Abstract

We analyze the performance of two optical shadow-casting image correlators that use two-dimensional source arrays to encode the system point-spread function (PSF). The analysis of a standard shadow-casting correlator suggests that the angular divergence of the source array is a critical parameter in the determination of the maximum space–bandwidth product of the image and of the PSF that can be used with such a system. Further, the energy efficiency of a standard shadow-casting correlator is related inversely to the size of the PSF. We show that the constraints on energy efficiency and on the space–bandwidth product of the PSF can be overcome by beam steering the source elements. A modified shadow-casting correlator is proposed that uses phase-only blazed gratings to beam steer the sources. Experimental results generated by a mechanically beam-steered array are presented.

© 1993 Optical Society of America

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References

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  1. A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
    [CrossRef]
  2. L. S. G. Kovasnay, A. Arman, “Optical autocorrelation measurement of two-dimensional random patterns,” Rev. Sci. Instrum. 28, 793 (1957).
    [CrossRef]
  3. S. Jutamulia, T. W. Lin, F. T. S. Yu, “Real-time noncoherent correlator using liquid crystal television,” Opt. Commun. 64, 115–119 (1987).
    [CrossRef]
  4. Y. Ichioka, J. Tanida, “Optical parallel logic gates using a shadow-casting system for optical digital computing,” Proc. IEEE 72, 787–801 (1984).
    [CrossRef]
  5. Y. Li, A. Kostrzewski, D. H. Kim, G. Eichmann, “Compact parallel real-time programmable optical morphological image processor,” Opt. Lett. 14, 981–983 (1989).
    [CrossRef] [PubMed]
  6. A. Louri, “Efficient optical implementation method for symbolic substitution logic based on shadow casting,” Appl. Opt. 28, 3264–3267 (1989).

1989 (2)

A. Louri, “Efficient optical implementation method for symbolic substitution logic based on shadow casting,” Appl. Opt. 28, 3264–3267 (1989).

Y. Li, A. Kostrzewski, D. H. Kim, G. Eichmann, “Compact parallel real-time programmable optical morphological image processor,” Opt. Lett. 14, 981–983 (1989).
[CrossRef] [PubMed]

1987 (1)

S. Jutamulia, T. W. Lin, F. T. S. Yu, “Real-time noncoherent correlator using liquid crystal television,” Opt. Commun. 64, 115–119 (1987).
[CrossRef]

1984 (1)

Y. Ichioka, J. Tanida, “Optical parallel logic gates using a shadow-casting system for optical digital computing,” Proc. IEEE 72, 787–801 (1984).
[CrossRef]

1964 (1)

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

1957 (1)

L. S. G. Kovasnay, A. Arman, “Optical autocorrelation measurement of two-dimensional random patterns,” Rev. Sci. Instrum. 28, 793 (1957).
[CrossRef]

Arman, A.

L. S. G. Kovasnay, A. Arman, “Optical autocorrelation measurement of two-dimensional random patterns,” Rev. Sci. Instrum. 28, 793 (1957).
[CrossRef]

Eichmann, G.

Ichioka, Y.

Y. Ichioka, J. Tanida, “Optical parallel logic gates using a shadow-casting system for optical digital computing,” Proc. IEEE 72, 787–801 (1984).
[CrossRef]

Jutamulia, S.

S. Jutamulia, T. W. Lin, F. T. S. Yu, “Real-time noncoherent correlator using liquid crystal television,” Opt. Commun. 64, 115–119 (1987).
[CrossRef]

Kim, D. H.

Kostrzewski, A.

Kovasnay, L. S. G.

L. S. G. Kovasnay, A. Arman, “Optical autocorrelation measurement of two-dimensional random patterns,” Rev. Sci. Instrum. 28, 793 (1957).
[CrossRef]

Li, Y.

Lin, T. W.

S. Jutamulia, T. W. Lin, F. T. S. Yu, “Real-time noncoherent correlator using liquid crystal television,” Opt. Commun. 64, 115–119 (1987).
[CrossRef]

Louri, A.

A. Louri, “Efficient optical implementation method for symbolic substitution logic based on shadow casting,” Appl. Opt. 28, 3264–3267 (1989).

Tanida, J.

Y. Ichioka, J. Tanida, “Optical parallel logic gates using a shadow-casting system for optical digital computing,” Proc. IEEE 72, 787–801 (1984).
[CrossRef]

VanderLugt, A. B.

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Yu, F. T. S.

S. Jutamulia, T. W. Lin, F. T. S. Yu, “Real-time noncoherent correlator using liquid crystal television,” Opt. Commun. 64, 115–119 (1987).
[CrossRef]

Appl. Opt. (1)

A. Louri, “Efficient optical implementation method for symbolic substitution logic based on shadow casting,” Appl. Opt. 28, 3264–3267 (1989).

IEEE Trans. Inf. Theory (1)

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Opt. Commun. (1)

S. Jutamulia, T. W. Lin, F. T. S. Yu, “Real-time noncoherent correlator using liquid crystal television,” Opt. Commun. 64, 115–119 (1987).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

Y. Ichioka, J. Tanida, “Optical parallel logic gates using a shadow-casting system for optical digital computing,” Proc. IEEE 72, 787–801 (1984).
[CrossRef]

Rev. Sci. Instrum. (1)

L. S. G. Kovasnay, A. Arman, “Optical autocorrelation measurement of two-dimensional random patterns,” Rev. Sci. Instrum. 28, 793 (1957).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Conventional shadow-casting correlator configuration, (b) angle subtended (δθ) by adjacent sources at the input, angle subtended (δϕ) by a single pixel at the source plane. LED/LD array, light-emitting-diode–laser-diode array.

Fig. 2
Fig. 2

(a) Shadow-casting correlator configuration with blazed phase-only gratings, (b) shadow-casting correlator with sources on a spherical surface.

Fig. 3
Fig. 3

(a) Parallel source array design, (b) beam-steered source array design, (c) single slit (upper) and two slits spaced eight units apart (lower) used in the experiment.

Fig. 4
Fig. 4

(a) Pixel shifts produced by all parallel-array souce elements illuminating a single pixel, (b) pixel shifts produced by all beam-steered source elements illuminating a single pixel, (c) eight-pixel-shift correlation produced by an on-axis array, (d) eight-pixel-shift correlation produced by a beam-steered array. In (c) and (d), the central and an end LED are turned on to illuminate two pixels separated by eight pixels.

Equations (10)

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δ = L ( Δ / d ) .
δ = α ( β 2 Δ 2 / λ ) ,
2 L tan ( Ψ / 2 ) = N Δ + M d .
tan ( Ψ / 2 ) = ½ [ N ( Δ / L ) + M ( d / L ) = ½ ( N tan δ ϕ + M tan δ θ ) , δ θ = d / L , δ ϕ = Δ / L ,
η = N Δ 2 L tan ( ψ / 2 ) = [ N tan ϕ 2 tan ( ψ / 2 ) ] .
N = 256 ,             Δ = 100 μ m , δ = 5 mm ,             d = 2 mm , M = 64 ,             β = 1 , λ = 600 nm ,     L = 100 mm ,
α = 0.3 ,             ψ = 75 ° ,             η = 16.68 % .
2 L tan ( Ψ / 2 ) = N Δ .
tan θ = ( M d / 2 ) L ,
f = ( sin θ ) / λ = ( 1 / λ ) sin { tan - 1 [ ( M d / 2 ) L ] } .

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