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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Appl. Opt.

Appl. Phys. Lett.

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.

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

Opt. Eng.

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

Opt. Express

L. Ge, M. Duelli, and R. W. Cohn, �??Enumeration of illumination and scanning modes from real-time spatial light modulators,�?? Opt. Express 7, 403-416 (2000), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-12-403">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-12-403</a>
[CrossRef] [PubMed]

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), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-421">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-421</a>
[CrossRef] [PubMed]

Opt. Lasers Eng.

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.

Optik

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).

Proc. SIGGRAPH

M. Lucente and T. A. Galyean, �??Rendering interactive holographic images,�?? in Computer Graphics and Interactive Techniques, S. G. Mair, eds., Proc. SIGGRAPH 95, 387-394 (1995).

Proc. SPIE

H. Dammann, �??Synthetic digital-phase gratings �?? design, features, applications,�?? in Computer-Generated Holography, S. H. Lee, eds., Proc. SPIE 437, 72-78 (1983).

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. SPIE 4659, 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. SPIE 4659, 242-249 (2002).

Science

S. Kirkpatric, C. D. Gelatt, and M. P. Vecchi, �??Optimization by simulated annealing,�?? Science 220, 671-680 (1983).
[CrossRef]

Other

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).

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

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).

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Figures (5)

Fig. 1.
Fig. 1.

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

Fig. 2.
Fig. 2.

Schematic diagram of the proposed IFTA method.

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.

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).

Fig. 5.
Fig. 5.

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

Tables (1)

Tables Icon

Table 1. Simulated performance characteristics of the designed phase holograms

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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