Abstract

An optical configuration for parallel two-step phase-shifting digital holographic microscopy (DHM) based on a grating pair is proposed for the purpose of real-time phase microscopy. Orthogonally circularly polarized object and reference waves are diffracted twice by a pair of gratings, and two parallel copies for each beams come into being. Combined with polarization elements, parallel two-step phase-shifting holograms are obtained. Based on the proposed configuration, two schemes of DHM, i.e., slightly off-axis and on-axis DHM, have been implemented. The slightly off-axis DHM suppresses the dc term by subtracting the two phase-shifting holograms from each other, thus the requirement on the off-axis angle and sampling power of the CCD camera is reduced greatly. The on-axis DHM has the least requirement on the resolving power of the CCD camera, while it requires that the reference wave is premeasured and its intensity is no less than 2 times the maximal intensity of the object wave.

© 2011 Optical Society of America

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References

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  1. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
    [CrossRef]
  2. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432(1983).
    [CrossRef] [PubMed]
  3. X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31, 1414–1416(2006).
    [CrossRef] [PubMed]
  4. E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000).
    [CrossRef]
  5. B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52–A61 (2008).
    [CrossRef] [PubMed]
  6. W. J. Qu, K. Bhattacharya, C. Q. Choo, Y. J. Yu, and A. Asundi, “Transmission digital holographic microscopy based on a beam-splitter cube interferometer,” Appl. Opt. 48, 2778–2783 (2009).
    [CrossRef] [PubMed]
  7. T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30, 1165–1167 (2005).
    [CrossRef] [PubMed]
  8. Y. Takaki, H. Kawai, and H. Ohzu, “Hybrid holographic microscopy free of conjugate and zero-order images,” Appl. Opt. 38, 4990–4996 (1999).
    [CrossRef]
  9. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  10. G.-L. Chen, C.-Y. Lin, M.-K. Kuo, and C.-C. Chang, “Numerical suppression of zero-order image in digital holography,” Opt. Express 15, 8851–8856 (2007).
    [CrossRef] [PubMed]
  11. N. Pavillon, C. Arfire, I. Bergoënd, and C. Depeursinge, “Iterative method for zero-order suppression in off-axis digital holography,” Opt. Express 18, 15318–15331 (2010).
    [CrossRef] [PubMed]
  12. N. T. Shaked, Y. Zhu, M. T. Rinehart, and A. Wax, “Two-step only phase-shifting interferometry with optimized camera bandwidth for microscopy of live cells,” Opt. Express 17, 15585–15591(2009).
    [CrossRef] [PubMed]
  13. N. T. Shaked, M. T. Rinehart, and A. Wax, “Dual-interference-channel quantitative-phase microscopy of live cell dynamics,” Opt. Lett. 34, 767–769 (2009).
    [CrossRef] [PubMed]
  14. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef] [PubMed]
  15. I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40, 6177–6186 (2001).
    [CrossRef]
  16. V. Mico, Z. Zalevsky, and J. García, “Common-path phase-shifting digital holographic microscopy: a way to quantitative phase imaging and superresolution,” Opt. Commun. 2814273–4281 (2008).
    [CrossRef]
  17. J.-P. Liu and T.-C. Poon, “Two-step-only quadrature phase-shifting digital holography,” Opt. Lett. 34, 250–252 (2009).
    [CrossRef] [PubMed]
  18. R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).
  19. C. L. Koliopoulos, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1992).
    [CrossRef]
  20. N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting interferometry,” Opt. Eng. 42, 367–372 (2003).
    [CrossRef]
  21. M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44, 6861–6868 (2005).
    [CrossRef] [PubMed]
  22. Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47, D183–D189 (2008).
    [CrossRef] [PubMed]
  23. T. Kakue, Y. Moritani, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Image quality improvement of parallel four-step phase-shifting digital holography by using the algorithm of parallel two-step phase-shifting digital holography,” Opt. Express 18, 9555–9560 (2010).
    [CrossRef] [PubMed]
  24. G. Rodriguez-Zurita, C. Meneses-Fabian, N.-I. Toto-Arellano, J. F. Vázquez-Castillo, and C. Robledo-Sánchez, “One-shot phase-shifting phase-grating interferometry with modulation of polarization: case of four interferograms,” Opt. Express 16, 7806–7817 (2008).
    [CrossRef] [PubMed]
  25. N.-I. Toto-Arellano, G. Rodriguez-Zurita, C. Meneses-Fabian, and J. Vazquez-Castillo, “Phase shifts in the Fourier spectra of phase gratings and phase grids: an application for one-shot phase-shifting interferometry,” Opt. Express 16, 19330–19341 (2008).
    [CrossRef]
  26. C. Meneses-Fabian, G. Rodriguez-Zurita, M. Encarnacion-Gutierrez, N.-I. Toto-Arellano, “Phase-shifting interferometry with four interferograms using linear polarization modulation and a Ronchi grating displaced by only a small unknown amount,” Opt. Commun. 2823063–3068 (2009).
    [CrossRef]
  27. G. Rodriguez-Zurita, N.-I. Toto-Arellano, C. Meneses-Fabian, and J. F. Vázquez-Castillo, “One-shot phase-shifting interferometry: five, seven, and nine interferograms,” Opt. Lett. 33, 2788–2790(2008).
    [CrossRef] [PubMed]
  28. C. Meneses-Fabian and G. Rodriguez-Zurita, “Optical tomography of transparent objects with phase-shifting interferometry and stepwise-shifted Ronchi ruling,” J. Opt. Soc. Am. A 23, 298–305 (2006).
    [CrossRef]
  29. T. Kiire, S. Nakadate, and M. Shibuya, “Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating,” Appl. Opt. 47, 4787–4792 (2008).
    [CrossRef] [PubMed]
  30. N. T. Shaked, T. M. Newpher, M. D. Ehlers, and A. Wax, “Parallel on-axis holographic phase microscopy of biological cells and unicellular microorganism dynamics,” Appl. Opt. 49, 2872–2878(2010).
    [CrossRef] [PubMed]
  31. M. Kujawinska and D. W. Robinson, “Multichannel phase-stepped holographic interferometry,” Appl. Opt. 27, 312–320(1988).
    [CrossRef] [PubMed]
  32. L. Chen, S. Yeh, A. Tapilouw, and J. Chang, “3-D surface profilometry using simultaneous phase-shifting interferometry,” Opt. Commun. 283, 3376–3382 (2010).
    [CrossRef]
  33. B. B. García, A. J. Moore, C. Pérez-López, L. Wang, and T. Tschudi, “Transient deformation measurement with electronic speckle pattern interferometry by use of a holographic optical element for spatial phase stepping,” Appl. Opt. 38, 5944–5947(1999).
    [CrossRef]
  34. E. N. Leith and R. Hershey, “Transfer functions and spatial filtering in grating interferometers,” Appl. Opt. 24, 237–239(1985).
    [CrossRef] [PubMed]
  35. G. J. Swanson and E. N. Leith, “Lau effect and grating imaging,” J. Opt. Soc. Am. 72, 552–555 (1982).
    [CrossRef]
  36. G. J. Swanson and E. N. Leith, “Analysis of the Lau effect and generalized grating imaging,” J. Opt. Soc. Am. A 2, 789–793 (1985).
    [CrossRef]
  37. J. Schwider, “Continuous lateral shearing interferometer,” Appl. Opt. 23, 4403–4409 (1984).
    [CrossRef] [PubMed]
  38. P. J. de Groot, “Grating interferometer for flatness testing,” Opt. Lett. 21, 228–230 (1996).
    [CrossRef] [PubMed]
  39. P. Gao, I. Harder, V. Nercissian, K. Mantel, and B. Yao, “Phase-shifting point-diffraction interferometry with common-path and in-line configuration for microscopy,” Opt. Lett. 35, 712–714 (2010).
    [CrossRef] [PubMed]
  40. V. Ronchi, “On the phase grating interferometer,” Appl. Opt. 4, 1041–1042 (1965).
    [CrossRef]
  41. G. Vogl, “A phase grating interferometer,” Appl. Opt. 3, 1089–1089 (1964).
    [CrossRef]

2010 (5)

2009 (5)

2008 (7)

B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52–A61 (2008).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, and J. García, “Common-path phase-shifting digital holographic microscopy: a way to quantitative phase imaging and superresolution,” Opt. Commun. 2814273–4281 (2008).
[CrossRef]

G. Rodriguez-Zurita, C. Meneses-Fabian, N.-I. Toto-Arellano, J. F. Vázquez-Castillo, and C. Robledo-Sánchez, “One-shot phase-shifting phase-grating interferometry with modulation of polarization: case of four interferograms,” Opt. Express 16, 7806–7817 (2008).
[CrossRef] [PubMed]

N.-I. Toto-Arellano, G. Rodriguez-Zurita, C. Meneses-Fabian, and J. Vazquez-Castillo, “Phase shifts in the Fourier spectra of phase gratings and phase grids: an application for one-shot phase-shifting interferometry,” Opt. Express 16, 19330–19341 (2008).
[CrossRef]

Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47, D183–D189 (2008).
[CrossRef] [PubMed]

G. Rodriguez-Zurita, N.-I. Toto-Arellano, C. Meneses-Fabian, and J. F. Vázquez-Castillo, “One-shot phase-shifting interferometry: five, seven, and nine interferograms,” Opt. Lett. 33, 2788–2790(2008).
[CrossRef] [PubMed]

T. Kiire, S. Nakadate, and M. Shibuya, “Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating,” Appl. Opt. 47, 4787–4792 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (2)

2005 (2)

2003 (1)

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting interferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

2001 (1)

2000 (1)

1999 (2)

1997 (1)

1996 (1)

1992 (1)

C. L. Koliopoulos, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1992).
[CrossRef]

1988 (1)

1985 (2)

1984 (2)

J. Schwider, “Continuous lateral shearing interferometer,” Appl. Opt. 23, 4403–4409 (1984).
[CrossRef] [PubMed]

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

1983 (1)

1982 (2)

1967 (1)

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

1965 (1)

1964 (1)

Arfire, C.

Asundi, A.

Awatsuji, Y.

Bergoënd, I.

Bhattacharya, K.

Brock, N.

Burow, R.

Cai, L. Z.

Chang, C.-C.

Chang, J.

L. Chen, S. Yeh, A. Tapilouw, and J. Chang, “3-D surface profilometry using simultaneous phase-shifting interferometry,” Opt. Commun. 283, 3376–3382 (2010).
[CrossRef]

Chen, G.-L.

Chen, L.

L. Chen, S. Yeh, A. Tapilouw, and J. Chang, “3-D surface profilometry using simultaneous phase-shifting interferometry,” Opt. Commun. 283, 3376–3382 (2010).
[CrossRef]

Choo, C. Q.

Cuche, E.

Dasari, R. R.

de Groot, P. J.

Depeursinge, C.

Dong, G. Y.

Ehlers, M. D.

Elssner, K.-E.

Encarnacion-Gutierrez, M.

C. Meneses-Fabian, G. Rodriguez-Zurita, M. Encarnacion-Gutierrez, N.-I. Toto-Arellano, “Phase-shifting interferometry with four interferograms using linear polarization modulation and a Ronchi grating displaced by only a small unknown amount,” Opt. Commun. 2823063–3068 (2009).
[CrossRef]

Feld, M. S.

Gao, P.

García, B. B.

García, J.

V. Mico, Z. Zalevsky, and J. García, “Common-path phase-shifting digital holographic microscopy: a way to quantitative phase imaging and superresolution,” Opt. Commun. 2814273–4281 (2008).
[CrossRef]

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]

Grzanna, J.

Harder, I.

Hayes, J.

Hershey, R.

Hui, W. K.

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting interferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Ikeda, T.

Ina, H.

Ito, K.

Kakue, T.

Kaneko, A.

Kato, J.

Kawai, H.

Kemper, B.

Kiire, T.

Kobayashi, S.

Koliopoulos, C. L.

C. L. Koliopoulos, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1992).
[CrossRef]

Koyama, T.

Kubota, T.

Kujawinska, M.

Kuo, M.-K.

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]

Leith, E. N.

Lin, C.-Y.

Liu, J.-P.

Mantel, K.

Marquet, P.

Matoba, O.

Meneses-Fabian, C.

Meng, X. F.

Merkel, K.

Mico, V.

V. Mico, Z. Zalevsky, and J. García, “Common-path phase-shifting digital holographic microscopy: a way to quantitative phase imaging and superresolution,” Opt. Commun. 2814273–4281 (2008).
[CrossRef]

Millerd, J.

Mizuno, J.

Moore, A. J.

Moore, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

Moritani, Y.

Nakadate, S.

Nercissian, V.

Newpher, T. M.

Ngoi, B. K. A.

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting interferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Nishio, K.

North-Morris, M.

Novak, M.

Ohta, S.

Ohzu, H.

Pavillon, N.

Pérez-López, C.

Poon, T.-C.

Popescu, G.

Qu, W. J.

Rinehart, M. T.

Robinson, D. W.

Robledo-Sánchez, C.

Rodriguez-Zurita, G.

Ronchi, V.

Schwider, J.

Shaked, N. T.

Shen, X. X.

Shibuya, M.

Shimozato, Y.

Sivakumar, N. R.

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting interferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Smythe, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

Spolaczyk, R.

Swanson, G. J.

Tahara, T.

Takaki, Y.

Takeda, M.

Tapilouw, A.

L. Chen, S. Yeh, A. Tapilouw, and J. Chang, “3-D surface profilometry using simultaneous phase-shifting interferometry,” Opt. Commun. 283, 3376–3382 (2010).
[CrossRef]

Toto-Arellano, N.-I.

Tschudi, T.

Ura, S.

Vazquez-Castillo, J.

Vázquez-Castillo, J. F.

Venkatakrishnan, K.

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting interferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Vogl, G.

von Bally, G.

Wang, L.

Wang, Y. R.

Wax, A.

Wyant, J.

Xu, X. F.

Yamaguchi, I.

Yang, X. L.

Yao, B.

Yeh, S.

L. Chen, S. Yeh, A. Tapilouw, and J. Chang, “3-D surface profilometry using simultaneous phase-shifting interferometry,” Opt. Commun. 283, 3376–3382 (2010).
[CrossRef]

Yu, Y. J.

Zalevsky, Z.

V. Mico, Z. Zalevsky, and J. García, “Common-path phase-shifting digital holographic microscopy: a way to quantitative phase imaging and superresolution,” Opt. Commun. 2814273–4281 (2008).
[CrossRef]

Zhang, T.

Zhu, Y.

Appl. Opt. (16)

E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000).
[CrossRef]

B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52–A61 (2008).
[CrossRef] [PubMed]

W. J. Qu, K. Bhattacharya, C. Q. Choo, Y. J. Yu, and A. Asundi, “Transmission digital holographic microscopy based on a beam-splitter cube interferometer,” Appl. Opt. 48, 2778–2783 (2009).
[CrossRef] [PubMed]

Y. Takaki, H. Kawai, and H. Ohzu, “Hybrid holographic microscopy free of conjugate and zero-order images,” Appl. Opt. 38, 4990–4996 (1999).
[CrossRef]

J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432(1983).
[CrossRef] [PubMed]

I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40, 6177–6186 (2001).
[CrossRef]

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44, 6861–6868 (2005).
[CrossRef] [PubMed]

Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47, D183–D189 (2008).
[CrossRef] [PubMed]

T. Kiire, S. Nakadate, and M. Shibuya, “Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating,” Appl. Opt. 47, 4787–4792 (2008).
[CrossRef] [PubMed]

N. T. Shaked, T. M. Newpher, M. D. Ehlers, and A. Wax, “Parallel on-axis holographic phase microscopy of biological cells and unicellular microorganism dynamics,” Appl. Opt. 49, 2872–2878(2010).
[CrossRef] [PubMed]

M. Kujawinska and D. W. Robinson, “Multichannel phase-stepped holographic interferometry,” Appl. Opt. 27, 312–320(1988).
[CrossRef] [PubMed]

B. B. García, A. J. Moore, C. Pérez-López, L. Wang, and T. Tschudi, “Transient deformation measurement with electronic speckle pattern interferometry by use of a holographic optical element for spatial phase stepping,” Appl. Opt. 38, 5944–5947(1999).
[CrossRef]

E. N. Leith and R. Hershey, “Transfer functions and spatial filtering in grating interferometers,” Appl. Opt. 24, 237–239(1985).
[CrossRef] [PubMed]

J. Schwider, “Continuous lateral shearing interferometer,” Appl. Opt. 23, 4403–4409 (1984).
[CrossRef] [PubMed]

V. Ronchi, “On the phase grating interferometer,” Appl. Opt. 4, 1041–1042 (1965).
[CrossRef]

G. Vogl, “A phase grating interferometer,” Appl. Opt. 3, 1089–1089 (1964).
[CrossRef]

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]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Commun. (3)

C. Meneses-Fabian, G. Rodriguez-Zurita, M. Encarnacion-Gutierrez, N.-I. Toto-Arellano, “Phase-shifting interferometry with four interferograms using linear polarization modulation and a Ronchi grating displaced by only a small unknown amount,” Opt. Commun. 2823063–3068 (2009).
[CrossRef]

L. Chen, S. Yeh, A. Tapilouw, and J. Chang, “3-D surface profilometry using simultaneous phase-shifting interferometry,” Opt. Commun. 283, 3376–3382 (2010).
[CrossRef]

V. Mico, Z. Zalevsky, and J. García, “Common-path phase-shifting digital holographic microscopy: a way to quantitative phase imaging and superresolution,” Opt. Commun. 2814273–4281 (2008).
[CrossRef]

Opt. Eng. (2)

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting interferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

Opt. Express (6)

Opt. Lett. (8)

Proc. SPIE (1)

C. L. Koliopoulos, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1992).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Parallel two-step phase-shifting configuration. (a) Schematic of beam division by a grating pair; (b) two obtained parallel phase-shifting interferograms with phase shift of π / 2 . O and R, input object wave and reference wave, respectively; G 1 and G 2 , Ronchi phase gratings with the same period P. “a” and “b” denote the ± 1 diffraction order of the grating G 1 , and they have the diffraction angle θ = ± λ / P , respectively. Polarizer-array comprises two polarizers with their polarization crossed at angle γ.

Fig. 2
Fig. 2

Experimental setup. NF, neutral variable attenuator; P, linear polarizer; PBS, polarizing beam splitter; BS, nonpolarizing beam splitter; M 1 and M 2 , mirrors; BE 1 and BE 2 , beam expanders; MO, microscope objective with magnification M = 40 × and NA = 0.60 ; G 1 and G 2 , Ronchi gratings with period of P = 15 μm ; L, lens with focal length f L = 160 mm ; QW, quarter-wave plate. The principal axis of QW has the angle π / 4 with respect to the polarization direction of the object wave.

Fig. 3
Fig. 3

Results of parallel two-step phase-shifting DHM with slightly off-axis configuration. (a) Two parallel phase-shifting holograms with phase-shift π / 2 of a microscopic rectangular phase step; (b) spatial frequency spectrum of I 1 R D ; (c) spatial frequency spectrum of ( ( I 1 I 2 ) R D ; (d) reconstructed phase distribution of the specimen with the traditional off-axis approach; (e) reconstructed phase distribution of the specimen with the proposed method. The distance between the hologram plane and the image plane is Δ z = 90 mm . The carrier frequency in Fig. 3a is 6   fringes / mm , corresponding to an angle of 0.22 ° between the object and reference waves.

Fig. 4
Fig. 4

Results of parallel two-step phase-shifting DHM with on-axis configuration. (a) Two parallel phase-shifting holograms with phase shift π / 2 of a microscopic rectangular phase step; (b) reconstructed phase distribution of the specimen. The distance between the hologram plane and the image plane is Δ z = 46 mm .

Equations (7)

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{ I 1 ( x , y ) = | O | 2 + | R | 2 + O * R + O R * ; I 2 ( x , y ) = | O | 2 + | R | 2 + exp ( i α ) O * R + exp ( i α ) O R * .
I 1 I 2 = [ 1 exp ( i α ) ] O * R + [ 1 exp ( i α ) ] O R * .
O r ( x , y , Δ z ) = I F T { F T { ( I 1 I 2 ) R D } · W ^ ( ξ , η ) · exp [ i k Δ z 1 ( λ ξ ) 2 ( λ η ) 2 ] } / [ 1 exp ( i α ) ] .
{ I 1 = I O + I R + 2 I O I R cos φ I 2 = I O + I R 2 I O I R sin φ ,
4 I O I R = ( I 1 I O I R ) 2 + ( I 2 I O I R ) 2 .
I O ( x , y ) = ( I 1 + I 2 ) ± ( I 1 + I 2 ) 2 2 ( I 1 I R ) 2 2 ( I 2 I R ) 2 2 , O 0 ( x , y ) = I 1 I O I R i ( I 2 I O I R ) ( I 1 I O I R ) 2 + ( I 2 I O I R ) 2 .
O r ( x , y , Δ z ) = I F T { F T { O 0 } · exp [ i k Δ z 1 ( λ ξ ) 2 ( λ η ) 2 ] } .

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