Abstract

A Fourier-transformed synthetic phase hologram for an auto-stereoscopic image display system is proposed and implemented. The system uses a phase-only spatial light modulator and a simple projection lens module. A modified iterative Fresnel transform algorithm method, for the reconstruction of gray-level quantized stereo images with fast convergence, high diffraction efficiency and large signal-to-noise ratio is also described. Using this method, it is possible to obtain a high diffraction efficiency(~90%), an excellent signal-to-noise ratio(> 9.6dB), and a short calculation time(~3min). Experimentally, the proposed auto-stereoscopic display system was able to generate stereoscopic 3D images very well.

© 2004 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  22. A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems (Kluwer academic publishers, Boston, 1995).
  23. H. Kim, B. Yang, J. Park, and B. Lee, “Optimal design of boundary-modulated diffractive optical elements for general beam shaping,” in Practical Holography XVI and Holographic Materials VIII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE4659, 129–138 (2002).
  24. K. Choi, B. Choi, Y. Choi, S. Kim, J. Kim, N. Kim, and S. Gil, “Multiphase computer-generated holograms for full-color image generation,” in Practical Holography XVI and Holographic Materials VIII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE4659, 242–249 (2002).

2004 (1)

2002 (1)

2001 (1)

2000 (1)

1998 (1)

V. V. Kotlyar, P. G. Seraphimovich, and V. A. Soifer, “An iterative algorithm for designing diffractive optical elements with regularization,” Opt. Lasers Eng. 29, 261–268 (1998).
[Crossref]

1995 (1)

1992 (1)

1991 (1)

S. Fukushima, T. Kurokawa, and M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[Crossref]

1990 (1)

F. Wyrowsiki, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. 7, 961–969 (1990).
[Crossref]

1987 (1)

1983 (1)

S. Kirkpatric, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref]

1982 (1)

1975 (1)

O. Bryngdahl, “Computer-generated holograms as generalized optical components,” Opt. Eng. 14, 426–435 (1975).

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm of the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

1968 (1)

Ahn, C. H.

Allebach, J. P.

Benton, S. A.

Bryngdahl, O.

O. Bryngdahl, “Computer-generated holograms as generalized optical components,” Opt. Eng. 14, 426–435 (1975).

Cho, H, J.

Choi, B.

K. Choi, B. Choi, Y. Choi, S. Kim, J. Kim, N. Kim, and S. Gil, “Multiphase computer-generated holograms for full-color image generation,” in Practical Holography XVI and Holographic Materials VIII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE4659, 242–249 (2002).

Choi, H.

Choi, K.

K. Choi, B. Choi, Y. Choi, S. Kim, J. Kim, N. Kim, and S. Gil, “Multiphase computer-generated holograms for full-color image generation,” in Practical Holography XVI and Holographic Materials VIII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE4659, 242–249 (2002).

Choi, Y.

K. Choi, B. Choi, Y. Choi, S. Kim, J. Kim, N. Kim, and S. Gil, “Multiphase computer-generated holograms for full-color image generation,” in Practical Holography XVI and Holographic Materials VIII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE4659, 242–249 (2002).

Cohn, R. W.

Dammann, H.

H. Dammann, “Synthetic digital-phase gratings — design, features, applications,” in Computer-Generated Holography, S. H. Lee, eds., Proc. SPIE437, 72–78 (1983).

Doskolovich, L.

V. A. Soifer, V. V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis Ltd, 1997).

Duelli, M.

Fienup, J. R.

Fukushima, S.

S. Fukushima, T. Kurokawa, and M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[Crossref]

Galyean, T. A.

M. Lucente and T. A. Galyean, “Rendering interactive holographic images,” in Computer Graphics and Interactive Techniques, S. G. Mair, eds., Proc. SIGGRAPH95, 387–394 (1995).

Ge, L.

Gelatt, C. D.

S. Kirkpatric, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm of the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Gil, S.

K. Choi, B. Choi, Y. Choi, S. Kim, J. Kim, N. Kim, and S. Gil, “Multiphase computer-generated holograms for full-color image generation,” in Practical Holography XVI and Holographic Materials VIII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE4659, 242–249 (2002).

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search Optimization and Machine Learning (Addison Wesley, Massachusetts, 1989).

Goncharsky, A. V.

A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems (Kluwer academic publishers, Boston, 1995).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hilaire, P. S.

Javidi, B.

Jones, M.

Jung, S.

Kim, H.

H. Kim, B. Yang, J. Park, and B. Lee, “Optimal design of boundary-modulated diffractive optical elements for general beam shaping,” in Practical Holography XVI and Holographic Materials VIII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE4659, 129–138 (2002).

Kim, J.

K. Choi, B. Choi, Y. Choi, S. Kim, J. Kim, N. Kim, and S. Gil, “Multiphase computer-generated holograms for full-color image generation,” in Practical Holography XVI and Holographic Materials VIII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE4659, 242–249 (2002).

Kim, N.

K. Choi, B. Choi, Y. Choi, S. Kim, J. Kim, N. Kim, and S. Gil, “Multiphase computer-generated holograms for full-color image generation,” in Practical Holography XVI and Holographic Materials VIII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE4659, 242–249 (2002).

Kim, S.

K. Choi, B. Choi, Y. Choi, S. Kim, J. Kim, N. Kim, and S. Gil, “Multiphase computer-generated holograms for full-color image generation,” in Practical Holography XVI and Holographic Materials VIII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE4659, 242–249 (2002).

Kim, Y.

Kirkpatric, S.

S. Kirkpatric, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref]

Kotlyar, V. V.

V. V. Kotlyar, P. G. Seraphimovich, and V. A. Soifer, “An iterative algorithm for designing diffractive optical elements with regularization,” Opt. Lasers Eng. 29, 261–268 (1998).
[Crossref]

V. A. Soifer, V. V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis Ltd, 1997).

Kowel, S. T.

Kulick, J. H.

Kurokawa, T.

S. Fukushima, T. Kurokawa, and M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[Crossref]

Lee, B.

Lindquist, R. G.

Lohmann, A. W.

Lucente, M.

P. S. Hilaire, S. A. Benton, and M. Lucente, “Synthetic aperture holography: a novel approach to three dimensional displays,” J. Opt. Soc. Am. A 9, 1969–1977 (1992).
[Crossref]

M. Lucente and T. A. Galyean, “Rendering interactive holographic images,” in Computer Graphics and Interactive Techniques, S. G. Mair, eds., Proc. SIGGRAPH95, 387–394 (1995).

Min, S.

Min, S. W.

Nasiatka, P.

Nordin, G. P.

Ohno, M.

S. Fukushima, T. Kurokawa, and M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[Crossref]

Okoshi, T.

T. Okoshi, Three-dimensional Imaging Techniques (Academic Press, New York, 1976).

Paris, D. P.

Park, J.

Y. Kim, J. Park, H. Choi, S. Jung, S. Min, and B. Lee, “Viewing-angle-enhanced integral imaging system using a curved lens array,” Opt. Express 12, 421–429 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-421
[Crossref] [PubMed]

H. Kim, B. Yang, J. Park, and B. Lee, “Optimal design of boundary-modulated diffractive optical elements for general beam shaping,” in Practical Holography XVI and Holographic Materials VIII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE4659, 129–138 (2002).

Parker, A.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm of the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Seldowitz, M. A.

Seraphimovich, P. G.

V. V. Kotlyar, P. G. Seraphimovich, and V. A. Soifer, “An iterative algorithm for designing diffractive optical elements with regularization,” Opt. Lasers Eng. 29, 261–268 (1998).
[Crossref]

Soifer, V. A.

V. V. Kotlyar, P. G. Seraphimovich, and V. A. Soifer, “An iterative algorithm for designing diffractive optical elements with regularization,” Opt. Lasers Eng. 29, 261–268 (1998).
[Crossref]

V. A. Soifer, V. V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis Ltd, 1997).

Stepanov, V. V.

A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems (Kluwer academic publishers, Boston, 1995).

Sweeney, D. W.

Tikhonov, A. N.

A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems (Kluwer academic publishers, Boston, 1995).

Vecchi, M. P.

S. Kirkpatric, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref]

Wyrowsiki, F.

F. Wyrowsiki, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. 7, 961–969 (1990).
[Crossref]

Yagola, A. G.

A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems (Kluwer academic publishers, Boston, 1995).

Yan, J.

Yang, B.

H. Kim, B. Yang, J. Park, and B. Lee, “Optimal design of boundary-modulated diffractive optical elements for general beam shaping,” in Practical Holography XVI and Holographic Materials VIII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE4659, 129–138 (2002).

Appl. Opt. (4)

Appl. Phys. Lett. (1)

S. Fukushima, T. Kurokawa, and M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[Crossref]

J. Opt. Soc. Am. (1)

F. Wyrowsiki, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. 7, 961–969 (1990).
[Crossref]

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

O. Bryngdahl, “Computer-generated holograms as generalized optical components,” Opt. Eng. 14, 426–435 (1975).

Opt. Express (2)

Opt. Lasers Eng. (1)

V. V. Kotlyar, P. G. Seraphimovich, and V. A. Soifer, “An iterative algorithm for designing diffractive optical elements with regularization,” Opt. Lasers Eng. 29, 261–268 (1998).
[Crossref]

Opt. Lett. (1)

Optik (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm of the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Science (1)

S. Kirkpatric, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref]

Other (9)

D. E. Goldberg, Genetic Algorithms in Search Optimization and Machine Learning (Addison Wesley, Massachusetts, 1989).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

V. A. Soifer, V. V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis Ltd, 1997).

A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems (Kluwer academic publishers, Boston, 1995).

H. Kim, B. Yang, J. Park, and B. Lee, “Optimal design of boundary-modulated diffractive optical elements for general beam shaping,” in Practical Holography XVI and Holographic Materials VIII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE4659, 129–138 (2002).

K. Choi, B. Choi, Y. Choi, S. Kim, J. Kim, N. Kim, and S. Gil, “Multiphase computer-generated holograms for full-color image generation,” in Practical Holography XVI and Holographic Materials VIII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE4659, 242–249 (2002).

M. Lucente and T. A. Galyean, “Rendering interactive holographic images,” in Computer Graphics and Interactive Techniques, S. G. Mair, eds., Proc. SIGGRAPH95, 387–394 (1995).

H. Dammann, “Synthetic digital-phase gratings — design, features, applications,” in Computer-Generated Holography, S. H. Lee, eds., Proc. SPIE437, 72–78 (1983).

T. Okoshi, Three-dimensional Imaging Techniques (Academic Press, New York, 1976).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of the proposed auto-stereoscopic 3D display system.

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Fig. 2.
Fig. 2.

Schematic diagram of the proposed IFTA method.

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Fig. 3.
Fig. 3.

Converging process for the diffraction efficiency and RMS deviation of the designed phase hologram (a) DBS method and (b) our proposed IFTA method.

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Fig. 4.
Fig. 4.

Mona Lisa input images for (a) left view and (b) right view of the synthetic phase hologram, (c) combined synthetic phase hologram, and (d) reconstructed stereoscopic image (simulation) of the hologram (c).

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Fig. 5.
Fig. 5.

(a) Experimental setup using a phase-only SLM and (b) reconstructed image.

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Tables (1)

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Table 1. Simulated performance characteristics of the designed phase holograms

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Equations (6)

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F ̂ ( x , y ) = ik 2 π z exp ( ikz ) ∫ − ∞ ∞ ∫ W ( u , v ) H ( u − x , v − y , z ) dudv
F ̂ ′ ( x , y ) = B 0 ( x , y ) F ̂ ( x , y ) ∣ F ̂ ( x , y ) ∣ − 1
W ( u , v ) = ik 2 π z exp ( − ikz ) ∫ − ∞ ∞ ∫ F ̂ ′ ( x , y ) H * ( x − u , y − v , z ) dxdy
W ′ ( u , v ) = { A 0 ( u , v ) W ( u , v ) ∣ W ( u , v ) ∣ − 1 , ( u , v ) ∈ Q 0 , ( u , v ) ∉ Q
ε 0 = λ F ∫ − ∞ ∞ ∫ [ ∣ F ̂ ( x , y ) ∣ − B 0 ( x , y ) ] 2 dxdy + λ S ∫ S ∫ [ ∣ F ̂ ( x , y ) ∣ − B 0 ( x , y ) ] 2 dxdy
+ λ N ∫ N ∫ ∣ F ̂ ( x , y ) ∣ 2 dxdy + α D ∫ S ∫ [ ( ∂ x ∣ F ̂ ∣ ) 2 + ( ∂ y ∣ F ̂ ∣ ) 2 ] dxdy

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