Abstract

An accurate aperture synthesis method in generalized phase-shifting interferometry is suggested to improve the quality of the reconstructed object wavefront by stitching both the phase and the real amplitude of the object wave on the recording plane. Since the phase distribution affects the reconstruction of the original object wavefront, phase stitching is also important in aperture synthesis. Double correlations are used to find the proper relative locations and correct the phase error of subwavefronts on the recording plane. By using phase correction, the phase distributions of subwavefronts are combined perfectly. Corresponding optical experimental results have verified the effectiveness of this method, which can stitch not only the real amplitudes but also the phases of the complex amplitudes of the object wave on the recording plane and improve the quality of the reconstructed object image.

© 2013 Optical Society of America

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2013 (2)

R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, and L. M. Arévalo Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Opt. Lasers Eng. 51, 626–632 (2013).
[CrossRef]

X. F. Xu, G. C. Lu, Y. J. Tian, G. X. Han, H. G. Yuan, F. Gao, X. X. Miao, and Z. Y. Jiao, “High-precision phase-shifting interferometry with spherical wavefront reference,” Appl. Opt. 52, A188–A194 (2013).
[CrossRef]

2012 (2)

X. F. Xu, L. Z. Cai, G. C. Lu, G. X. Han, Y. J. Tian, Q. Zhang, and Z. Y. Jiao, “Advanced Aperture synthesis by wave-front combination in generalized phase-shifting interferometry,” Chin. Phys. Lett. 29, 084202 (2012).
[CrossRef]

M. K. Kim, “Adaptive optics by incoherent digital holography,” Opt. Lett. 37, 2694–2696 (2012).
[CrossRef]

2011 (5)

2010 (3)

J. C. Xu, Q. Xu, L. Q. Chai, Y. Li, and H. Wang, “Direct phase extraction from interferograms with random phase shifts,” Opt. Express 18, 20620–20627 (2010).
[CrossRef]

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, and R. S. Yan, “Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry,” J. Opt. 12, 015301 (2010).
[CrossRef]

2009 (1)

2008 (3)

J. Novák, P. Novák, and A. Mikš, “Multi-step phase-shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (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. 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 10, 085008 (2008).
[CrossRef]

2007 (2)

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]

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803 (2007).
[CrossRef]

2005 (1)

2004 (3)

2000 (1)

1998 (1)

1997 (2)

1996 (1)

1991 (1)

1984 (1)

J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 234350 (1984).
[CrossRef]

1967 (1)

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

Akin, T.

Arévalo Aguilar, L. M.

R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, and L. M. Arévalo Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Opt. Lasers Eng. 51, 626–632 (2013).
[CrossRef]

Basaran, C.

Cai, L. Z.

X. F. Xu, L. Z. Cai, G. C. Lu, G. X. Han, Y. J. Tian, Q. Zhang, and Z. Y. Jiao, “Advanced Aperture synthesis by wave-front combination in generalized phase-shifting interferometry,” Chin. Phys. Lett. 29, 084202 (2012).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, and R. S. Yan, “Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry,” J. Opt. 12, 015301 (2010).
[CrossRef]

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]

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 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]

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, “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]

Chai, L. Q.

Chen, B. C.

Chen, X.

Cheng, C. J.

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]

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 10, 085008 (2008).
[CrossRef]

Cheung, W. K.

Creath, K.

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. 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 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]

Gao, F.

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]

Gramaglia, M.

Greivenkamp, J. E.

J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 234350 (1984).
[CrossRef]

Guerrero-Sánchez, F.

R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, and L. M. Arévalo Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Opt. Lasers Eng. 51, 626–632 (2013).
[CrossRef]

Guo, H. W.

Gutman, B.

Han, G. X.

X. F. Xu, G. C. Lu, Y. J. Tian, G. X. Han, H. G. Yuan, F. Gao, X. X. Miao, and Z. Y. Jiao, “High-precision phase-shifting interferometry with spherical wavefront reference,” Appl. Opt. 52, A188–A194 (2013).
[CrossRef]

X. F. Xu, L. Z. Cai, G. C. Lu, G. X. Han, Y. J. Tian, Q. Zhang, and Z. Y. Jiao, “Advanced Aperture synthesis by wave-front combination in generalized phase-shifting interferometry,” Chin. Phys. Lett. 29, 084202 (2012).
[CrossRef]

Indebetouw, G.

Jiao, Z. Y.

X. F. Xu, G. C. Lu, Y. J. Tian, G. X. Han, H. G. Yuan, F. Gao, X. X. Miao, and Z. Y. Jiao, “High-precision phase-shifting interferometry with spherical wavefront reference,” Appl. Opt. 52, A188–A194 (2013).
[CrossRef]

X. F. Xu, L. Z. Cai, G. C. Lu, G. X. Han, Y. J. Tian, Q. Zhang, and Z. Y. Jiao, “Advanced Aperture synthesis by wave-front combination in generalized phase-shifting interferometry,” Chin. Phys. Lett. 29, 084202 (2012).
[CrossRef]

Jin, W. M.

Juarez-Salazar, R.

R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, and L. M. Arévalo Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Opt. Lasers Eng. 51, 626–632 (2013).
[CrossRef]

Kim, M. K.

Kim, T.

Kreis, T.

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803 (2007).
[CrossRef]

Lai, G.

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]

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]

Li, Y.

Lin, Y. C.

Liu, Q.

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, “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]

Lu, G. C.

X. F. Xu, G. C. Lu, Y. J. Tian, G. X. Han, H. G. Yuan, F. Gao, X. X. Miao, and Z. Y. Jiao, “High-precision phase-shifting interferometry with spherical wavefront reference,” Appl. Opt. 52, A188–A194 (2013).
[CrossRef]

X. F. Xu, L. Z. Cai, G. C. Lu, G. X. Han, Y. J. Tian, Q. Zhang, and Z. Y. Jiao, “Advanced Aperture synthesis by wave-front combination in generalized phase-shifting interferometry,” Chin. Phys. Lett. 29, 084202 (2012).
[CrossRef]

Meneses-Fabian, C.

R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, and L. M. Arévalo Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Opt. Lasers Eng. 51, 626–632 (2013).
[CrossRef]

Meng, X. F.

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. 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 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]

Miao, X. X.

Mikš, A.

J. Novák, P. Novák, and A. Mikš, “Multi-step phase-shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
[CrossRef]

Novák, J.

J. Novák, P. Novák, and A. Mikš, “Multi-step phase-shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
[CrossRef]

Novák, P.

J. Novák, P. Novák, and A. Mikš, “Multi-step phase-shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
[CrossRef]

Patil, A.

Poon, T. C.

Raphael, B.

Rastogi, P.

Robledo-Sánchez, C.

R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, and L. M. Arévalo Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Opt. Lasers Eng. 51, 626–632 (2013).
[CrossRef]

Schlüter, K.

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803 (2007).
[CrossRef]

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]

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 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]

Sun, W. J.

Surrel, Y.

Tian, Y. J.

X. F. Xu, G. C. Lu, Y. J. Tian, G. X. Han, H. G. Yuan, F. Gao, X. X. Miao, and Z. Y. Jiao, “High-precision phase-shifting interferometry with spherical wavefront reference,” Appl. Opt. 52, A188–A194 (2013).
[CrossRef]

X. F. Xu, L. Z. Cai, G. C. Lu, G. X. Han, Y. J. Tian, Q. Zhang, and Z. Y. Jiao, “Advanced Aperture synthesis by wave-front combination in generalized phase-shifting interferometry,” Chin. Phys. Lett. 29, 084202 (2012).
[CrossRef]

Tsang, P.

Wang, H.

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, and R. S. Yan, “Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry,” J. Opt. 12, 015301 (2010).
[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 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]

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.

Xu, J. C.

Xu, Q.

Xu, X. F.

X. F. Xu, G. C. Lu, Y. J. Tian, G. X. Han, H. G. Yuan, F. Gao, X. X. Miao, and Z. Y. Jiao, “High-precision phase-shifting interferometry with spherical wavefront reference,” Appl. Opt. 52, A188–A194 (2013).
[CrossRef]

X. F. Xu, L. Z. Cai, G. C. Lu, G. X. Han, Y. J. Tian, Q. Zhang, and Z. Y. Jiao, “Advanced Aperture synthesis by wave-front combination in generalized phase-shifting interferometry,” Chin. Phys. Lett. 29, 084202 (2012).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, and R. S. Yan, “Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry,” J. Opt. 12, 015301 (2010).
[CrossRef]

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]

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 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]

Yamaguchi, I.

Yan, R. S.

X. F. Xu, L. Z. Cai, Y. R. Wang, and R. S. Yan, “Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry,” J. Opt. 12, 015301 (2010).
[CrossRef]

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]

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.

Yuan, H. G.

Zhang, H.

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 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]

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]

Zhang, Q.

X. F. Xu, L. Z. Cai, G. C. Lu, G. X. Han, Y. J. Tian, Q. Zhang, and Z. Y. Jiao, “Advanced Aperture synthesis by wave-front combination in generalized phase-shifting interferometry,” Chin. Phys. Lett. 29, 084202 (2012).
[CrossRef]

Zhang, T.

Zhou, C.

Appl. Opt. (8)

Appl. Phys. Lett (1)

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

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. (2)

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, G. C. Lu, G. X. Han, Y. J. Tian, Q. Zhang, and Z. Y. Jiao, “Advanced Aperture synthesis by wave-front combination in generalized phase-shifting interferometry,” Chin. Phys. Lett. 29, 084202 (2012).
[CrossRef]

J. Opt. (1)

X. F. Xu, L. Z. Cai, Y. R. Wang, and R. S. Yan, “Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry,” J. Opt. 12, 015301 (2010).
[CrossRef]

J. Opt. A (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 10, 085008 (2008).
[CrossRef]

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

Opt. Commun. (2)

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]

J. Novák, P. Novák, and A. Mikš, “Multi-step phase-shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
[CrossRef]

Opt. Eng. (2)

J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 234350 (1984).
[CrossRef]

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803 (2007).
[CrossRef]

Opt. Express (5)

Opt. Lasers Eng. (1)

R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, and L. M. Arévalo Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Opt. Lasers Eng. 51, 626–632 (2013).
[CrossRef]

Opt. Lett. (5)

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Figures (9)

Fig. 1.
Fig. 1.

Flow chart for complex amplitude synthesis.

Fig. 2.
Fig. 2.

Experiment setup for aperture synthesis. SF, space filter; L, lens; D, diaphragm; PO, object plane; PH, recording plane; PSD, phase-shifting device.

Fig. 3.
Fig. 3.

Reference intensities and interferograms (a), (b) from the upper and (c), (d) from the lower set of GPSI frames.

Fig. 4.
Fig. 4.

Correlation models: (a) intensity matching model and (b) phase correction model.

Fig. 5.
Fig. 5.

Correlation value distributions on the recording plane.

Fig. 6.
Fig. 6.

Correlation value distributions (a) in one direction and (b) for phase correction.

Fig. 7.
Fig. 7.

Phases and intensities of object wavefront retrieved on original plane (a), (b) from the upper set of frames and (c), (d) from the lower set of frames.

Fig. 8.
Fig. 8.

Phases and intensities of the object wave combined on recording plane (a), (b) without phase correction and (c), (d) with phase correction.

Fig. 9.
Fig. 9.

Phases and intensities of object wave on original plane (a), (b) without phase correction and (c), (d) with phase correction.

Equations (9)

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ci(x,y)=ir1(x1,y1)ir2(x2,y2),
αq=2tan1[|(I1qI2q)/(4IoqIrq)||(I1q+I2q2Ioq2Irq)/(4IoqIrq)|],q=1,2.
Uq=I1qIoqIrq2Irq+iI2qI1qcosαq(1cosαq)(Ioq+Irq)2Irqsinαq.
Δφ=2πd/λ.
φo2=φo1+2πd/λ.
φo2=φo1+Δφo.
cp(x,y)=φo1(x1,y1)[φo2(x2,y2)Δφo].
O=IFFT[FFT(h)FFT(U)],
h=exp(ikz)exp[ik(x2+y2)/(2z)]/(iλz),

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