Abstract

The distortion of the image of an object, produced by diffraction, can be reduced by filtering. A class of filters is developed for minimizing the first term in the moment expansion of the error. The resulting spread functions have high attenuation rate, negligible side lobes, and are optimum for imaging smooth objects. One- and two-dimensional systems are considered; the analysis includes coherent and incoherent illumination.

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  1. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).
  2. A. Papoulis, The Fourier Integral and its Applications (McGraw-Hill, New York, 1962).
  3. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964).
  4. J. E. Wilkins, Jr., J. Opt. Soc. Am. 53, 420 (1963).
  5. G. Lansraux and G. Boivin, Can. J. Phys. 76, 1696 (1958).
  6. R. Barakat, J. Opt. Soc. Am. 52, 264 (1962).
  7. R. Barakat and E. Levin, J. Opt. Soc. Am. 53, 274 (1963).
  8. A. Papoulis, J. Opt. Soc. Am. 62, 77 (1972).
  9. A. Papoulis, Probability Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965).
  10. N. I. Akhiezer, The Calculus of Variations (Blaisdell, New York, 1962).
  11. N. I. Akhiezer, Theory of Approximation, (Ungar, New York, 1956).
  12. E. Marchand, J. Opt. Soc. 54, 915 (1964).
  13. A. Papoulis, IEEE Trans. IT-14, 164 (1968).

Akhiezer, N. I.

N. I. Akhiezer, The Calculus of Variations (Blaisdell, New York, 1962).

N. I. Akhiezer, Theory of Approximation, (Ungar, New York, 1956).

Barakat, R.

R. Barakat and E. Levin, J. Opt. Soc. Am. 53, 274 (1963).

R. Barakat, J. Opt. Soc. Am. 52, 264 (1962).

Boivin, G.

G. Lansraux and G. Boivin, Can. J. Phys. 76, 1696 (1958).

Lansraux, G.

G. Lansraux and G. Boivin, Can. J. Phys. 76, 1696 (1958).

Levin, E.

R. Barakat and E. Levin, J. Opt. Soc. Am. 53, 274 (1963).

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964).

Marchand, E.

E. Marchand, J. Opt. Soc. 54, 915 (1964).

Papoulis, A.

A. Papoulis, J. Opt. Soc. Am. 62, 77 (1972).

A. Papoulis, Probability Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965).

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

A. Papoulis, IEEE Trans. IT-14, 164 (1968).

A. Papoulis, The Fourier Integral and its Applications (McGraw-Hill, New York, 1962).

Wilkins, Jr., J. E.

J. E. Wilkins, Jr., J. Opt. Soc. Am. 53, 420 (1963).

Other

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

A. Papoulis, The Fourier Integral and its Applications (McGraw-Hill, New York, 1962).

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964).

J. E. Wilkins, Jr., J. Opt. Soc. Am. 53, 420 (1963).

G. Lansraux and G. Boivin, Can. J. Phys. 76, 1696 (1958).

R. Barakat, J. Opt. Soc. Am. 52, 264 (1962).

R. Barakat and E. Levin, J. Opt. Soc. Am. 53, 274 (1963).

A. Papoulis, J. Opt. Soc. Am. 62, 77 (1972).

A. Papoulis, Probability Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965).

N. I. Akhiezer, The Calculus of Variations (Blaisdell, New York, 1962).

N. I. Akhiezer, Theory of Approximation, (Ungar, New York, 1956).

E. Marchand, J. Opt. Soc. 54, 915 (1964).

A. Papoulis, IEEE Trans. IT-14, 164 (1968).

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