Abstract

A simple estimation method of the relative phase shift for generalized phase-shifting digital holography based on a statistical method is proposed. This method consists of a selection procedure of an optimum cost function and a simple root-finding procedure. The value and sign of the relative phase shift are determined using the coefficient and the solution of the optimum cost function. The complex field of an object wave is obtained using the estimated relative phase shift. The proposed method lifts the typical restriction on the range of the phase shift due to the phase ambiguity problem. Computer simulations and optical experiments are performed to verify the proposed method.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2009 (1)

2008 (3)

2007 (1)

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

2006 (1)

2004 (1)

2003 (1)

1999 (1)

1997 (1)

1994 (1)

1967 (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Bally, G. V.

Bruning, J. H.

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 547–666.

Cai, L. Z.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments,” Opt. Lett. 33, 776–778 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

X. F. Xu, L. Z. Cai, X. F. Meng, G. Y. Dong, and X. X. Shen, “Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry,” Opt. Lett. 31, 1966–1968 (2006).
[CrossRef]

L. Z. Cai, Q. Liu, and X. L. Yang, “Generalized phase-shifting interferometry with arbitrary unknown phase steps for diffraction objects,” Opt. Lett. 29, 183–185 (2004).
[CrossRef]

L. Z. Cai, Q. Liu, and X. L. Yang, “Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps,” Opt. Lett. 28, 1808–1810 (2003).
[CrossRef]

Cheng, X. C.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments,” Opt. Lett. 33, 776–778 (2008).
[CrossRef]

Dong, G. Y.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments,” Opt. Lett. 33, 776–778 (2008).
[CrossRef]

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

X. F. Xu, L. Z. Cai, X. F. Meng, G. Y. Dong, and X. X. Shen, “Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry,” Opt. Lett. 31, 1966–1968 (2006).
[CrossRef]

Gao, P.

Geist, E.

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

J. W. Goodman, “Introduction to Fourier Optics,” 2nd ed. (McGraw-Hill, 1996).

Harder, I.

Jüptner, W.

Kemper, B.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Lindlein, N.

Liu, Q.

Mantel, K.

Meng, X. F.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments,” Opt. Lett. 33, 776–778 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

X. F. Xu, L. Z. Cai, X. F. Meng, G. Y. Dong, and X. X. Shen, “Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry,” Opt. Lett. 31, 1966–1968 (2006).
[CrossRef]

Osten, W.

Schnars, U.

Schreiber, H.

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 547–666.

Seebacher, S.

Shen, X. X.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments,” Opt. Lett. 33, 776–778 (2008).
[CrossRef]

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

X. F. Xu, L. Z. Cai, X. F. Meng, G. Y. Dong, and X. X. Shen, “Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry,” Opt. Lett. 31, 1966–1968 (2006).
[CrossRef]

Sun, W. J.

Wagner, C.

Wang, Y. R.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments,” Opt. Lett. 33, 776–778 (2008).
[CrossRef]

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Xu, X. F.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments,” Opt. Lett. 33, 776–778 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

X. F. Xu, L. Z. Cai, X. F. Meng, G. Y. Dong, and X. X. Shen, “Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry,” Opt. Lett. 31, 1966–1968 (2006).
[CrossRef]

Yamaguchi, I.

Yang, X. L.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

L. Z. Cai, Q. Liu, and X. L. Yang, “Generalized phase-shifting interferometry with arbitrary unknown phase steps for diffraction objects,” Opt. Lett. 29, 183–185 (2004).
[CrossRef]

L. Z. Cai, Q. Liu, and X. L. Yang, “Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps,” Opt. Lett. 28, 1808–1810 (2003).
[CrossRef]

Yao, B.

Zhang, H.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments,” Opt. Lett. 33, 776–778 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Zhang, T.

Appl. Opt. (3)

Appl. Phys. Lett. (2)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Opt. Commun. (1)

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

Opt. Lett. (6)

Other (2)

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), pp. 547–666.

J. W. Goodman, “Introduction to Fourier Optics,” 2nd ed. (McGraw-Hill, 1996).

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