Abstract

Although digital holography is a powerful technique obtaining a phase image of a transparent object, the image reconstructed by the technique merely expresses phase distribution of the light wave after transmitting through the object. Phase variation of inside of the object is difficult to be obtained. Then, we applied Abel inversion method to the high-speed phase image of a dynamic transparent object assumed axially symmetric. The phase is accurately recorded by phase-shifting method. We experimentally recorded transparent dynamic gas flow, assumed axially symmetric along the direction in which gas flowed, at 3,000 frame/s and reconstructed motion picture of 3D distribution of the refractive index of the gas from the high-speed phase motion picture obtained by parallel phase-shifting digital holography.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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  14. P. Xia, Y. Awatsuji, K. Nishio, and O. Matoba, “One million fps digital holography,” Electron. Lett. 50(23), 1693–1695 (2014).
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    [Crossref]

2017 (2)

2016 (4)

2014 (3)

2011 (1)

2004 (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

2000 (1)

1997 (1)

1988 (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23(4), 713–720 (1988).
[Crossref]

1967 (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[Crossref]

1961 (1)

Awatsuji, Y.

Aylo, R.

Bockasten, K.

Dai, S.

Di, J.

Engwer, C.

Gao, J.

Goldstein, R. M.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23(4), 713–720 (1988).
[Crossref]

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[Crossref]

Greve, B.

He, Y.

Horisaki, R.

Ito, Y.

Javidi, B.

Jiao, S.

Kakue, T.

Kemper, B.

Ketelhut, S.

Kim, M. K.

Y. Wan, T. Man, F. Wu, M. K. Kim, and D. Wang, “Parallel phase-shifting self-interference digital holography with faithful reconstruction using compressive sensing,” Opt. Lasers Eng. 86, 38–43 (2016).
[Crossref]

Kubota, T.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[Crossref]

Lee, Y.

Li, Y.

Lin, H.

Liu, J.

Ma, C.

Man, T.

Y. Wan, T. Man, F. Wu, M. K. Kim, and D. Wang, “Parallel phase-shifting self-interference digital holography with faithful reconstruction using compressive sensing,” Opt. Lasers Eng. 86, 38–43 (2016).
[Crossref]

Mathews, S.

Matoba, O.

Mei, Q.

Min, J.

Nehmetallah, G.

Nguyen, T.

Nishio, K.

Raub, C.

Sasada, M.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Shimozato, Y.

Tahara, T.

Tajahuerce, E.

Takahashi, Y.

Ura, S.

Wan, Y.

Y. Wan, T. Man, F. Wu, M. K. Kim, and D. Wang, “Parallel phase-shifting self-interference digital holography with faithful reconstruction using compressive sensing,” Opt. Lasers Eng. 86, 38–43 (2016).
[Crossref]

Wang, D.

Y. Wan, T. Man, F. Wu, M. K. Kim, and D. Wang, “Parallel phase-shifting self-interference digital holography with faithful reconstruction using compressive sensing,” Opt. Lasers Eng. 86, 38–43 (2016).
[Crossref]

Wang, X.

Werner, C. L.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23(4), 713–720 (1988).
[Crossref]

Wu, F.

Y. Wan, T. Man, F. Wu, M. K. Kim, and D. Wang, “Parallel phase-shifting self-interference digital holography with faithful reconstruction using compressive sensing,” Opt. Lasers Eng. 86, 38–43 (2016).
[Crossref]

Xi, T.

Xia, P.

Yamaguchi, I.

Yao, B.

Yonesaka, R.

Zebker, H. A.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23(4), 713–720 (1988).
[Crossref]

Zhang, J.

Zhang, T.

Zhao, J.

Zou, W.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[Crossref]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Electron. Lett. (1)

P. Xia, Y. Awatsuji, K. Nishio, and O. Matoba, “One million fps digital holography,” Electron. Lett. 50(23), 1693–1695 (2014).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Express (1)

Opt. Lasers Eng. (1)

Y. Wan, T. Man, F. Wu, M. K. Kim, and D. Wang, “Parallel phase-shifting self-interference digital holography with faithful reconstruction using compressive sensing,” Opt. Lasers Eng. 86, 38–43 (2016).
[Crossref]

Opt. Lett. (8)

T. Tahara, Y. Lee, Y. Ito, P. Xia, Y. Shimozato, Y. Takahashi, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Superresolution of interference fringes in parallel four-step phase-shifting digital holography,” Opt. Lett. 39(6), 1673–1676 (2014).
[Crossref] [PubMed]

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(21), 4131–4133 (2011).
[Crossref] [PubMed]

S. Jiao and W. Zou, “High-resolution parallel phase-shifting digital holography using a low-resolution phase-shifting array device based on image inpainting,” Opt. Lett. 42(3), 482–485 (2017).
[Crossref] [PubMed]

R. Horisaki and T. Tahara, “Phase-shift binary digital holography,” Opt. Lett. 39(22), 6375–6378 (2014).
[Crossref] [PubMed]

B. Javidi and E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett. 25(9), 610–612 (2000).
[Crossref] [PubMed]

J. Zhang, C. Ma, S. Dai, J. Di, Y. Li, T. Xi, and J. Zhao, “Transmission and total internal reflection integrated digital holographic microscopy,” Opt. Lett. 41(16), 3844–3847 (2016).
[Crossref] [PubMed]

J. Min, B. Yao, S. Ketelhut, C. Engwer, B. Greve, and B. Kemper, “Simple and fast spectral domain algorithm for quantitative phase imaging of living cells with digital holographic microscopy,” Opt. Lett. 42(2), 227–230 (2017).
[Crossref] [PubMed]

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
[Crossref] [PubMed]

Radio Sci. (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23(4), 713–720 (1988).
[Crossref]

Other (1)

M. Sasada, 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.

Supplementary Material (3)

NameDescription
» Visualization 1       Motion pictures of the object we used.
» Visualization 2       Motion pictures of the reconstructed 3D distribution of the refractive index of the object.
» Visualization 3       Motion pictures of the reconstructed 3D distribution of the refractive index of the object.

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Figures (6)

Fig. 1
Fig. 1 Principle of parallel phase-shifting digital holography.
Fig. 2
Fig. 2 Calculation of 3D distribution of refractive index by Abel inversion and parallel phase-shifting digital holography. The transparent object has axially symmetric refractive index around y-axis, the light wave propagates along z-axis and transmits through an object.
Fig. 3
Fig. 3 Experimental set up of the system of parallel phase-shifting digital holography. (a) Schematic of the system. PBS, polarizing beam splitter; QWP, quarter wave plate; PIC, polarization-imaging camera. (b) Motion pictures of the transparent gas flow as the object (see Visualization 1). To visualize the flow, a black paper was used and bent in the motion pictures.
Fig. 4
Fig. 4 Reconstructed 2D phase distribution and 3D distribution of refractive index. These distribution (a) 3 and (b) 120 ms after the gas flow started were obtained.
Fig. 5
Fig. 5 Motion pictures of the reconstructed 3D distribution of the refractive index. These motion pictures show the distribution (a) from the flow start of the gas to 10 ms after (see Visualization 2), (b) from 90 ms to 140 ms after the flow start (see Visualization 3).
Fig. 6
Fig. 6 Line profiles of the radial distribution of the refractive index. (a) The radius distribution of the refractive index at 120 ms after the gas flow started. Line profiles is along (b) line 1, (c) line 2, (d) line 3, and (e) line 4.

Equations (3)

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φ( x,y )= 2π λ Δn( x,y,z )dz ,
φ( x,y )= z 0 z 0 2π λ Δn( r,y )dz .
n( r,y )= n 0 + λ 2 π 2 r R [ dφ( x,y ) dx ] dx x 2 r 2 ,

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