Abstract

We propose an algorithm for compensating the phase-shift error of polarization-based parallel two-step phase-shifting digital holography, which is a technique for recording a spatial two-step phase-shifted hologram. Although a polarization-based system of the technique has been experimentally demonstrated, there had been the problem that the phase difference of two phase-shifted holograms had been changed by the extinction ratio of the micropolarizer array attached to the image sensor used in the system. To improve the performance of the system, we established and formulated an algorithm for compensating the phase-shift error. Accurate spatial phase-shifting interferometry in the system can be conducted by the algorithm regardless of phase-shift error due to the extinction ratio. By the numerical simulation, the proposed algorithm was capable of reducing the root mean square errors of the reconstructed image by 1/4 and 1/5 in amplitude and phase, respectively. Also, the algorithm was experimentally demonstrated, and the experimental results showed that the system employing the proposed algorithm suppressed the conjugate image, which slightly appeared in the image reconstructed by the system not employing the algorithm, even when the extinction ratio was 10:1. Thus, the effectiveness of the proposed algorithm was numerically and experimentally verified.

© 2011 Optical Society of America

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2010 (7)

E. Darakis, T. Khanama, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044(2010).
[CrossRef]

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]

T. Tahara, Y. Awatsuji, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography using polarization,” Opt. Rev. 17, 108–113 (2010).
[CrossRef]

H. Suzuki, T. Nomura, E. Nitanai, and T. Numata, “Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method,” Opt. Rev. 17, 176–180(2010).
[CrossRef]

T. Kiire, T. Yatagai, S. Nakadate, and M. Shibuya, “Quadrature phase-shifting interferometer with a polarization imaging camera,” Opt. Rev. 17, 210–213 (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] [PubMed]

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]

2009 (3)

2008 (3)

2007 (3)

2006 (3)

2005 (4)

S. Yoneyama, H. Kikuta, and K. Moriwaki, “Instantaneous phase-stepping interferometry using polarization imaging with a micro-retarder array,” Exp. Mech. 45, 451–456 (2005).
[CrossRef]

B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express 13, 4492–4506 (2005).
[CrossRef] [PubMed]

T. Colomb, F. Dürr, E. Cuche, P. Marquet, H. Limberger, R.-P. Salathé, and Ch. Depeursinge, “Polarization microscopy by use of digital holography: application to optical fiber birefringence measurements,” Appl. Opt. 44, 4461–4469 (2005).
[CrossRef] [PubMed]

T. Yamaguchi, S. Murata, and T. Morihara, “Three-dimensional flow measurement by digital holographic particle image velocimetry with spatio-temporal derivative method,” JSME Int. J. 49, 1133–1140 (2005).
[CrossRef]

2004 (2)

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

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

2002 (1)

2001 (1)

2000 (2)

B. Javidi and E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett. 25, 610–612 (2000).
[CrossRef]

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574(2000).
[CrossRef]

1998 (1)

1997 (1)

1995 (1)

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

1994 (1)

1967 (1)

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

Alferi, D.

Andrés, P.

Araiza-E, M.

Asundi, A. K.

E. Darakis, T. Khanama, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044(2010).
[CrossRef]

Awatsuji, Y.

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]

T. Tahara, Y. Awatsuji, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography using polarization,” Opt. Rev. 17, 108–113 (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] [PubMed]

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. Kakue, T. Tahara, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting color digital holography using two phase shifts,” Appl. Opt. 48, H244–H250 (2009).
[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]

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

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.

M. Sasada, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187–188.

Beghuin, D.

Brock, N.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Cai, L. Z.

Carapezza, E.

Charrière, F.

Climent, V.

Colomb, T.

Cuche, E.

Dahlgren, P.

Darakis, E.

E. Darakis, T. Khanama, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044(2010).
[CrossRef]

Depeursinge, C.

Depeursinge, Ch.

Doh, K.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Dong, G. Y.

Dürr, F.

Emery, Y.

Ferraro, P.

Finizio, A.

Fujii, A.

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.

Fujii, M.

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]

Harada, D.

S. Murata, D. Harada, and Y. Tanaka, “Spatial phase-shifting digital holography for three-dimensional particle tracking velocimetry,” Jpn. J. Appl. Phys. 48, 09LB01 (2009).
[CrossRef]

Hayes, J.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Ito, K.

Javidi, B.

Jüptner, W. P.

Kakue, T.

Kaneko, A.

T. Tahara, Y. Awatsuji, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography using polarization,” Opt. Rev. 17, 108–113 (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, D183–D189 (2008).
[CrossRef] [PubMed]

Kariwala, V.

E. Darakis, T. Khanama, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044(2010).
[CrossRef]

Khanama, T.

E. Darakis, T. Khanama, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044(2010).
[CrossRef]

Kiire, T.

T. Kiire, T. Yatagai, S. Nakadate, and M. Shibuya, “Quadrature phase-shifting interferometer with a polarization imaging camera,” Opt. Rev. 17, 210–213 (2010).
[CrossRef]

Kikuta, H.

S. Yoneyama, H. Kikuta, and K. Moriwaki, “Instantaneous phase-stepping interferometry using polarization imaging with a micro-retarder array,” Exp. Mech. 45, 451–456 (2005).
[CrossRef]

Kim, Myung

Koyama, T.

T. Tahara, Y. Awatsuji, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography using polarization,” Opt. Rev. 17, 108–113 (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, D183–D189 (2008).
[CrossRef] [PubMed]

Kubota, T.

T. Tahara, Y. Awatsuji, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography using polarization,” Opt. Rev. 17, 108–113 (2010).
[CrossRef]

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]

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] [PubMed]

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. Kakue, T. Tahara, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting color digital holography using two phase shifts,” Appl. Opt. 48, H244–H250 (2009).
[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]

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

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.

M. Sasada, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187–188.

Kühn, J.

Lancis, J.

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]

León, L. M.

Limberger, H.

Marquet, P.

Matoba, O.

T. Tahara, Y. Awatsuji, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography using polarization,” Opt. Rev. 17, 108–113 (2010).
[CrossRef]

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]

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] [PubMed]

T. Kakue, T. Tahara, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting color digital holography using two phase shifts,” Appl. Opt. 48, H244–H250 (2009).
[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]

E. Tajahuerce, O. Matoba, and B. Javidi, “Shift invariant three-dimensional object recognition by means of digital holography,” Appl. Opt. 40, 3877–3886 (2001).
[CrossRef]

Matsushima, K.

Meng, X. F.

Millerd, J.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Montfort, F.

Moon, I.

Morihara, T.

T. Yamaguchi, S. Murata, and T. Morihara, “Three-dimensional flow measurement by digital holographic particle image velocimetry with spatio-temporal derivative method,” JSME Int. J. 49, 1133–1140 (2005).
[CrossRef]

Moritani, Y.

Moriwaki, K.

S. Yoneyama, H. Kikuta, and K. Moriwaki, “Instantaneous phase-stepping interferometry using polarization imaging with a micro-retarder array,” Exp. Mech. 45, 451–456 (2005).
[CrossRef]

Murata, S.

S. Murata, D. Harada, and Y. Tanaka, “Spatial phase-shifting digital holography for three-dimensional particle tracking velocimetry,” Jpn. J. Appl. Phys. 48, 09LB01 (2009).
[CrossRef]

T. Nomura, B. Javidi, S. Murata, E. Nitanai, and T. Numata, “Polarization imaging of a three-dimensional object by use of on-axis phase-shifting digital holography,” Opt. Lett. 32, 481–483 (2007).
[CrossRef] [PubMed]

T. Nomura, S. Murata, E. Nitanai, and T. Numata, “Phase-shifting digital holography with a phase difference between orthogonal polarizations,” Appl. Opt. 45, 4873–4877 (2006).
[CrossRef] [PubMed]

T. Yamaguchi, S. Murata, and T. Morihara, “Three-dimensional flow measurement by digital holographic particle image velocimetry with spatio-temporal derivative method,” JSME Int. J. 49, 1133–1140 (2005).
[CrossRef]

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574(2000).
[CrossRef]

Nakadate, S.

T. Kiire, T. Yatagai, S. Nakadate, and M. Shibuya, “Quadrature phase-shifting interferometer with a polarization imaging camera,” Opt. Rev. 17, 210–213 (2010).
[CrossRef]

Nakatsuji, T.

Naughton, T. J.

E. Darakis, T. Khanama, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044(2010).
[CrossRef]

Nicola, S. D.

Nishio, K.

Nitanai, E.

Nomura, T.

North-Morris, M.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Novak, M.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Numata, T.

Parshall, D.

Poon, T.-C.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Rajendran, A.

E. Darakis, T. Khanama, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044(2010).
[CrossRef]

Salathé, R.-P.

Sasada, M.

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

M. Sasada, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187–188.

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.

Schilling, B.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Schnars, U.

Shen, X. X.

Shibuya, M.

T. Kiire, T. Yatagai, S. Nakadate, and M. Shibuya, “Quadrature phase-shifting interferometer with a polarization imaging camera,” Opt. Rev. 17, 210–213 (2010).
[CrossRef]

Shimozato, Y.

Shinoda, K.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Suzuki, H.

H. Suzuki, T. Nomura, E. Nitanai, and T. Numata, “Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method,” Opt. Rev. 17, 176–180(2010).
[CrossRef]

Suzuki, Y.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Tahara, T.

Tajahuerce, E.

Tanaka, Y.

S. Murata, D. Harada, and Y. Tanaka, “Spatial phase-shifting digital holography for three-dimensional particle tracking velocimetry,” Jpn. J. Appl. Phys. 48, 09LB01 (2009).
[CrossRef]

Ura, S.

Wang, Y. R.

Wu, M.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Wyant, J.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Xu, X. F.

Yamaguchi, I.

Yamaguchi, T.

T. Yamaguchi, S. Murata, and T. Morihara, “Three-dimensional flow measurement by digital holographic particle image velocimetry with spatio-temporal derivative method,” JSME Int. J. 49, 1133–1140 (2005).
[CrossRef]

Yang, X. L.

Yasuda, N.

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574(2000).
[CrossRef]

Yatagai, T.

T. Kiire, T. Yatagai, S. Nakadate, and M. Shibuya, “Quadrature phase-shifting interferometer with a polarization imaging camera,” Opt. Rev. 17, 210–213 (2010).
[CrossRef]

Yeom, S.

Yeon, S.

Yokota, M.

Yoneyama, S.

S. Yoneyama, H. Kikuta, and K. Moriwaki, “Instantaneous phase-stepping interferometry using polarization imaging with a micro-retarder array,” Exp. Mech. 45, 451–456 (2005).
[CrossRef]

Zhang, T.

Appl. Opt. (10)

U. Schnars and W. P. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[CrossRef] [PubMed]

D. Parshall and Myung Kim, “Digital holographic microscopy with dual wavelength phase unwrapping,” Appl. Opt. 45, 451–459 (2006).
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E. Tajahuerce, O. Matoba, and B. Javidi, “Shift invariant three-dimensional object recognition by means of digital holography,” Appl. Opt. 40, 3877–3886 (2001).
[CrossRef]

T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, and C. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. 41, 27–37 (2002).
[CrossRef] [PubMed]

T. Colomb, F. Dürr, E. Cuche, P. Marquet, H. Limberger, R.-P. Salathé, and Ch. Depeursinge, “Polarization microscopy by use of digital holography: application to optical fiber birefringence measurements,” Appl. Opt. 44, 4461–4469 (2005).
[CrossRef] [PubMed]

M. Yokota, “Polarization analysis by off-axis digital holography with an improved optical system and an evaluation of its performance by simulation,” Appl. Opt. 47, 6325–6333(2008).
[CrossRef] [PubMed]

T. Nakatsuji and K. Matsushima, “Free-viewpoint images captured using phase-shifting synthetic aperture digital holography,” Appl. Opt. 47, D136–D143 (2008).
[CrossRef] [PubMed]

T. Nomura, S. Murata, E. Nitanai, and T. Numata, “Phase-shifting digital holography with a phase difference between orthogonal polarizations,” Appl. Opt. 45, 4873–4877 (2006).
[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. Kakue, T. Tahara, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting color digital holography using two phase shifts,” Appl. Opt. 48, H244–H250 (2009).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

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

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

Biomed. Opt. Express (1)

Chem. Eng. Sci. (1)

E. Darakis, T. Khanama, A. Rajendran, V. Kariwala, T. J. Naughton, and A. K. Asundi, “Microparticle characterization using digital holography,” Chem. Eng. Sci. 65, 1037–1044(2010).
[CrossRef]

Exp. Mech. (1)

S. Yoneyama, H. Kikuta, and K. Moriwaki, “Instantaneous phase-stepping interferometry using polarization imaging with a micro-retarder array,” Exp. Mech. 45, 451–456 (2005).
[CrossRef]

Jpn. J. Appl. Phys. (1)

S. Murata, D. Harada, and Y. Tanaka, “Spatial phase-shifting digital holography for three-dimensional particle tracking velocimetry,” Jpn. J. Appl. Phys. 48, 09LB01 (2009).
[CrossRef]

JSME Int. J. (1)

T. Yamaguchi, S. Murata, and T. Morihara, “Three-dimensional flow measurement by digital holographic particle image velocimetry with spatio-temporal derivative method,” JSME Int. J. 49, 1133–1140 (2005).
[CrossRef]

Opt. Eng. (1)

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Opt. Express (6)

B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express 13, 4492–4506 (2005).
[CrossRef] [PubMed]

J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Real-time dual wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15, 7231–7242 (2007).
[CrossRef] [PubMed]

S. Yeon, B. Javidi, P. Ferraro, D. Alferi, S. D. Nicola, and A. Finizio, “Three-dimensional color object visualization and recognition using multi-wavelength computational holography,” Opt. Express 15, 9394–9402 (2007).
[CrossRef]

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]

L. M. León, M. Araiza-E, B. Javidi, P. Andrés, V. Climent, J. Lancis, and E. Tajahuerce, “Single-shot digital holography by use of the fractional Talbot effect,” Opt. Express 17, 12900–12909 (2009).
[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] [PubMed]

Opt. Laser Technol. (1)

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574(2000).
[CrossRef]

Opt. Lett. (5)

Opt. Rev. (3)

T. Tahara, Y. Awatsuji, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography using polarization,” Opt. Rev. 17, 108–113 (2010).
[CrossRef]

H. Suzuki, T. Nomura, E. Nitanai, and T. Numata, “Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method,” Opt. Rev. 17, 176–180(2010).
[CrossRef]

T. Kiire, T. Yatagai, S. Nakadate, and M. Shibuya, “Quadrature phase-shifting interferometer with a polarization imaging camera,” Opt. Rev. 17, 210–213 (2010).
[CrossRef]

Proc. SPIE (1)

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Other (4)

M. Sasada, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187–188.

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.

U.Schnars and W.Jüptner, eds., Digital Holography(Springer, 2005).

T.-C.Poon, ed., Digital Holography and Three-Dimensional Display: Principles and Applications (Springer, 2006).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Basic concept of parallel two-step phase-shifting digital holography.

Fig. 2
Fig. 2

Schematic of the PBP2SPSDH system: (a) whole system, (b) camera having the image sensor with the micropolarizer array, and (c) configuration of the micropolarizer array.

Fig. 3
Fig. 3

Object used in the numerical simulation: (a) amplitude distribution and (b) phase distribution, respectively.

Fig. 4
Fig. 4

Numerical results in case that the extinction ratio of the micropolarizer array is x = 2 : (a) amplitude distribution, (b) phase distribution reconstructed without compensation, (c) amplitude distribution and (d) phase distribution reconstructed by using the proposed algorithm.

Fig. 5
Fig. 5

RMSEs between the object and the reconstructed images: (a) amplitude and (b) phase.

Fig. 6
Fig. 6

Photograph of the objects.

Fig. 7
Fig. 7

Experimental results: (a), (b) focused images of a die on which a mark of a diamond is drawn, (c), (d) focused images of the other die on which a mark of a spade is drawn, (a), (c) images reconstructed without compensation, and (b), (d) images reconstructed by using the proposed algorithm.

Fig. 8
Fig. 8

Backpropagation results: focused images of the conjugate of a die (a) without compensation and (b) by using the proposed algorithm and magnified images (c) at the lower right of (a) and (d) at the lower right of (b).

Equations (20)

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

I 1 = I ( 0 ) + 1 x I ( π / 2 ) = A o ( 0 ) 2 + A r ( 0 ) 2 + 2 A o ( 0 ) A r ( 0 ) cos ϕ o + 1 x { A o ( π / 2 ) 2 + A r ( π / 2 ) 2 + 2 A o ( π / 2 ) A r ( π / 2 ) sin ϕ o } ,
A o ( 0 ) 2 = A o ( π / 2 ) 2 = A o 2 ,
A r ( 0 ) 2 = A r ( π / 2 ) 2 = A r 2 .
I 1 = x + 1 x ( A o 2 + A r 2 ) + 2 x 2 + 1 x A o A r cos ( ϕ o tan 1 1 x ) .
I 2 = x + 1 x ( A o 2 + A r 2 ) + 2 x 2 + 1 x A o A r sin ( ϕ o + tan 1 1 x ) .
X = x + 1 x ,
Y = 2 x 2 + 1 x ,
ϕ o = ϕ o tan 1 1 x ,
α = π 2 2 tan 1 1 x ,
IDC = X ( A o 2 + A r 2 ) ,
A r 2 = X A r 2 .
I 1 = DC + Y A o A r cos ϕ o ,
I 2 = DC + Y A o A r cos ( ϕ o α ) .
A o cos ϕ o = I 1 DC Y A r ,
A o sin ϕ o = I 2 I 1 cos α ( 1 cos α ) DC Y A r sin α .
DC = v v 2 4 u w 2 u ,
u = 2 ( 1 cos α ) ,
v = 2 ( 1 cos α ) ( I 1 + I 2 ) + ( Y X ) 2 A r 2 sin 2 α ,
w = I 1 2 + I 2 2 2 I 1 I 2 cos α + ( Y X ) 2 A r 4 sin 2 α .
A o = ( A o cos ϕ o ) 2 + ( A o sin ϕ o ) 2 .

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