Abstract

This paper presents an analysis of error in parallel two-step phase-shifting method. From the analysis, it is clarified that the maximum bandwidth of the object that this technique can capture is a half bandwidth of recording devices. Also, the recording distance must be two times longer than the conventional method to have a good reconstruction image. The analysis was verified by simulations and experimental results.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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  11. 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]
  12. L. Miao, K. Nitta, O. Matoba, and Y. Awatsuji, “Parallel phase-shifting digital holography with adaptive function using phase-mode spatial light modulator,” Appl. Opt. 51, pp. 2633–2637 (2012).
    [CrossRef]
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  14. P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt. 50, H177–H182 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012 (2)

T. Tahara, Y. Shimozato, T. Kakue, M. Fujii, P. Xia, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative evaluation of the image-reconstruction algorithms of single-shot phase-shifting digital holography,” J. Electron. Imaging 21, 13021–13030 (2012).
[CrossRef]

L. Miao, K. Nitta, O. Matoba, and Y. Awatsuji, “Parallel phase-shifting digital holography with adaptive function using phase-mode spatial light modulator,” Appl. Opt. 51, pp. 2633–2637 (2012).
[CrossRef]

2011 (2)

2010 (4)

2008 (1)

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, 183–189 (2008).
[CrossRef]

2006 (3)

2004 (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

1997 (1)

1964 (1)

1963 (1)

1962 (1)

Awatsuji, Y.

L. Miao, K. Nitta, O. Matoba, and Y. Awatsuji, “Parallel phase-shifting digital holography with adaptive function using phase-mode spatial light modulator,” Appl. Opt. 51, pp. 2633–2637 (2012).
[CrossRef]

T. Tahara, Y. Shimozato, T. Kakue, M. Fujii, P. Xia, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative evaluation of the image-reconstruction algorithms of single-shot phase-shifting digital holography,” J. Electron. Imaging 21, 13021–13030 (2012).
[CrossRef]

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Compensation algorithm for the phase-shift error of polarization-based parallel two-step phase-shifting digital holography,” Appl. Opt. 50, B31–B37 (2011).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt. 50, H177–H182 (2011).
[CrossRef]

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting digital holographic microscopy,” Biomed. Opt. Express 1, 610–616 (2010).
[CrossRef]

T. Tahara, K. Ito, M. Fujii, T. Kakue, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Experimental demonstration of parallel two-step phase-shifting digital holography,” Opt. Express 18, 18975–18980 (2010).
[CrossRef]

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative analysis and quantitative evaluation of the field of view and the viewing zone of single-shot phase-shifting digital holography using space-division multiplexing,” Opt. Rev. 17, 519–524 (2010).
[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, 183–189 (2008).
[CrossRef]

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45, 2995–3002 (2006).
[CrossRef]

Y. Awatsuji, M. Sasada, A. Fujii, and T. Kubota, “Scheme to improve the reconstructed image in parallel quasi-phase-shifting digital holography,” Appl. Opt. 45, 968–974 (2006).
[CrossRef]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

Cai, L. Z.

Dong, G. Y.

Ehlers, M. D.

Fujii, A.

Fujii, M.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2002), Chap. 9.

Ito, K.

Ito, Y.

Kakue, T.

Kaneko, A.

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, 183–189 (2008).
[CrossRef]

Koyama, T.

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, 183–189 (2008).
[CrossRef]

Kubota, T.

T. Tahara, Y. Shimozato, T. Kakue, M. Fujii, P. Xia, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative evaluation of the image-reconstruction algorithms of single-shot phase-shifting digital holography,” J. Electron. Imaging 21, 13021–13030 (2012).
[CrossRef]

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Compensation algorithm for the phase-shift error of polarization-based parallel two-step phase-shifting digital holography,” Appl. Opt. 50, B31–B37 (2011).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt. 50, H177–H182 (2011).
[CrossRef]

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting digital holographic microscopy,” Biomed. Opt. Express 1, 610–616 (2010).
[CrossRef]

T. Tahara, K. Ito, M. Fujii, T. Kakue, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Experimental demonstration of parallel two-step phase-shifting digital holography,” Opt. Express 18, 18975–18980 (2010).
[CrossRef]

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative analysis and quantitative evaluation of the field of view and the viewing zone of single-shot phase-shifting digital holography using space-division multiplexing,” Opt. Rev. 17, 519–524 (2010).
[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, 183–189 (2008).
[CrossRef]

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45, 2995–3002 (2006).
[CrossRef]

Y. Awatsuji, M. Sasada, A. Fujii, and T. Kubota, “Scheme to improve the reconstructed image in parallel quasi-phase-shifting digital holography,” Appl. Opt. 45, 968–974 (2006).
[CrossRef]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

Leith, E. N.

Matoba, O.

L. Miao, K. Nitta, O. Matoba, and Y. Awatsuji, “Parallel phase-shifting digital holography with adaptive function using phase-mode spatial light modulator,” Appl. Opt. 51, pp. 2633–2637 (2012).
[CrossRef]

T. Tahara, Y. Shimozato, T. Kakue, M. Fujii, P. Xia, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative evaluation of the image-reconstruction algorithms of single-shot phase-shifting digital holography,” J. Electron. Imaging 21, 13021–13030 (2012).
[CrossRef]

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Compensation algorithm for the phase-shift error of polarization-based parallel two-step phase-shifting digital holography,” Appl. Opt. 50, B31–B37 (2011).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt. 50, H177–H182 (2011).
[CrossRef]

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting digital holographic microscopy,” Biomed. Opt. Express 1, 610–616 (2010).
[CrossRef]

T. Tahara, K. Ito, M. Fujii, T. Kakue, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Experimental demonstration of parallel two-step phase-shifting digital holography,” Opt. Express 18, 18975–18980 (2010).
[CrossRef]

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative analysis and quantitative evaluation of the field of view and the viewing zone of single-shot phase-shifting digital holography using space-division multiplexing,” Opt. Rev. 17, 519–524 (2010).
[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, 183–189 (2008).
[CrossRef]

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45, 2995–3002 (2006).
[CrossRef]

Meng, X. F.

Miao, L.

Newpher, T. M.

Nishio, K.

T. Tahara, Y. Shimozato, T. Kakue, M. Fujii, P. Xia, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative evaluation of the image-reconstruction algorithms of single-shot phase-shifting digital holography,” J. Electron. Imaging 21, 13021–13030 (2012).
[CrossRef]

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Compensation algorithm for the phase-shift error of polarization-based parallel two-step phase-shifting digital holography,” Appl. Opt. 50, B31–B37 (2011).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt. 50, H177–H182 (2011).
[CrossRef]

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting digital holographic microscopy,” Biomed. Opt. Express 1, 610–616 (2010).
[CrossRef]

T. Tahara, K. Ito, M. Fujii, T. Kakue, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Experimental demonstration of parallel two-step phase-shifting digital holography,” Opt. Express 18, 18975–18980 (2010).
[CrossRef]

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative analysis and quantitative evaluation of the field of view and the viewing zone of single-shot phase-shifting digital holography using space-division multiplexing,” Opt. Rev. 17, 519–524 (2010).
[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, 183–189 (2008).
[CrossRef]

Nitta, K.

Sasada, M.

Y. Awatsuji, M. Sasada, A. Fujii, and T. Kubota, “Scheme to improve the reconstructed image in parallel quasi-phase-shifting digital holography,” Appl. Opt. 45, 968–974 (2006).
[CrossRef]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

Shaked, N. T.

Shen, X. X.

Shimozato, Y.

Tahara, T.

T. Tahara, Y. Shimozato, T. Kakue, M. Fujii, P. Xia, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative evaluation of the image-reconstruction algorithms of single-shot phase-shifting digital holography,” J. Electron. Imaging 21, 13021–13030 (2012).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt. 50, H177–H182 (2011).
[CrossRef]

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Compensation algorithm for the phase-shift error of polarization-based parallel two-step phase-shifting digital holography,” Appl. Opt. 50, B31–B37 (2011).
[CrossRef]

T. Tahara, K. Ito, M. Fujii, T. Kakue, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Experimental demonstration of parallel two-step phase-shifting digital holography,” Opt. Express 18, 18975–18980 (2010).
[CrossRef]

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting digital holographic microscopy,” Biomed. Opt. Express 1, 610–616 (2010).
[CrossRef]

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative analysis and quantitative evaluation of the field of view and the viewing zone of single-shot phase-shifting digital holography using space-division multiplexing,” Opt. Rev. 17, 519–524 (2010).
[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, 183–189 (2008).
[CrossRef]

Upatnieks, J.

Ura, S.

T. Tahara, Y. Shimozato, T. Kakue, M. Fujii, P. Xia, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative evaluation of the image-reconstruction algorithms of single-shot phase-shifting digital holography,” J. Electron. Imaging 21, 13021–13030 (2012).
[CrossRef]

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Compensation algorithm for the phase-shift error of polarization-based parallel two-step phase-shifting digital holography,” Appl. Opt. 50, B31–B37 (2011).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt. 50, H177–H182 (2011).
[CrossRef]

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting digital holographic microscopy,” Biomed. Opt. Express 1, 610–616 (2010).
[CrossRef]

T. Tahara, K. Ito, M. Fujii, T. Kakue, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Experimental demonstration of parallel two-step phase-shifting digital holography,” Opt. Express 18, 18975–18980 (2010).
[CrossRef]

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative analysis and quantitative evaluation of the field of view and the viewing zone of single-shot phase-shifting digital holography using space-division multiplexing,” Opt. Rev. 17, 519–524 (2010).
[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, 183–189 (2008).
[CrossRef]

Wang, Y. R.

Wax, A.

Xia, P.

T. Tahara, Y. Shimozato, T. Kakue, M. Fujii, P. Xia, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative evaluation of the image-reconstruction algorithms of single-shot phase-shifting digital holography,” J. Electron. Imaging 21, 13021–13030 (2012).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt. 50, H177–H182 (2011).
[CrossRef]

Xu, X. F.

Yamaguchi, I.

Yang, X. L.

Zhang, T.

Appl. Opt. (7)

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, 183–189 (2008).
[CrossRef]

Y. Awatsuji, M. Sasada, A. Fujii, and T. Kubota, “Scheme to improve the reconstructed image in parallel quasi-phase-shifting digital holography,” Appl. Opt. 45, 968–974 (2006).
[CrossRef]

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45, 2995–3002 (2006).
[CrossRef]

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]

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Compensation algorithm for the phase-shift error of polarization-based parallel two-step phase-shifting digital holography,” Appl. Opt. 50, B31–B37 (2011).
[CrossRef]

P. Xia, Y. Shimozato, Y. Ito, T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Improvement of color reproduction in color digital holography by using spectral estimation technique,” Appl. Opt. 50, H177–H182 (2011).
[CrossRef]

L. Miao, K. Nitta, O. Matoba, and Y. Awatsuji, “Parallel phase-shifting digital holography with adaptive function using phase-mode spatial light modulator,” Appl. Opt. 51, pp. 2633–2637 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

Biomed. Opt. Express (1)

J. Electron. Imaging (1)

T. Tahara, Y. Shimozato, T. Kakue, M. Fujii, P. Xia, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative evaluation of the image-reconstruction algorithms of single-shot phase-shifting digital holography,” J. Electron. Imaging 21, 13021–13030 (2012).
[CrossRef]

J. Opt. Soc. Am. (3)

Opt. Express (1)

Opt. Lett. (2)

Opt. Rev. (1)

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Comparative analysis and quantitative evaluation of the field of view and the viewing zone of single-shot phase-shifting digital holography using space-division multiplexing,” Opt. Rev. 17, 519–524 (2010).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2002), Chap. 9.

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Figures (16)

Fig. 1.
Fig. 1.

Configuration for recording on-axis hologram.

Fig. 2.
Fig. 2.

Two holograms in two-step phase-shifting method. (a) Hologram of 0 phase in reference arm and (b) hologram of β phase in reference arm.

Fig. 3.
Fig. 3.

Phase distribution of micropolarizer array or phase image sensor.

Fig. 4.
Fig. 4.

Schematic diagram of the parallel two-step phase-shifting method. (a) Original hologram captured in camera, (b) after extraction process, and (c) after interpolation process.

Fig. 5.
Fig. 5.

Interference pattern between an object point’s wave and plane wave at recording plane.

Fig. 6.
Fig. 6.

Interference pattern in parallel two-step phase-shifting digital hologram. (a) Original hologram, (b) extraction hologram, and (c) hologram after interpolation.

Fig. 7.
Fig. 7.

Interference pattern at 2z0 after the extraction and interpolation process. (a) Interference from phase 0 and (b) interference from phase 90.

Fig. 8.
Fig. 8.

Reconstruction of one object point. (a) Reconstruction with the two-step phase-shifting method and (b) reconstruction with the parallel two-step phase-shifting method.

Fig. 9.
Fig. 9.

Reconstruction result of a chessboard. (I) Reconstruction with the two-step phase-shifting method and (II) reconstruction with parallel two-step phase-shifting method. (a) Chessboard cell is 1×1 pixels. (b) Chessboard cell is 2×2 pixels. (c) Chessboard cell is 3×3 pixels. (d) Chessboard cell is 4×4 pixels.

Fig. 10.
Fig. 10.

Correlation efficiency and NMRS error of the parallel and conventional (nonparallel) method (the second simulation).

Fig. 11.
Fig. 11.

Resolution test target USAF-1951.

Fig. 12.
Fig. 12.

Reconstruction result of test target USAF-1951. (I) Reconstruction with two-step phase-shifting method and (II) Reconstruction with parallel two-step phase-shifting method. (a) Recording distance z0, (b) recording distance 2z0, (c) recording distance 3z0, and (d) reconstruction at 4z0.

Fig. 13.
Fig. 13.

Correlation efficiency and NMRS error of parallel and conventional (nonparallel) method (the third simulation).

Fig. 14.
Fig. 14.

Reconstruction results of object point (light from pinhole). (a) Two-step phase-shifting method, (b) parallel two-step phase-shifting method, (I) 3D view, (II) x-axis view, and (III) y-axis view.

Fig. 15.
Fig. 15.

Reconstruction results of the chessboard. (a) Two-step phase-shifting method and (b) parallel two-step phase-shifting method.

Fig. 16.
Fig. 16.

Reconstruction result of a resolution test target. (a) Two-step phase shifting method and (b) parallel two-step phase-shifting method.

Equations (14)

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Λ=λsinαinteference angle.
sinαmax=λ/2Δ.
zmin_on_axis=ΔLCCD+Lλ.
Won_axis=1/Δ.
U(x,y)=exp(jkysinθ)+O(x,y),
I(x,y)=1+|O(x,y)|2+exp(jkysinθ)O(x,y)+exp(jkysinθ)O*(x,y),
O(x,y)=|O(x,y)|exp[jϕ(x,y)].
I(x,y)=1+|O(x,y)|2+2|O(x,y)|cos[ksinθϕ(x,y)]=1+|O(x,y)|2+2|O(x,y)|cos[2πγθyϕ(x,y)].
I(x,y)(jkysinθ)=1+|O(x,y)|2(jkysinθ)+O(x,y)+exp(j2kysinθ)O*(x,y).
I1=|O(x,y)|2+R2+|O(x,y)|Rcos(ϕ(x,y)),
I2=|O(x,y)|2+R2+|O(x,y)|Rcos(ϕ(x,y)β).
(I1a)2sin2β+[I2I1cosβ(1cosβ)a]2=4R2(aR2)sin2β.
O(x,y)=|O(x,y)|exp[jϕ(x,y)]=|O(x,y)|cosϕ(x,y)j|O(x,y)|sinϕ(x,y)=I1a2R+jI2I1cosβ(1cosβ)a2Rsinβ.
z0=256Δ2λ.

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