Abstract

The improved single-exposure phase-shifting digital holography using a random-phase reference wave is proposed. The algorithm for obtaining a complex amplitude of an object wave is improved. In the proposed algorithm, the reference wave is treated as not a random-phase but a random-complex amplitude. Therefore, the algorithm uses proper amplitude information of the reference wave. Both numerical simulations and experimental results are given to confirm the effectiveness of the proposed algorithm.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2011

2010

2009

W. Hsieh, M. Kuo, H. Yau, and C. Chang, “A simple arbitrary phase-step digital holographic reconstruction approach without blurring using two holograms,” Opt. Rev. 16, 466–471 (2009).
[CrossRef]

L. Martínez-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]

2008

2007

2006

2002

2000

1997

Adachi, T.

Andrés, P.

Araiza-E, M.

Araiza-Esquivel, M.

Awatsuji, Y.

Baumbach, T.

Cai, L. Z.

Chang, C.

W. Hsieh, M. Kuo, H. Yau, and C. Chang, “A simple arbitrary phase-step digital holographic reconstruction approach without blurring using two holograms,” Opt. Rev. 16, 466–471 (2009).
[CrossRef]

Charrière, F.

Cheng, X. C.

Climent, V.

Colomb, T.

Dong, G. Y.

Ferraro, P.

Finizio, A.

Fujii, M.

Hsieh, W.

W. Hsieh, M. Kuo, H. Yau, and C. Chang, “A simple arbitrary phase-step digital holographic reconstruction approach without blurring using two holograms,” Opt. Rev. 16, 466–471 (2009).
[CrossRef]

Imbe, M.

Ito, K.

Javidi, B.

Jüptner, W.

Kakue, T.

Kubota, T.

Kuehn, J.

Kuo, M.

W. Hsieh, M. Kuo, H. Yau, and C. Chang, “A simple arbitrary phase-step digital holographic reconstruction approach without blurring using two holograms,” Opt. Rev. 16, 466–471 (2009).
[CrossRef]

Lancis, J.

Marian, A.

Martínez-León, L.

Matoba, O.

Memmolo, P.

Meng, X. F.

Montfort, F.

Mori, Y.

Y. Mori and T. Nomura, “Optical reconstruction of digital hologram using spatial light modulator for binocular stereopsis,” in Digital Holography and Three-Dimensional Imaging, OSA Techinal Digest (CD) (Optical Society of America, 2011), paper DTuC7.

Murata, S.

Näsänen, R.

Naughton, T. J.

Nishio, K.

Nitanai, E.

Nomura, T.

Numata, T.

Osten, W.

Paturzo, M.

Shen, X. X.

Shimozato, Y.

Sun, W. J.

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]

Tahara, T.

Tajahuerce, E.

Ura, S.

Wang, Y. R.

Xu, X. F.

Yamaguchi, I.

Yang, X. L.

Yau, H.

W. Hsieh, M. Kuo, H. Yau, and C. Chang, “A simple arbitrary phase-step digital holographic reconstruction approach without blurring using two holograms,” Opt. Rev. 16, 466–471 (2009).
[CrossRef]

Yokota, M.

Yonesaka, R.

Zhang, H.

Zhang, T.

Appl. Opt.

Biomed. Opt. Express

Opt. Express

Opt. Lett.

T. Nomura and M. Imbe, “Single-exposure phase-shifting digital holography using a random-phase reference wave,” Opt. Lett. 35, 2281–2283 (2010).
[CrossRef]

T. Tahara, Y. Awatsuji, Y. Shimozato, T. Kakue, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Single-shot polarization-imaging digital holography based on simultaneous phase-shifting digital holography,” Opt. Lett. 36, 3254–3256(2011).
[CrossRef]

T. Kakue, R. Yonesaka, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “High-speed phase imaging by parallel phase-shifting digital holography,” Opt. Lett. 36, 4131–4133 (2011).
[CrossRef]

T. Nomura, B. Javidi, S. Murata, E. Nitanai, and T. Numata, “Polarization imaging of a 3D object by use of on-axis phase-shifting digital holography,” Opt. Lett. 32, 481–483 (2007).
[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]

B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25, 28–30 (2000).
[CrossRef]

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[CrossRef]

W. Osten, T. Baumbach, and W. Jüptner, “Comparative digital holography,” Opt. Lett. 27, 1764–1766 (2002).
[CrossRef]

F. Charrière, A. Marian, F. Montfort, J. Kuehn, and T. Colomb, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31, 178–180 (2006).
[CrossRef]

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]

Opt. Rev.

W. Hsieh, M. Kuo, H. Yau, and C. Chang, “A simple arbitrary phase-step digital holographic reconstruction approach without blurring using two holograms,” Opt. Rev. 16, 466–471 (2009).
[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]

Other

Y. Mori and T. Nomura, “Optical reconstruction of digital hologram using spatial light modulator for binocular stereopsis,” in Digital Holography and Three-Dimensional Imaging, OSA Techinal Digest (CD) (Optical Society of America, 2011), paper DTuC7.

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Figures (8)

Fig. 1.
Fig. 1.

Schematic diagram of the proposed method: arbitrary four neighboring pixels on the hologram, the reference wave, and the object wave.

Fig. 2.
Fig. 2.

Obtained complex amplitude distribution of the object wave.

Fig. 3.
Fig. 3.

Amplitude distribution of the object wave on the object plane used in numerical simulations.

Fig. 4.
Fig. 4.

Propagation from the object plane to the sensor plane or propagation from the sensor plane to the object plane in numerical simulations.

Fig. 5.
Fig. 5.

Procedure for applying a median filter.

Fig. 6.
Fig. 6.

Reconstructed images obtained by the improved and the previous algorithms with or without a median filter: (a) case of the improved algorithm without the median filter, (b) case of the previous algorithm without the median filter, (c) case of the improved algorithm with the median filter, and (d) case of the previous algorithm with the median filter.

Fig. 7.
Fig. 7.

Optical setup: OL, object lens; L1, L2, lenses; M1, M2, M3, mirrors; BS1, BS2, beam splitters; P, polarizer; QWP, quarter wavelength plate.

Fig. 8.
Fig. 8.

Reconstructed images obtained in experiments: (a) case of the improved algorithm and (b) case of the previous algorithm.

Tables (1)

Tables Icon

Table 1. Ratio of the Number of the Nonsignificant Quantity to the Number of the Whole Pixels of the Image Sensor

Equations (19)

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

I 1 = a o 2 + a r 1 2 + 2 a o a r 1 cos ( ϕ o ϕ r 1 ) ,
I 2 = a o 2 + a r 2 2 + 2 a o a r 2 cos ( ϕ o ϕ r 2 ) ,
I 3 = a o 2 + a r 3 2 + 2 a o a r 3 cos ( ϕ o ϕ r 3 ) ,
I 4 = a o 2 + a r 4 2 + 2 a o a r 4 cos ( ϕ o ϕ r 4 ) .
I u = I 1 I 2 ( a r 1 2 a r 2 2 ) ,
I l = I 3 I 4 ( a r 3 2 a r 4 2 ) ,
A = a r 1 cos ϕ r 1 a r 2 cos ϕ r 2 ,
B = a r 1 sin ϕ r 1 a r 2 sin ϕ r 2 ,
C = a r 3 cos ϕ r 3 a r 4 cos ϕ r 4 ,
D = a r 3 sin ϕ r 3 a r 4 sin ϕ r 4 .
a o = ( I u D I l B ) 2 + ( I l A I u C ) 2 2 ( A D B C ) ,
ϕ o = tan 1 I l A I u C I u D I l B .
A o ( x , y ) = a o ( x , y ) exp { i ϕ o ( x , y ) } .
I u = I 1 I 2 ,
I l = I 3 I 4 ,
A = cos ϕ r 1 cos ϕ r 2 ,
B = sin ϕ r 1 sin ϕ r 2 ,
C = cos ϕ r 3 cos ϕ r 4 ,
D = sin ϕ r 3 sin ϕ r 4 .

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