Abstract

This paper treats the problem of restoring the detail to an optical image which has been degraded by diffraction and noise. The particular contribution of the paper is a more complete analysis of the effects of various types of noise on system performance than has been given previously. Background noise, measurement noise, and computer roundoff error are considered, and the errors in the reconstructed image caused by these noise processes are evaluated. Numerical results for the special case of a perfect one-dimensional slit aperture are obtained. A general conclusion is that the reconstruction technique described here is most useful when the smoothing is severe and when a modest improvement of resolution may be worthwhile.

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  1. J. L. Harris, J. Opt. Soc. Am. 54, 931 (1964).
  2. C. W. Barnes, J. Opt. Soc. Am. 56, 575 (1966).
  3. B. R. Frieden, J. Opt. Soc. Am. 57, 1013 (1967).
  4. G. J. Buck and J. J. Gustincic, IEEE Trans. Antennas Propagation AP-15, 376 (1967).
  5. E. L. O'Neill, Introduction to Statistical Optics, (Addison-Wesley Publishing Co., Reading, Mass., 1964).
  6. R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience Publishers, John Wiley & Sons, Inc., New York, 1953).
  7. E. N. Keith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).
  8. D. Slepian and H. O. Pollack, Bell System Tech. J. 40, 43 (1961).
  9. C. Flammer, Spheroidal Wave Functions (Stanford University Press, Stanford, Calif., 1957).
  10. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill Book Co., N. Y., 1965).
  11. D. Slepian and E. Sonnenblick, Bell System Tech. J. 44, 1745 (1965).

Barnes, C. W.

C. W. Barnes, J. Opt. Soc. Am. 56, 575 (1966).

Buck, G. J.

G. J. Buck and J. J. Gustincic, IEEE Trans. Antennas Propagation AP-15, 376 (1967).

Courant, R.

R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience Publishers, John Wiley & Sons, Inc., New York, 1953).

Flammer, C.

C. Flammer, Spheroidal Wave Functions (Stanford University Press, Stanford, Calif., 1957).

Frieden, B. R.

B. R. Frieden, J. Opt. Soc. Am. 57, 1013 (1967).

Gustincic, J. J.

G. J. Buck and J. J. Gustincic, IEEE Trans. Antennas Propagation AP-15, 376 (1967).

Harris, J. L.

J. L. Harris, J. Opt. Soc. Am. 54, 931 (1964).

Hilbert, D.

R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience Publishers, John Wiley & Sons, Inc., New York, 1953).

Keith, E. N.

E. N. Keith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

O’Neill, E. L.

E. L. O'Neill, Introduction to Statistical Optics, (Addison-Wesley Publishing Co., Reading, Mass., 1964).

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill Book Co., N. Y., 1965).

Pollack, H. O.

D. Slepian and H. O. Pollack, Bell System Tech. J. 40, 43 (1961).

Slepian, D.

D. Slepian and H. O. Pollack, Bell System Tech. J. 40, 43 (1961).

D. Slepian and E. Sonnenblick, Bell System Tech. J. 44, 1745 (1965).

Sonnenblick, E.

D. Slepian and E. Sonnenblick, Bell System Tech. J. 44, 1745 (1965).

Upatnieks, J.

E. N. Keith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

Other (11)

J. L. Harris, J. Opt. Soc. Am. 54, 931 (1964).

C. W. Barnes, J. Opt. Soc. Am. 56, 575 (1966).

B. R. Frieden, J. Opt. Soc. Am. 57, 1013 (1967).

G. J. Buck and J. J. Gustincic, IEEE Trans. Antennas Propagation AP-15, 376 (1967).

E. L. O'Neill, Introduction to Statistical Optics, (Addison-Wesley Publishing Co., Reading, Mass., 1964).

R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience Publishers, John Wiley & Sons, Inc., New York, 1953).

E. N. Keith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

D. Slepian and H. O. Pollack, Bell System Tech. J. 40, 43 (1961).

C. Flammer, Spheroidal Wave Functions (Stanford University Press, Stanford, Calif., 1957).

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill Book Co., N. Y., 1965).

D. Slepian and E. Sonnenblick, Bell System Tech. J. 44, 1745 (1965).

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