance of a shearing interferometer in strong scintillation in the absence of additive measurement noise," Appl. Opt. 41, 3674-3684 (2002).
[CrossRef] [PubMed]

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

G. Toraldo di Francia, "Resolving power and information," J. Opt. Soc. Am. 45, 497-501 (1955).
[CrossRef]

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

D. G. Sandler, L. Cuellar, M. Lefebvre, T. Barrett, R. Arnold, P. Johnson, A. Rego, G. Smith, G. Taylor, and B. Spivey, "Shearing interferometry for laser-guide-star atmospheric correction at large D/r00," J. Opt. Soc. Am. A 11, 858-873 (1994).
[CrossRef]

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

Meas. Sci. Technol. (1)

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, A. Finizio, and S. Grilli, "A digital holographic microscope for complete characterization of microelectromechanical systems," Meas. Sci. Technol. 15, 529-539 (2004).
[CrossRef]

Proc. IEEE (1)

M. Unser, "Sampling--50 years after Shannon," Proc. IEEE 88, 569-589 (2000).
[CrossRef]

Proc. SPIE (2)

J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Fugate, "The performance of wavefront sensors in strong scintillation," Proc. SPIE 4839, 217-227 (2003).
[CrossRef]

C. D. Depeursinge, E. Cuche, P. Marquet, T. Colomb, P. Dahlgren, A. M. Marian, F. Montfort, and P. J. Magistretti, "Digital holography applied to microscopy," Proc. SPIE 4659, 30-34 (2002).
[CrossRef]

Proc. IEEE (1)

A. V. Oppenheim and J. S. Lim, "The importance of phase in signals," Proc. IEEE 69, 529 (1981).
[CrossRef]

Other (11)

J. Curlander and R. McDonough, Synthetic Aperture Radar, Systems and Signal Processing (Wiley, 1991).

T. Colomb, E. Cuche, P. Dahgren, A. M. Marian, F. Montfort, C. D. Depeursinge, P. Marquet, and P. J. Magistretti, "3D imaging of surfaces and cells by numerical reconstruction of wavefronts in digital holography applied to transmission and reflection microscopy," in Proceedings of 2002 IEEE International Symposium on Biomedical Imaging (IEEE, 2002), pp. 773-776.

Kodak KAI-4021 Image Sensor, Eastman Kodak Company (2006).

DALSA IA-G3 CMOS Area Array Sensor, Dalsa Corp. (2006).

A. Papoulis, Signal Analysis (McGraw-Hill, 1977).

H. E. Bennett and J. M. Bennett, "Polarization," in Handbook of Optics, W.G.Driscoll and W.Vaughan, eds. (McGraw-Hill, 1978).

R. Tumbar and D. J. Brady, " Interferometric sensor and method to detect optical fields," U.S. patent 6,639,683 (28 October 2003).

K. Creath, "Phase-measurement interferometry techniques," in Progress in Optics, E.Wolf, ed. (North-Holland, 1988), Vol. 26, pp. 349-393.
[CrossRef]

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

D. S. Kliger, J. W. Lewis, and C. Einterz Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

M. Laikin, Lens Design, 3rd ed. (Marcel Dekker, 2001).

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Figures (6)

Fig. 1
Fig. 1

(a) Sampling mask; (b) birefringent fan-out (one sample shown) producing extraordinary (“E”) and ordinary (“O”) images [6]; (c) 4 × beam splitting with polarization phase shifting; (d) 4-point fan-out.

Fig. 2
Fig. 2

Polarization phase shifted SFS and optical profilometer: (a) SFS system layout, (b) the infinity microscope, (c) raw CCD image, (d) layout of optical profilometer.

Fig. 3
Fig. 3

(a) Phase shifting signal and (b) error.

Fig. 4
Fig. 4

Insensitivity to vibrations: (a) raw signal and (b) difference of consecutive samples (noise).

Fig. 5
Fig. 5

Wafer surface microstructure. (a) Intensity image of a relatively low complexity target and (b) its reconstructed phase image. (c) Intensity image of a high complexity target and (d) its phase image. For better viewing of details, phase images are shown with false gray scale, showing white as the largest phase value and dark as the lowest, in addition to surface illumination.

Fig. 6
Fig. 6

Representation on the Poincare sphere of phase shifting using a variable retarder. Squares represent polarization states of the ordinary wave exiting the last shearing plate and after passing through the variable retarder. LCP is left circular polarization.

Equations (4)

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P ( θ ) = ( cos 2 θ sin θ cos θ sin θ cos θ sin 2 θ ) .
O f i n a l = i ( cos θ sin θ ) e i θ , E f i n a l = i ( cos θ sin θ ) e i θ ,
J = ( cos ( β ) sin ( β ) e i Δ ) o r ( cos ( β ) e i Δ / 2 sin ( β ) e i Δ / 2 ) ,
Δ = i n v tan [ tan ( 2 ω ) ] × { tan ( ω ) > 0  light  is  right-handed  and   Δ > 0 tan ( ω ) < 0 light  is  left-handed  and   Δ < 0 .

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