Abstract

An advanced phase-shifting interferometry approach with a spherical wavefront reference is proposed to improve the quality of the holographic image by avoiding errors caused by noncollimated reference and lowering the resolution of the recording device. By considering not only the real amplitude but also the phase distribution of a spherical wavefront reference, a singular object-wave reconstruction formula is deduced. The suggested method here can work without using the collimator in the reference wave and can then remove all the errors incurred by it. Computer simulations demonstrate that this technique is more convenient in the recording process and can improve the precision of the reconstructed wavefront by more than one order of magnitude after considering the real reference amplitude. Optical experiment results show the feasibility and effectiveness of this method.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [CrossRef]
  2. J. E. Greivenkamp, “General data reduction for heterodyne interferometry,” Opt. Eng. 23, 350–352 (1984).
  3. T. C. Poon, T. Akin, G. Indebetouw, and T. Kim, “Horizontal-parallax-only electronic holography,” Opt. Express 13, 2427–2432 (2005).
    [CrossRef]
  4. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef]
  5. I. Yamaguchi, T. Matsumura, and J. Kato, “Phase-shifting color digital holography,” Opt. Lett. 27, 1108–1110 (2002).
    [CrossRef]
  6. B. Gutman and H. Weber, “Phase-shifter calibration and error detection in phase-shifting applications: a new method,” Appl. Opt. 37, 7624–7631 (1998).
    [CrossRef]
  7. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, “Phase-shifting for nonsinusoidal waveforms with phase-shift errors,” J. Opt. Soc. Am. A 12, 761–768 (1997).
    [CrossRef]
  8. 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]
  9. L. Z. Cai, Q. Liu, and X. L. Yang, “Phase-shift extraction and wavefront reconstruction in phase-shifting interferometry with arbitrary phase steps,” Opt. Lett. 28, 1808–1810 (2003).
    [CrossRef]
  10. G.-S. Han and S.-W. Kim, “Numerical correction of reference phases in phase-shifting interferometry by iterative least-squares fitting,” Appl. Opt. 33, 7321–7325 (1994).
    [CrossRef]
  11. 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]
  12. A. Patil, B. Raphael, and P. Rastogi, “Generalized phase-shifting interferometry by use of a direct stochastic algorithm for global search,” Opt. Lett. 29, 1381–1383 (2004).
    [CrossRef]
  13. J. C. Xu, W. M. Jin, L. Q. Chai, and Q. Xu, “Phase extraction from randomly phase-shifted interferograms by combining principal component analysis and least squares method,” Opt. Express 19, 20483–20492 (2011).
    [CrossRef]
  14. 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]
  15. 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]
  16. 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]
  17. 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]
  18. 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]
  19. 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]
  20. 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]
  21. 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]
  22. L. Z. Cai, Q. Liu, and X. L. Yang, “Effects of measurement errors on both the amplitude and phase reconstruction in phase shifting interferometry,” J. Mod. Opt. 52, 45–59 (2005).
    [CrossRef]
  23. 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]
  24. 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]
  25. L. Z. Cai and R. S. Yan, “Correction of wave front retrieval errors caused by the collimation errors of reference wave in phase-shifting interferometry,” J. Optoelectron. Laser 22, 725–728 (2011).
  26. D. Dieter, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
    [CrossRef]
  27. T. Nomura and M. Imbe, “Single-exposure phase-shifting digital holography using a random phase reference wave,” Opt. Lett. 35, 2281–2283 (2010).
    [CrossRef]

2011 (3)

J. C. Xu, W. M. Jin, L. Q. Chai, and Q. Xu, “Phase extraction from randomly phase-shifted interferograms by combining principal component analysis and least squares method,” Opt. Express 19, 20483–20492 (2011).
[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]

L. Z. Cai and R. S. Yan, “Correction of wave front retrieval errors caused by the collimation errors of reference wave in phase-shifting interferometry,” J. Optoelectron. Laser 22, 725–728 (2011).

2010 (4)

T. Nomura and M. Imbe, “Single-exposure phase-shifting digital holography using a random phase reference wave,” Opt. Lett. 35, 2281–2283 (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]

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]

2008 (3)

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]

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, 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]

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]

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 (2)

T. C. Poon, T. Akin, G. Indebetouw, and T. Kim, “Horizontal-parallax-only electronic holography,” Opt. Express 13, 2427–2432 (2005).
[CrossRef]

L. Z. Cai, Q. Liu, and X. L. Yang, “Effects of measurement errors on both the amplitude and phase reconstruction in phase shifting interferometry,” J. Mod. Opt. 52, 45–59 (2005).
[CrossRef]

2004 (3)

2003 (1)

2002 (1)

2001 (1)

D. Dieter, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

1998 (1)

1997 (2)

1994 (1)

1984 (1)

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

1974 (1)

Akin, T.

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.

L. Z. Cai and R. S. Yan, “Correction of wave front retrieval errors caused by the collimation errors of reference wave in phase-shifting interferometry,” J. Optoelectron. Laser 22, 725–728 (2011).

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, “Effects of measurement errors on both the amplitude and phase reconstruction in phase shifting interferometry,” J. Mod. Opt. 52, 45–59 (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]

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

Chai, L. Q.

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]

Deiwick, M.

D. Dieter, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

Deleré, H.

D. Dieter, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

Dieter, D.

D. Dieter, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

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 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]

Droste, H.

D. Dieter, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

Farrant, D. I.

Gallagher, J. E.

Greivenkamp, J. E.

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

Gutman, B.

Han, G.-S.

Herriott, D. R.

Hibino, K.

Imbe, M.

Indebetouw, G.

Jin, W. M.

Kato, J.

Kemper, B.

D. Dieter, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

Kim, S.-W.

Kim, T.

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]

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]

Li, Y.

Liu, Q.

L. Z. Cai, Q. Liu, and X. L. Yang, “Effects of measurement errors on both the amplitude and phase reconstruction in phase shifting interferometry,” J. Mod. Opt. 52, 45–59 (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]

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

Matsumura, T.

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]

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]

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]

Nomura, T.

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]

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.

Poon, T. C.

Raphael, B.

Rastogi, P.

Rosenfeld, D. P.

Scheld, H. H.

D. Dieter, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

Shen, X. X.

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]

Sun, W. J.

von Bally, G.

D. Dieter, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

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.

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.

White, A. D.

Xu, J. C.

Xu, Q.

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, 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]

Yamaguchi, I.

Yan, R. S.

L. Z. Cai and R. S. Yan, “Correction of wave front retrieval errors caused by the collimation errors of reference wave in phase-shifting interferometry,” J. Optoelectron. Laser 22, 725–728 (2011).

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, “Effects of measurement errors on both the amplitude and phase reconstruction in phase shifting interferometry,” J. Mod. Opt. 52, 45–59 (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]

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

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. 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]

Zhang, S.

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]

Zhang, T.

Appl. Opt. (4)

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)

L. Z. Cai, Q. Liu, and X. L. Yang, “Effects of measurement errors on both the amplitude and phase reconstruction in phase shifting interferometry,” J. Mod. Opt. 52, 45–59 (2005).
[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)

J. Optoelectron. Laser (1)

L. Z. Cai and R. S. Yan, “Correction of wave front retrieval errors caused by the collimation errors of reference wave in phase-shifting interferometry,” J. Optoelectron. Laser 22, 725–728 (2011).

Opt. Commun. (3)

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]

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. (1)

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

Opt. Express (3)

Opt. Lasers Eng. (2)

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]

D. Dieter, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. H. Scheld, and G. von Bally, “Lensless Fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[CrossRef]

Opt. Lett. (7)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

Optical setup for simulation.

Fig. 2.
Fig. 2.

Three-dimensional display of the object surface.

Fig. 3.
Fig. 3.

Amplitude and phase distributions of the object wavefront on the original objective plane: (a) and (b) are the intensity and phase distribution of the original object wave, respectively.

Fig. 4.
Fig. 4.

Reconstructed objective wavefront with two cases of approximations: (a) and (b) are the intensity and phase distributions, respectively, of the object wave reconstructed with a constant real amplitude of A r ; (c) and (d) are the intensity and phase distributions, respectively, of the object wave reconstructed with a constant phase of A r .

Fig. 5.
Fig. 5.

Error distributions of relative amplitude and phase of object wave: (a) relative amplitude and (b) phase on the central line of CCD chip; (c) relative amplitude and (d) phase on the central line of the original object wave plane.

Fig. 6.
Fig. 6.

Relative amplitude and phase error distributions of the reconstructed object wave on the horizontal central line on the recording plane by using a spherical wavefront reference amplitude and phase: (a) relative amplitude error and (b) phase error.

Fig. 7.
Fig. 7.

Experimental results: (a) and (b) are the holograms by interferences of a spherical objective wave with plane and spherical references, respectively; (c) is the phase map of the reconstructed object wave.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

A r = a / ( x 2 + y 2 + R 2 ) 1 / 2 ,
φ r = 2 π ( x 2 + y 2 + R 2 ) 1 / 2 / λ .
I j ( x , y ) = A o 2 ( x , y ) + A r 2 ( x , y ) + 2 A o ( x , y ) A r ( x , y ) cos [ φ o r ( x , y ) δ j ] , j = 1 , 2 , 3 , 4 ,
φ o r ( x , y ) = φ o ( x , y ) φ r ( x , y )
I 1 = A o 2 + A r 2 + 2 A o A r cos φ o r ,
I 2 = A o 2 + A r 2 + 2 A o A r sin φ o r ,
I 3 = A o 2 + A r 2 2 A o A r cos φ o r ,
I 4 = A o 2 + A r 2 2 A o A r sin φ o r .
4 A o A r cos φ o r = I 1 I 3 ,
4 A o A r sin φ o r = I 2 I 4 .
4 A o A r exp ( i φ o r ) = ( I 1 I 3 ) + i ( I 2 I 4 ) .
4 A o A r exp ( i φ o i φ r ) = ( I 1 I 3 ) + i ( I 2 I 4 ) .
U = 1 4 A r [ ( I 1 I 3 ) + i ( I 2 I 4 ) ] exp ( i φ r ) .
h ( x , y ) = 20 λ sin { [ ( x + x 0 ) 2 + ( y + y 0 ) 2 ] / 38 } + [ ( x x 1 ) 2 + ( y y 1 ) 2 ] / ( 2 r ) ,
A r = a ( 1 x 2 + y 2 2 R 2 ) .

Metrics