Abstract

An optical transfer function consisting of a phase-only term and an optimized passband is synthesized for constructing an incoherent optical correlator for recognition of a noisy gray-tone image. The proposed incoherent correlator can yield a sharp correlation peak with excellent noise tolerance.

© 1995 Optical Society of America

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References

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  1. H. Stark, Application of Optical Fourier Transforms (Academic, New York, 1982), Chap. 12, p. 514.
  2. J. D. Armitage, A. W. Lohmann, Appl. Opt. 4, 461 (1965).
    [CrossRef]
  3. See, for example, B. V. K. V. Kumar, Appl. Opt. 31, 4773 (1992).
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    [CrossRef]
  5. A. W. Lohmann, H. W. Werlich, Appl. Opt. 10, 670 (1971).
    [CrossRef] [PubMed]
  6. Y. Katzir, M. Young, I. Glaser, Appl. Opt. 24, 863 (1985).
    [CrossRef] [PubMed]
  7. J. van der Gracht, J. N. Mait, Opt. Lett. 17, 1703 (1992).
    [CrossRef] [PubMed]
  8. R. C. Sherman, D. Grieser, F. Gamble, C. M. Verber, T. Dolash, Appl. Opt. 22, 3579 (1983).
    [CrossRef] [PubMed]
  9. P. Chavel, S. Lowenthal, J. Opt. Soc. Am. 68, 721 (1978).
    [CrossRef]
  10. A. W. Lohmann, W. T. Rhodes, Appl. Opt. 17, 1141 (1978).
    [CrossRef] [PubMed]
  11. J. N. Mait, W. T. Rhodes, Appl. Opt. 28, 1474 (1989).
    [CrossRef] [PubMed]
  12. J. Ding, M. Itoh, T. Yatagai, Opt. Commun. 118, 90 (1995).
    [CrossRef]
  13. J. R. Fienup, Opt. Eng. 19, 297 (1980).

1995 (1)

J. Ding, M. Itoh, T. Yatagai, Opt. Commun. 118, 90 (1995).
[CrossRef]

1992 (2)

1989 (1)

1985 (1)

1983 (1)

1980 (1)

J. R. Fienup, Opt. Eng. 19, 297 (1980).

1978 (2)

1971 (1)

1968 (1)

1965 (1)

Armitage, J. D.

Chavel, P.

Ding, J.

J. Ding, M. Itoh, T. Yatagai, Opt. Commun. 118, 90 (1995).
[CrossRef]

Dolash, T.

Fienup, J. R.

J. R. Fienup, Opt. Eng. 19, 297 (1980).

Gamble, F.

Glaser, I.

Grieser, D.

Itoh, M.

J. Ding, M. Itoh, T. Yatagai, Opt. Commun. 118, 90 (1995).
[CrossRef]

Katzir, Y.

Kumar, B. V. K. V.

Lohmann, A. W.

Lowenthal, S.

Mait, J. N.

Rhodes, W. T.

Sherman, R. C.

Stark, H.

H. Stark, Application of Optical Fourier Transforms (Academic, New York, 1982), Chap. 12, p. 514.

van der Gracht, J.

Verber, C. M.

Werlich, H. W.

Yatagai, T.

J. Ding, M. Itoh, T. Yatagai, Opt. Commun. 118, 90 (1995).
[CrossRef]

Young, M.

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Figures (4)

Fig. 1
Fig. 1

Configuration of the incoherent correlator: CL1, CL2, condenser lenses; IF, interference filter; FL1, FL2, Fourier lenses with a focal length F = 1000 mm.

Fig. 2
Fig. 2

Images of Einstein’s face used in experiments: the original noise-free image (left) and the noisy image (right) with an additive Gaussian noise of variance σ2 = Eav, where Eav is the average intensity of the original image.

Fig. 3
Fig. 3

Correlation distribution along a slice across the correlation peak. The same scale is used to plot the two correlation slices corresponding to the proposed synthesized filter (solid curve) and the matched filter (dotted curve).

Fig. 4
Fig. 4

Correlation output of the original image (left) and the noisy input image (right) with the synthesized filter (positive filter minus the negative filter).

Equations (8)

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C ( u ) = I ( u ) O ( u ) ,
O ( u ) = P ( u ) exp [ - i φ ( u ) ] ,
SNR = I ( u ) P ( u ) d u R n ( u ) P ( u ) d u .
O ( u ) = { a exp [ - i φ ( u ) ] u = 0 P ( u ) exp [ - i φ ( u ) ] u 0 ,
a = b S I ( 0 ) ,
g ( x ) = g + ( x ) - g - ( x ) .
H + ( u ) = F { g + ( x ) exp [ i α + ( x ) ] } ,
H - ( u ) = F { g - ( x ) exp [ i α - ( x ) ] } ,

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