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References

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  1. H. Kato, J. W. Goodman, Appl. Opt. 14, 1813 (1975).
    [CrossRef] [PubMed]
  2. A. Tai, T. Cheng, F. T. S. Yu, Appl. Opt. 16, 2559 (1977).
    [CrossRef] [PubMed]
  3. A. V. Oppenheim, R. W. Schafer, T. G. Stockham, Proc. IEEE 56, 1264 (1968).
    [CrossRef]
  4. F. T. S. Yu, Introduction to Diffraction, Information Processing, and Holography (MIT Press, Cambridge, 1973).
  5. Kodak Professional Black and White Films, Eastman Kodak Co.

1977 (1)

1975 (1)

1968 (1)

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, Proc. IEEE 56, 1264 (1968).
[CrossRef]

Cheng, T.

Goodman, J. W.

Kato, H.

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, Proc. IEEE 56, 1264 (1968).
[CrossRef]

Schafer, R. W.

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, Proc. IEEE 56, 1264 (1968).
[CrossRef]

Stockham, T. G.

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, Proc. IEEE 56, 1264 (1968).
[CrossRef]

Tai, A.

Yu, F. T. S.

A. Tai, T. Cheng, F. T. S. Yu, Appl. Opt. 16, 2559 (1977).
[CrossRef] [PubMed]

F. T. S. Yu, Introduction to Diffraction, Information Processing, and Holography (MIT Press, Cambridge, 1973).

Appl. Opt. (2)

Proc. IEEE (1)

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, Proc. IEEE 56, 1264 (1968).
[CrossRef]

Other (2)

F. T. S. Yu, Introduction to Diffraction, Information Processing, and Holography (MIT Press, Cambridge, 1973).

Kodak Professional Black and White Films, Eastman Kodak Co.

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Figures (4)

Fig. 1
Fig. 1

Optical homomorphic filtering system.

Fig. 2
Fig. 2

Exponential transformation using two-step contact printing process. Plots (a), (b), and (d) refer to Eqs. (2), (3), and (5), respectively.

Fig. 3
Fig. 3

Fourier spectra of multiplied perpendicular gratings after (a) linear transformation, (b) logarithmic transformation, (c) logarithmic and inverse transformations.

Fig. 4
Fig. 4

Nonlinear filtering of continuous-tone signal with multiplied noise: (a) input; (b) spatially filtered linearly transformed signals; (c) spatially filtered logarithmically transformed signals; (d) inverse transformation of (c).

Equations (5)

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I = ( K 1 log E ) 2 ,
I 1 = k 2 ( k 1 I - γ 1 ) - γ 2 = k 3 ( K 1 log E ) ,
T I 1 = c 1 exp ( K 2 I 1 ) .
T I 2 = c 2 exp ( γ K 1 K 2 log E ) .
T I 2 = C 2 E .

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