Abstract

A phase shift selection method is proposed to design algorithms immune against phase shift errors in two-step generalized phase-shifting interferometry. A general formula for wavefront reconstruction error is derived, and its specific expressions for two common errors are also given. Calculation results suggest that the proper range of phase shift for general application is about from 0.5 to 2.0rad for both the fixed and linear phase shift errors. Computer simulations have demonstrated the effectiveness of this phase shift selection method by decreasing the wave reconstruction errors to one-fifth.

© 2011 Optical Society of America

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2011 (1)

L. I. Muravsky, O. P. Ostash, A. B. Kmet, T. I. Voronyak, and I. M. Andreiko, “Two-frame phase-shifting interferometry for retrieval of smooth surface and its displacements,” Opt. Lasers Eng. 49, 305–312 (2011).
[CrossRef]

2010 (1)

X. F. Xu, L. Z. Cai, Y. R. Wang, and D. L. Li, “Accurate phase shift extraction for generalized phase-shifting interferometry,” Chin. Phys. Lett. 27, 024215 (2010).
[CrossRef]

2009 (1)

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805(2009).
[CrossRef]

2008 (3)

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry,” J. Mod. Opt. 55, 1291–1304 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, X. C. Cheng, H. Zhang, G. Y. Dong, and X. X. Shen, “Correction of wavefront reconstruction errors caused by light source intensity instability in phase-shifting interferometry,” J. Opt. A: Pure Appl. Opt. 10, 085008 (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] [PubMed]

2007 (2)

R. Langoju, A. Patil, and P. Rastogi, “Statistical study of generalized nonlinear phase step estimation methods in phase-shifting interferometry,” Appl. Opt. 46, 8007–8014(2007).
[CrossRef] [PubMed]

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 wavefront reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

2006 (1)

S. Zhang, “A non-iterative method for phase-shift estimation and wavefront reconstruction in phase-shifting digital holography,” Opt. Commun. 268, 231–234 (2006).
[CrossRef]

2005 (1)

L. Z. Cai, Q. Liu, M. Z. He, and X. F. Meng, “Common form of the complex wave error caused by arbitrary phase shift errors in generalized phase-shifting interferometry and its digital correction,” Opt. Commun. 249, 95–100 (2005).
[CrossRef]

2004 (3)

L. Zhang, C. Guo, Z. Rong, X. Ren, X. Liu, and H. Wang, “Phase-shifting angle choice and phase-shifting error elimination in in-line phase-shifting digital holography,” Acta Photon. Sin. 33, 353–356 (2004).

L. Z. Cai, Q. Liu, and X. L. Yang, “Simultaneous digital correction of amplitude and phase errors of retrieved wave-front in phase-shifting interferometry with arbitrary phase shift errors,” Opt. Commun. 233, 21–26 (2004).
[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] [PubMed]

2003 (1)

S. Almazan-Cuellar and D. Malacara-Hernandez, “Two-step phase-shifting algorithm,” Opt. Eng. 42, 3524–3531 (2003).
[CrossRef]

2000 (2)

1998 (1)

1997 (3)

1996 (1)

1992 (1)

1991 (1)

1988 (1)

1984 (1)

J. E. Greivenkamp, “General data reduction for heterodyne interferometry,” Opt. Eng. 23, 350–352 (1984).

1974 (1)

Almazan-Cuellar, S.

S. Almazan-Cuellar and D. Malacara-Hernandez, “Two-step phase-shifting algorithm,” Opt. Eng. 42, 3524–3531 (2003).
[CrossRef]

Andreiko, I. M.

L. I. Muravsky, O. P. Ostash, A. B. Kmet, T. I. Voronyak, and I. M. Andreiko, “Two-frame phase-shifting interferometry for retrieval of smooth surface and its displacements,” Opt. Lasers Eng. 49, 305–312 (2011).
[CrossRef]

Brangaccio, D. J.

Bruning, J. H.

Cai, L. Z.

X. F. Xu, L. Z. Cai, Y. R. Wang, and D. L. Li, “Accurate phase shift extraction for generalized phase-shifting interferometry,” Chin. Phys. Lett. 27, 024215 (2010).
[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] [PubMed]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, X. C. Cheng, H. Zhang, G. Y. Dong, and X. X. Shen, “Correction of wavefront reconstruction errors caused by light source intensity instability in phase-shifting interferometry,” J. Opt. A: Pure Appl. Opt. 10, 085008 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry,” J. Mod. Opt. 55, 1291–1304 (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 wavefront reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

L. Z. Cai, Q. Liu, M. Z. He, and X. F. Meng, “Common form of the complex wave error caused by arbitrary phase shift errors in generalized phase-shifting interferometry and its digital correction,” Opt. Commun. 249, 95–100 (2005).
[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] [PubMed]

L. Z. Cai, Q. Liu, and X. L. Yang, “Simultaneous digital correction of amplitude and phase errors of retrieved wave-front in phase-shifting interferometry with arbitrary phase shift errors,” Opt. Commun. 233, 21–26 (2004).
[CrossRef]

Chen, W.

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805(2009).
[CrossRef]

Chen, X.

Cheng, X. C.

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] [PubMed]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry,” J. Mod. Opt. 55, 1291–1304 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, X. C. Cheng, H. Zhang, G. Y. Dong, and X. X. Shen, “Correction of wavefront reconstruction errors caused by light source intensity instability in phase-shifting interferometry,” J. Opt. A: Pure Appl. Opt. 10, 085008 (2008).
[CrossRef]

Creath, K.

Dong, G. Y.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, X. C. Cheng, H. Zhang, G. Y. Dong, and X. X. Shen, “Correction of wavefront reconstruction errors caused by light source intensity instability in phase-shifting interferometry,” J. Opt. A: Pure Appl. Opt. 10, 085008 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry,” J. Mod. Opt. 55, 1291–1304 (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] [PubMed]

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 wavefront reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Dragostinov, T.

G. Stoilov and T. Dragostinov, “Phase-stepping interferometry: five-frame algorithm with an arbitrary step,” Opt. Lasers Eng. 28, 61–69 (1997).
[CrossRef]

Fu, Y.

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805(2009).
[CrossRef]

Gallagher, J. E.

Gramaglia, M.

Greivenkamp, J. E.

J. E. Greivenkamp, “General data reduction for heterodyne interferometry,” Opt. Eng. 23, 350–352 (1984).

Guo, C.

L. Zhang, C. Guo, Z. Rong, X. Ren, X. Liu, and H. Wang, “Phase-shifting angle choice and phase-shifting error elimination in in-line phase-shifting digital holography,” Acta Photon. Sin. 33, 353–356 (2004).

Gutman, B.

He, M. Z.

L. Z. Cai, Q. Liu, M. Z. He, and X. F. Meng, “Common form of the complex wave error caused by arbitrary phase shift errors in generalized phase-shifting interferometry and its digital correction,” Opt. Commun. 249, 95–100 (2005).
[CrossRef]

Herriott, D. R.

Kerr, D.

Kmet, A. B.

L. I. Muravsky, O. P. Ostash, A. B. Kmet, T. I. Voronyak, and I. M. Andreiko, “Two-frame phase-shifting interferometry for retrieval of smooth surface and its displacements,” Opt. Lasers Eng. 49, 305–312 (2011).
[CrossRef]

Lai, G.

Langoju, R.

Larkin, K. G.

Li, D. L.

X. F. Xu, L. Z. Cai, Y. R. Wang, and D. L. Li, “Accurate phase shift extraction for generalized phase-shifting interferometry,” Chin. Phys. Lett. 27, 024215 (2010).
[CrossRef]

Liu, Q.

L. Z. Cai, Q. Liu, M. Z. He, and X. F. Meng, “Common form of the complex wave error caused by arbitrary phase shift errors in generalized phase-shifting interferometry and its digital correction,” Opt. Commun. 249, 95–100 (2005).
[CrossRef]

L. Z. Cai, Q. Liu, and X. L. Yang, “Simultaneous digital correction of amplitude and phase errors of retrieved wave-front in phase-shifting interferometry with arbitrary phase shift errors,” Opt. Commun. 233, 21–26 (2004).
[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] [PubMed]

Liu, X.

L. Zhang, C. Guo, Z. Rong, X. Ren, X. Liu, and H. Wang, “Phase-shifting angle choice and phase-shifting error elimination in in-line phase-shifting digital holography,” Acta Photon. Sin. 33, 353–356 (2004).

Malacara-Hernandez, D.

S. Almazan-Cuellar and D. Malacara-Hernandez, “Two-step phase-shifting algorithm,” Opt. Eng. 42, 3524–3531 (2003).
[CrossRef]

Mendoza-Santoyo, F.

Meng, X. F.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry,” J. Mod. Opt. 55, 1291–1304 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, X. C. Cheng, H. Zhang, G. Y. Dong, and X. X. Shen, “Correction of wavefront reconstruction errors caused by light source intensity instability in phase-shifting interferometry,” J. Opt. A: Pure Appl. Opt. 10, 085008 (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] [PubMed]

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 wavefront reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

L. Z. Cai, Q. Liu, M. Z. He, and X. F. Meng, “Common form of the complex wave error caused by arbitrary phase shift errors in generalized phase-shifting interferometry and its digital correction,” Opt. Commun. 249, 95–100 (2005).
[CrossRef]

Muravsky, L. I.

L. I. Muravsky, O. P. Ostash, A. B. Kmet, T. I. Voronyak, and I. M. Andreiko, “Two-frame phase-shifting interferometry for retrieval of smooth surface and its displacements,” Opt. Lasers Eng. 49, 305–312 (2011).
[CrossRef]

Oreb, B. F.

Ostash, O. P.

L. I. Muravsky, O. P. Ostash, A. B. Kmet, T. I. Voronyak, and I. M. Andreiko, “Two-frame phase-shifting interferometry for retrieval of smooth surface and its displacements,” Opt. Lasers Eng. 49, 305–312 (2011).
[CrossRef]

Patil, A.

Quan, C.

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805(2009).
[CrossRef]

Rastogi, P.

Ren, X.

L. Zhang, C. Guo, Z. Rong, X. Ren, X. Liu, and H. Wang, “Phase-shifting angle choice and phase-shifting error elimination in in-line phase-shifting digital holography,” Acta Photon. Sin. 33, 353–356 (2004).

Rong, Z.

L. Zhang, C. Guo, Z. Rong, X. Ren, X. Liu, and H. Wang, “Phase-shifting angle choice and phase-shifting error elimination in in-line phase-shifting digital holography,” Acta Photon. Sin. 33, 353–356 (2004).

Rosenfeld, D. P.

Schmit, J.

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] [PubMed]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, X. C. Cheng, H. Zhang, G. Y. Dong, and X. X. Shen, “Correction of wavefront reconstruction errors caused by light source intensity instability in phase-shifting interferometry,” J. Opt. A: Pure Appl. Opt. 10, 085008 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry,” J. Mod. Opt. 55, 1291–1304 (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 wavefront reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Stoilov, G.

G. Stoilov and T. Dragostinov, “Phase-stepping interferometry: five-frame algorithm with an arbitrary step,” Opt. Lasers Eng. 28, 61–69 (1997).
[CrossRef]

Sun, W. J.

Surrel, Y.

Tay, C. J.

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805(2009).
[CrossRef]

Tyrer, J. R.

Voronyak, T. I.

L. I. Muravsky, O. P. Ostash, A. B. Kmet, T. I. Voronyak, and I. M. Andreiko, “Two-frame phase-shifting interferometry for retrieval of smooth surface and its displacements,” Opt. Lasers Eng. 49, 305–312 (2011).
[CrossRef]

Wang, H.

L. Zhang, C. Guo, Z. Rong, X. Ren, X. Liu, and H. Wang, “Phase-shifting angle choice and phase-shifting error elimination in in-line phase-shifting digital holography,” Acta Photon. Sin. 33, 353–356 (2004).

Wang, Y. R.

X. F. Xu, L. Z. Cai, Y. R. Wang, and D. L. Li, “Accurate phase shift extraction for generalized phase-shifting interferometry,” Chin. Phys. Lett. 27, 024215 (2010).
[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] [PubMed]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry,” J. Mod. Opt. 55, 1291–1304 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, X. C. Cheng, H. Zhang, G. Y. Dong, and X. X. Shen, “Correction of wavefront reconstruction errors caused by light source intensity instability in phase-shifting interferometry,” J. Opt. A: Pure Appl. Opt. 10, 085008 (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 wavefront reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Weber, H.

White, A. D.

Xu, X. F.

X. F. Xu, L. Z. Cai, Y. R. Wang, and D. L. Li, “Accurate phase shift extraction for generalized phase-shifting interferometry,” Chin. Phys. Lett. 27, 024215 (2010).
[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] [PubMed]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, X. C. Cheng, H. Zhang, G. Y. Dong, and X. X. Shen, “Correction of wavefront reconstruction errors caused by light source intensity instability in phase-shifting interferometry,” J. Opt. A: Pure Appl. Opt. 10, 085008 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry,” J. Mod. Opt. 55, 1291–1304 (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 wavefront reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Yamaguchi, I.

Yang, X. L.

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 wavefront 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] [PubMed]

L. Z. Cai, Q. Liu, and X. L. Yang, “Simultaneous digital correction of amplitude and phase errors of retrieved wave-front in phase-shifting interferometry with arbitrary phase shift errors,” Opt. Commun. 233, 21–26 (2004).
[CrossRef]

Yatagai, T.

Yeazell, J. A.

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] [PubMed]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, X. C. Cheng, H. Zhang, G. Y. Dong, and X. X. Shen, “Correction of wavefront reconstruction errors caused by light source intensity instability in phase-shifting interferometry,” J. Opt. A: Pure Appl. Opt. 10, 085008 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry,” J. Mod. Opt. 55, 1291–1304 (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 wavefront reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

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[CrossRef]

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Acta Photon. Sin. (1)

L. Zhang, C. Guo, Z. Rong, X. Ren, X. Liu, and H. Wang, “Phase-shifting angle choice and phase-shifting error elimination in in-line phase-shifting digital holography,” Acta Photon. Sin. 33, 353–356 (2004).

Appl. Opt. (7)

Appl. Phys. Lett. (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 wavefront reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Chin. Phys. Lett. (1)

X. F. Xu, L. Z. Cai, Y. R. Wang, and D. L. Li, “Accurate phase shift extraction for generalized phase-shifting interferometry,” Chin. Phys. Lett. 27, 024215 (2010).
[CrossRef]

J. Mod. Opt. (1)

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry,” J. Mod. Opt. 55, 1291–1304 (2008).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, X. C. Cheng, H. Zhang, G. Y. Dong, and X. X. Shen, “Correction of wavefront reconstruction errors caused by light source intensity instability in phase-shifting interferometry,” J. Opt. A: Pure Appl. Opt. 10, 085008 (2008).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (4)

L. Z. Cai, Q. Liu, and X. L. Yang, “Simultaneous digital correction of amplitude and phase errors of retrieved wave-front in phase-shifting interferometry with arbitrary phase shift errors,” Opt. Commun. 233, 21–26 (2004).
[CrossRef]

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805(2009).
[CrossRef]

L. Z. Cai, Q. Liu, M. Z. He, and X. F. Meng, “Common form of the complex wave error caused by arbitrary phase shift errors in generalized phase-shifting interferometry and its digital correction,” Opt. Commun. 249, 95–100 (2005).
[CrossRef]

S. Zhang, “A non-iterative method for phase-shift estimation and wavefront reconstruction in phase-shifting digital holography,” Opt. Commun. 268, 231–234 (2006).
[CrossRef]

Opt. Eng. (2)

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[CrossRef]

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Opt. Lasers Eng. (2)

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[CrossRef]

L. I. Muravsky, O. P. Ostash, A. B. Kmet, T. I. Voronyak, and I. M. Andreiko, “Two-frame phase-shifting interferometry for retrieval of smooth surface and its displacements,” Opt. Lasers Eng. 49, 305–312 (2011).
[CrossRef]

Opt. Lett. (3)

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Figures (6)

Fig. 1
Fig. 1

RMSWFE for two different phase shift errors.

Fig. 2
Fig. 2

Optical setup for simulation.

Fig. 3
Fig. 3

Three-dimensional display of the object surface.

Fig. 4
Fig. 4

Original and reconstructed intensities and phase maps: (a) original object intensity distribution, (b) original object phase map, (c) reconstructed object intensity with phase shift 0.1801 rad , (d) reconstructed object phase map with phase shift 0.1801 rad , (e) reconstructed object intensity with phase shift 1.5938 rad , (f) reconstructed object phase map with phase shift 1.5938 rad .

Fig. 5
Fig. 5

Relative amplitude and phase error along the central line of plane P H : (a) amplitude error of object field retrieved by phase shift 0.1801 rad , (b) phase error of object field retrieved by phase shift 0.1801 rad , (c) amplitude error of object field retrieved by phase shift 1.5938 rad , (d) phase error of object field retrieved by phase shift 1.5938 rad .

Fig. 6
Fig. 6

Relative amplitude and phase error along the central line of plane P O : (a) amplitude error of object field retrieved by phase shift 0.1801 rad , (b) phase error of object field retrieved by phase shift 0.1801 rad , (c) amplitude error of object field retrieved by phase shift 1.5938 rad , (d) phase error of object field retrieved by phase shift 1.5938 rad .

Tables (1)

Tables Icon

Table 1 Calculation Results for the Surface in Eqs. (13, 14)

Equations (14)

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O ( x , y ) = A o ( x , y ) exp [ i φ ( x , y ) ] ,
O = 1 2 A r { ( I 1 A o 2 A r 2 ) + i sin α [ I 2 I 1 cos α + ( A o 2 + A r 2 ) ( cos α 1 ) ] } .
Δ O = O α Δ α ,
Δ O O = Δ O A o exp ( i φ ) .
Δ O O = sin ( α φ ) sin α ( sin φ + i cos φ ) Δ α .
Δ O O = ( Δ O O ) c + ( Δ O O ) v ,
( Δ O O ) c = Δ α 2 sin α ( cos α + i sin α )
( Δ O O ) v = Δ α 2 sin α [ cos ( 2 φ α ) + i sin ( α 2 φ ) ] .
| ( Δ O O ) v | 2 = ( Δ α ) 2 4 sin 2 α ,
| ( Δ O O Δ α ) v | 2 = 1 4 sin 2 α ,
Δ α = ε α ,
| ( Δ O O ε ) v | 2 = α 2 4 sin 2 α .
W ( x , y ) = 20 λ sin { [ ( x + x 0 ) 2 + ( y + y 0 ) 2 ] / 36 } + [ ( x + x 1 ) 2 + ( y + y 1 ) 2 ] / ( 2 R ) ,
W ( x , y ) = ( x 2 + y 2 ) / ( 2 R ) .

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