Abstract

Optical differentiation and integration are not only interesting from the standpoint of optical computation, but are also important in picture processing. Based on optical correlation, or convolution, and the applications of difference equations, a technique for synthesizing the differentiation and integration filters is presented. This technique compares favorably with other methods which now exist.

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  1. J. B. DeVelis and G. O. Reynolds, Theory and Applications of Holography (Addison–Wesley, Reading, Mass., 1967), p. 154.
  2. A. Rosenfeld, Picture Processing by Computer (Academic, New York, 1969), Sec. 6.5, p. 94.
  3. T. S. Huang and O. J. Tretiak, in Optical and Electro-optical Information Processing, edited by J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, and A. Vanderburgh (M.I.T. Press, Cambridge, Mass., 1965), Ch. 3, p. 45.
  4. A. W. Lohmann and D. P. Paris, Appl. Opt. 7, 651 (1968).
  5. A. Vander Lugt, Opt. Acta 15, 1 (1968).
  6. R. G. Eguchi and F. P. Carlson, Appl. Opt. 9, 687 (1970).
  7. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1968).
  8. In a somewhat different approach Trabka and Roetling [E. A. Trabka and P. G. Roetling, J. Opt. Soc. Am. 54, 1242 (1964)] have also arrived at similar expressions for the differential operators discussed in this section.
  9. A. Vander Lugt, IEEE Trans. IT-10, 139 (1964).
  10. These techniques for obtaining the negative sign have also been successfully applied to synthesizing a spatial filter for the combined operation of subtraction and correlation [S. K. Yao and S. H. Lee, J. Opt. Soc. Am. 60, 1547A (1970)].

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1968).

Carlson, F. P.

R. G. Eguchi and F. P. Carlson, Appl. Opt. 9, 687 (1970).

DeVelis, J. B.

J. B. DeVelis and G. O. Reynolds, Theory and Applications of Holography (Addison–Wesley, Reading, Mass., 1967), p. 154.

Eguchi, R. G.

R. G. Eguchi and F. P. Carlson, Appl. Opt. 9, 687 (1970).

Huang, T. S.

T. S. Huang and O. J. Tretiak, in Optical and Electro-optical Information Processing, edited by J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, and A. Vanderburgh (M.I.T. Press, Cambridge, Mass., 1965), Ch. 3, p. 45.

Lohmann, A. W.

A. W. Lohmann and D. P. Paris, Appl. Opt. 7, 651 (1968).

Lugt, A. Vander

A. Vander Lugt, Opt. Acta 15, 1 (1968).

A. Vander Lugt, IEEE Trans. IT-10, 139 (1964).

Paris, D. P.

A. W. Lohmann and D. P. Paris, Appl. Opt. 7, 651 (1968).

Reynolds, G. O.

J. B. DeVelis and G. O. Reynolds, Theory and Applications of Holography (Addison–Wesley, Reading, Mass., 1967), p. 154.

Rosenfeld, A.

A. Rosenfeld, Picture Processing by Computer (Academic, New York, 1969), Sec. 6.5, p. 94.

Tretiak, O. J.

T. S. Huang and O. J. Tretiak, in Optical and Electro-optical Information Processing, edited by J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, and A. Vanderburgh (M.I.T. Press, Cambridge, Mass., 1965), Ch. 3, p. 45.

Other (10)

J. B. DeVelis and G. O. Reynolds, Theory and Applications of Holography (Addison–Wesley, Reading, Mass., 1967), p. 154.

A. Rosenfeld, Picture Processing by Computer (Academic, New York, 1969), Sec. 6.5, p. 94.

T. S. Huang and O. J. Tretiak, in Optical and Electro-optical Information Processing, edited by J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, and A. Vanderburgh (M.I.T. Press, Cambridge, Mass., 1965), Ch. 3, p. 45.

A. W. Lohmann and D. P. Paris, Appl. Opt. 7, 651 (1968).

A. Vander Lugt, Opt. Acta 15, 1 (1968).

R. G. Eguchi and F. P. Carlson, Appl. Opt. 9, 687 (1970).

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1968).

In a somewhat different approach Trabka and Roetling [E. A. Trabka and P. G. Roetling, J. Opt. Soc. Am. 54, 1242 (1964)] have also arrived at similar expressions for the differential operators discussed in this section.

A. Vander Lugt, IEEE Trans. IT-10, 139 (1964).

These techniques for obtaining the negative sign have also been successfully applied to synthesizing a spatial filter for the combined operation of subtraction and correlation [S. K. Yao and S. H. Lee, J. Opt. Soc. Am. 60, 1547A (1970)].

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