Abstract

As is known, a coherent optical data processing system can be used to perform convolution and correlation with ease. Recently it has been shown that the system with diffraction gratings in the spatial filtering plane can also add or subtract complex patterns displayed symmetrically in the input plane. A method is described here for synthesizing a spatial filter so that the coherent system can perform both correlation and subtraction simultaneously in real time. As a particular application of this technique, we present results of using such filters in optical feature extraction.

© 1971 Optical Society of America

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References

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  1. S. H. Lee, S. K. Yao, A. G. Milnes, J. Opt. Soc. Amer. 60, 1037 (1970).
    [CrossRef]
  2. A. Vander Lugt, IEEE Trans. Information Theory IT-10, 139 (1964).
    [CrossRef]
  3. R. A. Binns, A. Dickinson, B. M. Watrasiewicz, Appl. Opt. 7, 1047 (1968).
    [CrossRef] [PubMed]
  4. J. M. Holeman, “Holographic Character Reader,” in Pattern Recognition, L. N. Kanal, Ed. (Thompson Book Co., Washington, D.C., 1968).
  5. A. Vander Lugt, F. B. Rotz, A. Klooster, “Character Reading by Optical Spatial Filtering,” in Optical and Electro-Optical Information Processing, J. T. Tippett, Ed. (MIT Press, Cambridge, 1965).

1970 (1)

S. H. Lee, S. K. Yao, A. G. Milnes, J. Opt. Soc. Amer. 60, 1037 (1970).
[CrossRef]

1968 (1)

1964 (1)

A. Vander Lugt, IEEE Trans. Information Theory IT-10, 139 (1964).
[CrossRef]

Binns, R. A.

Dickinson, A.

Holeman, J. M.

J. M. Holeman, “Holographic Character Reader,” in Pattern Recognition, L. N. Kanal, Ed. (Thompson Book Co., Washington, D.C., 1968).

Klooster, A.

A. Vander Lugt, F. B. Rotz, A. Klooster, “Character Reading by Optical Spatial Filtering,” in Optical and Electro-Optical Information Processing, J. T. Tippett, Ed. (MIT Press, Cambridge, 1965).

Lee, S. H.

S. H. Lee, S. K. Yao, A. G. Milnes, J. Opt. Soc. Amer. 60, 1037 (1970).
[CrossRef]

Milnes, A. G.

S. H. Lee, S. K. Yao, A. G. Milnes, J. Opt. Soc. Amer. 60, 1037 (1970).
[CrossRef]

Rotz, F. B.

A. Vander Lugt, F. B. Rotz, A. Klooster, “Character Reading by Optical Spatial Filtering,” in Optical and Electro-Optical Information Processing, J. T. Tippett, Ed. (MIT Press, Cambridge, 1965).

Vander Lugt, A.

A. Vander Lugt, IEEE Trans. Information Theory IT-10, 139 (1964).
[CrossRef]

A. Vander Lugt, F. B. Rotz, A. Klooster, “Character Reading by Optical Spatial Filtering,” in Optical and Electro-Optical Information Processing, J. T. Tippett, Ed. (MIT Press, Cambridge, 1965).

Watrasiewicz, B. M.

Yao, S. K.

S. H. Lee, S. K. Yao, A. G. Milnes, J. Opt. Soc. Amer. 60, 1037 (1970).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Information Theory (1)

A. Vander Lugt, IEEE Trans. Information Theory IT-10, 139 (1964).
[CrossRef]

J. Opt. Soc. Amer. (1)

S. H. Lee, S. K. Yao, A. G. Milnes, J. Opt. Soc. Amer. 60, 1037 (1970).
[CrossRef]

Other (2)

J. M. Holeman, “Holographic Character Reader,” in Pattern Recognition, L. N. Kanal, Ed. (Thompson Book Co., Washington, D.C., 1968).

A. Vander Lugt, F. B. Rotz, A. Klooster, “Character Reading by Optical Spatial Filtering,” in Optical and Electro-Optical Information Processing, J. T. Tippett, Ed. (MIT Press, Cambridge, 1965).

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Figures (6)

Fig. 1
Fig. 1

A typical coherent optical data processing system. With diffraction gratings in plane P2 the systems can perform complex addition of patterns displayed symmetrically in plane P1.

Fig. 2
Fig. 2

An optical system for synthesizing the spatial filter needed to obtain correlation and subtraction simultaneously in real time.

Fig. 3
Fig. 3

The output of a coherent system with a subtraction–correlation filter. Patterns from left to right are f2*f1, (f2f3)*f1, and f3*f1, where f1 stands for the horizontal stroke, f2 the character T. and f3 the character I.

Fig. 4
Fig. 4

The output of a coherent system with a subtraction–correlation filter. Patterns from left to right are f2*f1, (f2f3)*f1, and f3*f1, where f1, stands for the horizontal stroke and both f2 and f3 are the character I.

Fig. 5
Fig. 5

The output of a coherent system with a subtraction–correlation filter. Patterns from left to right are f2*f1, (f2f3)*f1, and f3*f1, where f1 stands for the tilted stroke, f2 the character R, and f3 the character P.

Fig. 6
Fig. 6

The output of a coherent system with a subtraction–correlation filter. Patterns from left to right are f2*f1, (f2f3)*f1, and f3*f1, where f1, stands for the tilted stroke and both f2 and f3 are the character P.

Equations (10)

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t 1 ( x ) = f 2 ( x - b 1 ) + f 3 ( x - b 2 ) .
A P 2 - ( v ) = F 2 ( v ) exp ( - i 2 π v · b 1 ) + F 3 ( v ) exp ( - i 2 π v · b 2 ) ,
t ( v ) = F 1 * ( v ) [ exp ( i 2 π v · b 1 ) - exp ( i 2 π v · b 2 ) ]
A P 2 + ( v ) = A P 2 - ( v ) t ( v ) = F 1 * ( v ) [ F 2 ( v ) - F 3 ( v ) ] + other terms with phase factors .
t 3 ( x ) = F . T . [ A P 2 + ( v ) ] = ( f 2 - f 3 ) * f 1 + other off - axis images .
t 2 ( v ) = 2 + 2 F 1 ( v ) 2 + F 1 ( v ) [ exp ( - i 2 π v · b 1 ) ] - exp ( - i 2 π v · b 2 ) ] + F 1 * ( v ) [ exp ( i 2 π v · b 1 ) - exp ( i 2 π v · b 2 ) ] = 1 + F 1 ( v ) exp ( - i 2 π v · b 1 ) 2 + 1 - F 1 ( v ) exp ( - i 2 π v · b 2 ) 2 .
t 2 ( v ) = 1 + F 1 ( v ) exp ( - i 2 π v · b 1 ) 2 + 1 + F 1 ( v + Δ ) exp - i 2 π ( v + Δ ) · b 2 2 = 2 + 2 F 1 ( v ) 2 + F 1 ( v ) exp ( - i 2 π v · b 1 ) + F 1 ( v + Δ ) exp ( - i 2 π Δ · b 2 ) exp ( - i 2 π v · b 2 ) + F 1 * ( v ) exp ( i 2 π v · b 1 ) + F 1 * ( v + Δ ) exp ( i 2 π Δ · b 2 ) exp ( i 2 π v · b 2 ) .
Δ = 1 / ( 2 b 2 ) .
x max 1 / Δ .
x max 2 b 2 .

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