Abstract

Iterative learning procedures on a hybrid electro-optic system can be employed to generate holograms on inexpensive liquid-crystal-television spatial light modulators. The algorithm takes into account random electronic noise in the system and compensates for spatial-light-modulator distortions. Experimental results are given for the reconstruction of intensity distribution, and computer simulations demonstrate the possibility of a complete complex amplitude reconstruction.

© 1990 Optical Society of America

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References

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  1. M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, Appl. Opt. 26, 2788 (1987).
    [CrossRef] [PubMed]
  2. B. K. Jennison, J. P. Allebach, D. W. Sweeney, Opt. Eng. 28, 629 (1989).
  3. J. P. Allebach, D. W. Sweeney, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 2 (1988).
  4. U. Mahlab, J. Shamir, Opt. Lett. 14, 1168 (1989).
    [CrossRef] [PubMed]

1989 (2)

B. K. Jennison, J. P. Allebach, D. W. Sweeney, Opt. Eng. 28, 629 (1989).

U. Mahlab, J. Shamir, Opt. Lett. 14, 1168 (1989).
[CrossRef] [PubMed]

1988 (1)

J. P. Allebach, D. W. Sweeney, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 2 (1988).

1987 (1)

Allebach, J. P.

B. K. Jennison, J. P. Allebach, D. W. Sweeney, Opt. Eng. 28, 629 (1989).

J. P. Allebach, D. W. Sweeney, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 2 (1988).

M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, Appl. Opt. 26, 2788 (1987).
[CrossRef] [PubMed]

Jennison, B. K.

B. K. Jennison, J. P. Allebach, D. W. Sweeney, Opt. Eng. 28, 629 (1989).

Mahlab, U.

Seldowitz, M. A.

Shamir, J.

Sweeney, D. W.

B. K. Jennison, J. P. Allebach, D. W. Sweeney, Opt. Eng. 28, 629 (1989).

J. P. Allebach, D. W. Sweeney, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 2 (1988).

M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, Appl. Opt. 26, 2788 (1987).
[CrossRef] [PubMed]

Appl. Opt. (1)

Opt. Eng. (1)

B. K. Jennison, J. P. Allebach, D. W. Sweeney, Opt. Eng. 28, 629 (1989).

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

J. P. Allebach, D. W. Sweeney, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 2 (1988).

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Figures (5)

Fig. 1
Fig. 1

Experimental system. The pattern generated on the SLM is Fourier transformed by the lens and observed by the CCD camera.

Fig. 2
Fig. 2

Probability (Pr.) distribution of the error function for different measurements on the same hologram.

Fig. 3
Fig. 3

Sequence of reconstructed patterns for consecutive iteration cycles. Each cycle is 64 × 64 single-pixel updates.

Fig. 4
Fig. 4

System for complex amplitude reconstruction.

Fig. 5
Fig. 5

Reconstructed object (with zero order suppressed) from (a) the hologram containing magnitude information only and from (b) the hologram conditioned by magnitude and phase information. (c) Cross-correlation function of the reference pattern with the point-spread function of hologram corresponding to (a), and (d) cross-correlation function of the reference pattern with the point-spread function of hologram corresponding to (b).

Equations (13)

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e n = 1 N 2 k , l = 1 N [ | f kl | 2 γ n I kl ( n ) ] 2 ,
γ n = I ij ( n ) | f ij | 2 [ I ij ( n ) ] 2 .
σ n = [ 1 n j = 1 n ( e j 1 n i = 1 n e i ) 2 ] 1 / 2 .
Δ e n + 1 = e n + 1 e n ,
| Δ e n + 1 | < σ n .
Δ e n + 1 < 0 ,
I kl = | h kl | 2 = | a f kl | 2 , k , l = 1 , 2 N ,
| k , l = 1 N h kl * f kl | 2 = | a k , l = 1 N | f kl | 2 | 2 ,
h kl = a f kl .
| k , l = 1 N h kl * f kl | 2 k , l = 1 N | h kl | 2 k , l = 1 N | f kl | 2 .
| k , l = 1 N h kl * f kl | 2 | a k , l = 1 N | f kl | 2 | 2 .
e n c = | | C ff ( 0 ) | 2 γ n | C hf ( n ) ( 0 ) | 2 | .
Δ e n + 1 c = e n + 1 c e n c 0

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