Abstract

A nonlinear matched filter based optical correlation is presented. The nonlinear filter is produced by applying a nonlinear transformation to the linear matched filter.

© 1989 Optical Society of America

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References

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  1. B. Javidi, C.-J. Kuo, “Joint Transform Image Correlation Using a Binary Spatial Light Modulator at the Fourier Plane,” Appl. Opt. 27, 663–665 (1988);also presented at the1987 OSA Annual Meeting, Rochester, NY [J. Opt. Soc. Am. A4 (13), P86 (1987)].
    [CrossRef] [PubMed]
  2. B. Javidi, J. L. Horner, “Single Spatial Light Modulator Joint Transform Correlator,” Appl. Opt. 28, 1027–1032 (1989).
    [CrossRef] [PubMed]
  3. B. Javidi, “Comparison of Bipolar Joint Transform Image Correlators and Phase-Only Matched Filter Correlators,” Opt. Eng. 28, 000–000 (Mar.1989).
    [CrossRef]
  4. B. Javidi, “Nonlinear Joint Power Spectrum Based Optical Correlation,” Appl. Opt. 28, 2358–2367 (1989).
    [CrossRef] [PubMed]
  5. C. S. Weaver, J. W. Goodman, “A Technique for Optically Convolving Two Functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  6. B. Javidi, “Generalization of the Linear Matched Filter Concept to Nonlinear Matched Filters,” submitted to Appl. Opt.
    [PubMed]
  7. J. L. Horner, P. D. Gianini, “Phase-Only Matched Filtering,” Appl. Opt. 24, 2889–2893 (1985).
    [CrossRef] [PubMed]

1989 (3)

1988 (1)

1985 (1)

1966 (1)

Gianini, P. D.

Goodman, J. W.

Horner, J. L.

Javidi, B.

Kuo, C.-J.

Weaver, C. S.

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Figures (4)

Fig. 1
Fig. 1

Nonlinear matched filter based optical correlator.

Fig. 2
Fig. 2

Reference function used in the correlation tests.

Fig. 3
Fig. 3

Correlation signal obtained by a linear matched filter.

Fig. 4
Fig. 4

Correlation signal obtaned by a binary nonlinear matched filter.

Equations (7)

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FT { s ( x , y ) } = s ( α , β ) exp [ i ϕ S ( α , β ) ] ,
FT { r ( x , y ) } = R ( α , β ) exp [ i ϕ R ( α , β ) ] ,
H ( α , β ) = R ( α , β ) exp [ i ϕ R ( α , β ) ] .
E ( α , β ) = R ( α , β ) cos [ x 0 α ϕ R ( α , β ) ] ,
h ( x , y ) = R 12 ( x + x 0 , y ) + M 12 ( x x 0 , y ) .
g k ( E ) = υ = 1 ( υ odd ) υ Γ ( k + 1 ) [ R ( α , β ) ] k 2 K Γ ( 1 υ k 2 ) Γ ( 1 + υ + k 2 ) × cos [ υ x 0 α υ φ R ( α , β ) ] ,
g 1 k ( E ) = Γ ( k + 1 ) 2 k + 1 Γ ( 1 1 k 2 ) Γ ( 1 + 1 + k 2 ) [ R ( α , β ) ] k × exp { i [ x 0 α ϕ R ( α , β ) ] } ,

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