Abstract

We report a multiple imaging capability of replicated binary Fresnel phase-encoded lenses written on programmable spatial light modulators (SLMs). These lenses produce a large number (up to 9 × 9) of equally intense replica images from either an external object or from a pattern which is encoded onto the SLM along with the phase-encoded lens. Theoretical details and experimental results using the magnetooptic spatial light modulator are presented.

© 1990 Optical Society of America

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References

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  1. J. A. Davis, D. M. Cottrell, R. A. Lilly, S. W. Connely, “Multiplexed Phase-Encoded Lenses Written on Spatial Light Modulators,” Opt. Lett. 14, 420–422 (1989).
    [CrossRef] [PubMed]
  2. J. A. Davis, D. M. Cottrell, J. E. Davis, R. A. Lilly, “Fresnel Lens-Encoded Binary Phase-Only Filters for Optical Pattern Recognition,” Opt. Lett. 14, 659–661 (1989).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  6. H. K. Liu, J. Graeme Duthie, “Real-Time Screen-Aided Multiple-Image Optical Holographic Matched-Filter Correlator,” Appl. Opt. 21, 3278–3286 (1982).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  11. H. Dammann, K. Gortler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312–000 (1971).
    [CrossRef]
  12. J. A. Davis, S. W. Flowers, D. M. Cottrell, R. A. Lilly, “Smoothing of the Edge-Enhanced Impulse Response from Binary Phase-Only Filters Using Random Binary Patterns,” Appl. Opt. 28, 2987–(1989).
    [CrossRef] [PubMed]
  13. W. E. Ross, D. Psaltis, R. H. Anderson, “Two-Dimensional MagnetoOptic Spatial Light Modulator for Signal Processing,” Opt. Eng. 22, 485–000 (1983).
    [CrossRef]
  14. D. M. Cottrell, R. A. Lilly, J. A. Davis, T. Day, “Optical Correlator Performance of Binary Phase-Only Filters Using Fourier and Hartley Transforms,” Appl. Opt. 26, 3755–3761 (1987).
    [CrossRef] [PubMed]
  15. R. W. Ditchburn, Light (Academic, London, 1976), Chap. 6C.

1989

1987

1984

1983

Y. A. Liang, D. Zhao, H.-K. Liu, “Multifocus Dichromated Gelatin Hololens,” Appl. Opt. 22, 3451–3456 (1983).
[CrossRef] [PubMed]

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-Dimensional MagnetoOptic Spatial Light Modulator for Signal Processing,” Opt. Eng. 22, 485–000 (1983).
[CrossRef]

1982

1980

1972

1971

H. Dammann, K. Gortler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312–000 (1971).
[CrossRef]

1966

Anderson, R. H.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-Dimensional MagnetoOptic Spatial Light Modulator for Signal Processing,” Opt. Eng. 22, 485–000 (1983).
[CrossRef]

Boivin, L. P.

Connely, S. W.

Cottrell, D. M.

Dammann, H.

H. Dammann, K. Gortler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312–000 (1971).
[CrossRef]

Davis, J. A.

Davis, J. E.

Day, T.

Ditchburn, R. W.

R. W. Ditchburn, Light (Academic, London, 1976), Chap. 6C.

Flowers, S. W.

Gortler, K.

H. Dammann, K. Gortler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312–000 (1971).
[CrossRef]

Graeme Duthie, J.

Grover, C. P.

Grumet, A.

A. Grumet, “Automatic Target Recognition System,” U.S. Patent3,779,492 (1972).

Kumar, A. S.

Liang, Y. A.

Lilly, R. A.

Liu, H. K.

Liu, H.-K.

Newman, P. A.

Psaltis, D.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-Dimensional MagnetoOptic Spatial Light Modulator for Signal Processing,” Opt. Eng. 22, 485–000 (1983).
[CrossRef]

Rible, V. E.

Rogers, G. L.

Ross, W. E.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-Dimensional MagnetoOptic Spatial Light Modulator for Signal Processing,” Opt. Eng. 22, 485–000 (1983).
[CrossRef]

Vasu, R. M.

Zhao, D.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Commun.

H. Dammann, K. Gortler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312–000 (1971).
[CrossRef]

Opt. Eng.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-Dimensional MagnetoOptic Spatial Light Modulator for Signal Processing,” Opt. Eng. 22, 485–000 (1983).
[CrossRef]

Opt. Lett.

Other

A. Grumet, “Automatic Target Recognition System,” U.S. Patent3,779,492 (1972).

R. W. Ditchburn, Light (Academic, London, 1976), Chap. 6C.

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Figures (2)

Fig. 1
Fig. 1

Fresnel phase-encoded lens appropriate for (A) z = zc, and (B) z = zc/3.

Fig. 2
Fig. 2

Output pattern distributions for Fresnel phase encoded lens which forms replica output images of letter R. Focal lengths are: (A) z = zc/3 forming about nine equally intense images; (B) z = zc/7, forming about forty-nine equally intense images.

Tables (4)

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Table I Theoretical Intensity Distribution of Fresnel Lens Made for z = zca

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Table II Theoretical Intensity distribution of Fresnel lens made for z = zc/5a

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Table III Experimental Intensity Distribution of Fresnel Lens Made for z = zca

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Table IV Experimental Intensity Distribution of Fresnel Lens Made for z = zc/5a

Equations (18)

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E 2 ( x 2 , y 2 ) = exp [ i 2 π ( x 2 2 + y 2 2 ) 2 z λ ] T ( x 1 , y 1 ) exp [ i 2 π ( x 1 2 + y 1 2 ) 2 z λ ] × [ i 2 π ( x 1 x 2 + y 1 y 2 ) z λ ] d x 1 d y 1 .
E 2 = Z 2 F { Z 1 T } ,
T = Z 1 * F - 1 { G Z 2 * } .
T = Z 1 * F - 1 { G } .
T = ½ [ Z 1 { F - 1 { G } } * + Z 1 * F - 1 { G } ] .
E 2 = ½ Z 2 F { F - 1 { G } } + ½ Z 2 F { Z 1 Z 1 { F - 1 { G } } * } .
E 2 = exp [ i 2 π 2 λ z ( x 2 2 + y 2 2 ) ] n , m = - N / 2 N / 2 - 1 T ( m d 1 , n d 1 ) exp [ i 2 π d 1 2 2 z λ ( m 2 + n 2 ) ] × exp [ - i 2 π d 1 z λ ( m x 2 + n y 2 ) ] x - b / 2 b / 2 exp [ i 2 π 2 z λ ( x ˜ 2 + y ˜ 2 ) ] × exp { - i 2 π z λ [ x ˜ ( x 2 - d 1 m ) + y ˜ ( y 2 - d 1 n ) ] } d x ˜ d y ˜ .
S x S y = sin [ π b λ z ( d 1 m - x 2 ) ] π λ z ( d 1 m - x 2 ) sin [ π b λ z ( d 1 n - y 2 ) ] π λ z ( d 1 n - y 2 ) .
E 2 = exp [ i 2 π 2 λ z ( x 2 2 + y 2 2 ) ] n , m = - N / 2 N / 2 - 1 T ( m d 1 , n d 1 ) × exp [ i 2 π d 1 2 2 z λ ( m 2 + n 2 ) ] exp [ - i 2 π d 1 z λ ( m x 2 + n y 2 ) ] S x S y .
exp [ - i 2 π d 1 z λ ( m x 2 + n y 2 ) ] ,
x 2 , y 2 = λ z / d 1 .
Z 1 = exp [ i 2 π ( x 1 2 + y 1 2 ) 2 z λ ] ,
z c = L 1 d 1 / λ = N 1 d 1 2 / λ .
Z 1 = exp [ i 2 π d 1 2 2 z λ ( m 2 + n 2 ) ] .
( x 1 , y 1 ) = λ z d 1 ( j , k ) ,
( 2 π ) ( λ z 2 d 1 2 ( j 2 + k 2 ) ) .
( x 2 , y 2 ) = λ z d 1 ( j , k )
x 2 , y 2 = λ z / d 1 .

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