Abstract

A three-dimensional (3D) object reconstruction technique that uses only phase information of a phase-shifting digital hologram and a phase-only spatial-light modulator is proposed. It is well known that a digital hologram can store both amplitude and phase information of an optical electric field and can reconstruct the original 3D object in a computer. We demonstrate that it is possible to reconstruct optically 3D objects using only phase information of the optical field calculated from phase-shifting digital holograms. The use of phase-only information enables us to reduce the amount of data in the digital hologram and reconstruct optically the 3D objects using a liquid-crystal spatial light modulator without optical power loss. Numerical evaluation of the reconstructed 3D object is presented.

© 2002 Optical Society of America

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References

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2001 (4)

2000 (3)

1999 (2)

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1999).
[CrossRef]

1997 (1)

1995 (1)

1994 (2)

1992 (1)

1970 (1)

Arai, J.

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1999).
[CrossRef]

Barnes, T. H.

Castro, M. A.

Caulfield, H. J.

H. J. Caulfield, Handbook of Optical Holography (Academic, New York, 1979).

Crossland, W. A.

Eiju, T.

Frauel, Y.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Hara, T.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Hirsch, P. M.

Hoshino, H.

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1999).
[CrossRef]

Ichikawa, H.

Igasaki, Y.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Inoue, T.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Itoh, K.

Javidi, B.

Jiang, Y.

Jordan, J. A.

Jüptner, W.

Kobayashi, Y.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Kujawinska, M.

M. Sutkowski, M. Kujawinska, “Application of liquid crystal (LC) devices for optoelectronic reconstruction of digitally stored holograms,” Opt. Lasers Eng. 33, 191–201 (2000).
[CrossRef]

Kuroda, D.

Lesem, L. B.

Li, F.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Li, Y.

Manolis, I. G.

Matoba, O.

Matuda, K.

McAulay, A. D.

A. D. McAulay, Optical Computer Architectures: The Application of Optical Concepts to the Next Generation of Computers (Wiley, New York, 1991).

Mears, R. J.

Mukohzaka, N.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Neto, L. G.

Nishii, J.

Okano, F.

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1999).
[CrossRef]

Redmond, M. M.

Roberge, D.

Robertson, B.

Schnars, U.

Sheng, Y.

Sutkowski, M.

M. Sutkowski, M. Kujawinska, “Application of liquid crystal (LC) devices for optoelectronic reconstruction of digitally stored holograms,” Opt. Lasers Eng. 33, 191–201 (2000).
[CrossRef]

Taghizadeh, M. R.

Tajahuerce, E.

Tan, K. L.

Toyoda, H.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Turunen, J.

Van Rooy, D. L.

Warr, S. T.

Watanabe, W.

Wilkinson, T. D.

Yamada, K.

Yamaguchi, I.

Yatagai, T.

Yoshida, N.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Yoshikawa, N.

Yuyama, I.

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1999).
[CrossRef]

Zhang, T.

Appl. Opt. (7)

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1999).
[CrossRef]

Opt. Lasers Eng. (1)

M. Sutkowski, M. Kujawinska, “Application of liquid crystal (LC) devices for optoelectronic reconstruction of digitally stored holograms,” Opt. Lasers Eng. 33, 191–201 (2000).
[CrossRef]

Opt. Lett. (4)

Opt. Rev. (1)

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Other (3)

A. D. McAulay, Optical Computer Architectures: The Application of Optical Concepts to the Next Generation of Computers (Wiley, New York, 1991).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

H. J. Caulfield, Handbook of Optical Holography (Academic, New York, 1979).

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Figures (9)

Fig. 1
Fig. 1

Proposed 3D object recording and reconstruction system. (a) Recording system for digital holograms by use of a phase-shifting interferometer, (b) optical reconstruction system by use of a phase-only information of digital holograms.

Fig. 2
Fig. 2

Numerically reconstructed 3D objects of die from (a) a fully complex field, (b) phase-only information, (c) low-pass filtered 3D objects with a mean filter of 11 × 11 pixels, (d) 21 × 21 pixels after reconstruction with phase-only information.

Fig. 3
Fig. 3

Numerically reconstructed 3D objects of a screw from (a) a fully complex field, (b) phase-only information, (c) low-pass filtered 3D objects with a mean filter of 11 × 11 pixels, (d) 21 × 21 pixels after reconstruction with phase-only information.

Fig. 4
Fig. 4

NRMS difference between reconstructed 3D objects from a fully complex field and reconstructions from phase-only information as a function of the side length of the mean filter.

Fig. 5
Fig. 5

Reconstructed 3D object of the die without quantization reduction and with quantization reductions to 4 bits and 1 bit.

Fig. 6
Fig. 6

Reconstructed 3D object of the screw without quantization reduction and with quantization reductions to 4 bits and 1 bit.

Fig. 7
Fig. 7

NRMS difference as a function of the number of phase levels of phase-only information when 3D objects are (a) a screw and (b) a die, respectively.

Fig. 8
Fig. 8

Experimental results: (a), (b), and (c) are reconstructed images of the die where the CCD is located at 113 mm, 123 mm, and 133 mm from the SLM, respectively.

Fig. 9
Fig. 9

Experimental results: (a), (b), and (c) are reconstructed images of the screw where the CCD is located at 135 mm, 155 mm, and 165 mm from the SLM, respectively.

Equations (5)

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

Ũx, y=Ax, yexpjϕx, y =1jλ  Ux, y, z1zexpjkz×expjk2zx-x2+y-y2dxdydz,
Rx, y; z=-1jλ  Ũx, y1zexp-jkz×exp- jk2zx-x2+y-y2dxdy.
Px, y; z=-ajλ  expjϕx, y1zexp-jkz×exp-jk2zx-x2+y-y2dxdy,
a= |Rx, y; z|2dxdy |Px, y; z|2dxdy1/2.
NRMS= |Rx, y; z|2-|Px, y; z|22dxdy]1/2|Rx, y; z|22dxdy1/2.

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