Abstract

A method for obtaining the optical transfer function from the edge spread function is described. The method involves the inversion of a Fredholm integral equation of the first kind using sampling-theory concepts. Typical examples for both symmetric and asymmetric edge spread functions are studied and compared with the known solutions.

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  1. F. Scott, R. M. Scott, and R. V. Shack, Phot. Sci. Engr. 7, 345 (1963).
  2. R. Barakat and A. Houston (to be published).
  3. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, England, 1952), p. 188, 4th ed.
  4. R. Barakat, J. Opt. Soc. Am. 54, 920 (1964).
  5. It is interesting to note that S is a Toeplitz matrix; that is, its elements (2.12) depend on the difference of m and n. Attempts were made to employ the theory of such matrices but unfortunately to no avail. The standard work on these forms is: U. Grenander and G. Szego, Toeplitz Forms and Their Applications (University of California Press, Berkeley, California, 1958).
  6. K. L. Nielsen, Methods in Numerical Analysis (The Macmillan Co., Inc., New York, 1956), Chap. 7.
  7. R. Barakat, J. Opt. Soc. Am. 54, 38 (1964).
  8. R. Barakat, J. Opt. Soc. Am. 52, 985 (1962).
  9. R. Barakat and M. V. Morello, J. Opt. Soc. Am. 52, 992 (1962).

Barakat, R.

R. Barakat and A. Houston (to be published).

R. Barakat, J. Opt. Soc. Am. 54, 920 (1964).

R. Barakat, J. Opt. Soc. Am. 54, 38 (1964).

R. Barakat, J. Opt. Soc. Am. 52, 985 (1962).

R. Barakat and M. V. Morello, J. Opt. Soc. Am. 52, 992 (1962).

Houston, A.

R. Barakat and A. Houston (to be published).

Morello, M. V.

R. Barakat and M. V. Morello, J. Opt. Soc. Am. 52, 992 (1962).

Nielsen, K. L.

K. L. Nielsen, Methods in Numerical Analysis (The Macmillan Co., Inc., New York, 1956), Chap. 7.

Scott, F.

F. Scott, R. M. Scott, and R. V. Shack, Phot. Sci. Engr. 7, 345 (1963).

Scott, R. M.

F. Scott, R. M. Scott, and R. V. Shack, Phot. Sci. Engr. 7, 345 (1963).

Shack, R. V.

F. Scott, R. M. Scott, and R. V. Shack, Phot. Sci. Engr. 7, 345 (1963).

Szego, G.

It is interesting to note that S is a Toeplitz matrix; that is, its elements (2.12) depend on the difference of m and n. Attempts were made to employ the theory of such matrices but unfortunately to no avail. The standard work on these forms is: U. Grenander and G. Szego, Toeplitz Forms and Their Applications (University of California Press, Berkeley, California, 1958).

Szego, U.

It is interesting to note that S is a Toeplitz matrix; that is, its elements (2.12) depend on the difference of m and n. Attempts were made to employ the theory of such matrices but unfortunately to no avail. The standard work on these forms is: U. Grenander and G. Szego, Toeplitz Forms and Their Applications (University of California Press, Berkeley, California, 1958).

Watson, G. N.

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, England, 1952), p. 188, 4th ed.

Whittaker, E. T.

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, England, 1952), p. 188, 4th ed.

Other (9)

F. Scott, R. M. Scott, and R. V. Shack, Phot. Sci. Engr. 7, 345 (1963).

R. Barakat and A. Houston (to be published).

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, England, 1952), p. 188, 4th ed.

R. Barakat, J. Opt. Soc. Am. 54, 920 (1964).

It is interesting to note that S is a Toeplitz matrix; that is, its elements (2.12) depend on the difference of m and n. Attempts were made to employ the theory of such matrices but unfortunately to no avail. The standard work on these forms is: U. Grenander and G. Szego, Toeplitz Forms and Their Applications (University of California Press, Berkeley, California, 1958).

K. L. Nielsen, Methods in Numerical Analysis (The Macmillan Co., Inc., New York, 1956), Chap. 7.

R. Barakat, J. Opt. Soc. Am. 54, 38 (1964).

R. Barakat, J. Opt. Soc. Am. 52, 985 (1962).

R. Barakat and M. V. Morello, J. Opt. Soc. Am. 52, 992 (1962).

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