Abstract

The eigenfunctions of the integral equation describing the image-formation process are used for studying the degrees of freedom of coherent images from point-like-element pupils. The possibility of determining the number of effective degrees of freedom without solving the integral equation is demonstrated for an important class of cases. Finally, the number of effective degrees of freedom is explicitly calculated for cases of practical interest.

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  1. F. Gori and G. Guattari, J. Opt. Soc. Am. 61, 36 (1971).
  2. G. Toraldo di Francia, J. Opt. Soc. Am. 59, 799 (1969).
  3. J. T. Winthrop, J. Opt. Soc. Am. 61, 15 (1971).
  4. C. K. Rushforth and R. W. Harris, J. Opt. Soc. Am. 58, 539 (1968).
  5. J. W. Goodman, in Progress in Optics, VIII, edited by E. Wolf (North-Holland, Amsterdam, 1970).
  6. B. R. Frieden, in Progress in Optics, IX, edited by E. Wolf (North-Holland, Amsterdam, 1971).
  7. A. Walther, J. Opt. Soc. Am. 57, 639 (1967).
  8. D. Slepian and H. O. Pollak, Bell Syst. Tech. J. 40, 43 (1961).
  9. H. J. Landau and H. O. Pollak, Bell Syst. Tech. J. 40, 65 (1961).
  10. H. J. Landau and H. O. Pollak, Bell Syst. Tech. J. 41, 1295 (1962).
  11. D. Slepian, Bell Syst. Tech. J. 43, 3009 (1964).
  12. D. Slepian and E. Sonnenblick, Bell Syst. Tech. J. 44, 1745 (1965).
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Ch. 6.
  14. F. Riesz and B. Sz.-Nagy, Functional Analysis (Ungar, New York, 1955), Ch. 6.
  15. The function R(x) can be considered as a solution of Eq. (3) corresponding to the eigenvalue λ = 0. In what follows, however, we will mean by eigenvalues only the λ's that differ from zero.
  16. F. Gori and G. Guattari, Opt. Commun. 7, 163 (1973).

Francia, G. Toraldo di

G. Toraldo di Francia, J. Opt. Soc. Am. 59, 799 (1969).

Frieden, B. R.

B. R. Frieden, in Progress in Optics, IX, edited by E. Wolf (North-Holland, Amsterdam, 1971).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Ch. 6.

J. W. Goodman, in Progress in Optics, VIII, edited by E. Wolf (North-Holland, Amsterdam, 1970).

Gori, F.

F. Gori and G. Guattari, J. Opt. Soc. Am. 61, 36 (1971).

F. Gori and G. Guattari, Opt. Commun. 7, 163 (1973).

Guattari, G.

F. Gori and G. Guattari, Opt. Commun. 7, 163 (1973).

F. Gori and G. Guattari, J. Opt. Soc. Am. 61, 36 (1971).

Harris, R. W.

C. K. Rushforth and R. W. Harris, J. Opt. Soc. Am. 58, 539 (1968).

Landau, H. J.

H. J. Landau and H. O. Pollak, Bell Syst. Tech. J. 40, 65 (1961).

H. J. Landau and H. O. Pollak, Bell Syst. Tech. J. 41, 1295 (1962).

-Nagy, B. Sz

F. Riesz and B. Sz.-Nagy, Functional Analysis (Ungar, New York, 1955), Ch. 6.

Pollak, H. O.

D. Slepian and H. O. Pollak, Bell Syst. Tech. J. 40, 43 (1961).

H. J. Landau and H. O. Pollak, Bell Syst. Tech. J. 41, 1295 (1962).

H. J. Landau and H. O. Pollak, Bell Syst. Tech. J. 40, 65 (1961).

Riesz, F.

F. Riesz and B. Sz.-Nagy, Functional Analysis (Ungar, New York, 1955), Ch. 6.

Rushforth, C. K.

C. K. Rushforth and R. W. Harris, J. Opt. Soc. Am. 58, 539 (1968).

Slepian, D.

D. Slepian and H. O. Pollak, Bell Syst. Tech. J. 40, 43 (1961).

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

D. Slepian, Bell Syst. Tech. J. 43, 3009 (1964).

Sonnenblick, E.

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

Walther, A.

A. Walther, J. Opt. Soc. Am. 57, 639 (1967).

Winthrop, J. T.

J. T. Winthrop, J. Opt. Soc. Am. 61, 15 (1971).

Other (16)

F. Gori and G. Guattari, J. Opt. Soc. Am. 61, 36 (1971).

G. Toraldo di Francia, J. Opt. Soc. Am. 59, 799 (1969).

J. T. Winthrop, J. Opt. Soc. Am. 61, 15 (1971).

C. K. Rushforth and R. W. Harris, J. Opt. Soc. Am. 58, 539 (1968).

J. W. Goodman, in Progress in Optics, VIII, edited by E. Wolf (North-Holland, Amsterdam, 1970).

B. R. Frieden, in Progress in Optics, IX, edited by E. Wolf (North-Holland, Amsterdam, 1971).

A. Walther, J. Opt. Soc. Am. 57, 639 (1967).

D. Slepian and H. O. Pollak, Bell Syst. Tech. J. 40, 43 (1961).

H. J. Landau and H. O. Pollak, Bell Syst. Tech. J. 40, 65 (1961).

H. J. Landau and H. O. Pollak, Bell Syst. Tech. J. 41, 1295 (1962).

D. Slepian, Bell Syst. Tech. J. 43, 3009 (1964).

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

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Ch. 6.

F. Riesz and B. Sz.-Nagy, Functional Analysis (Ungar, New York, 1955), Ch. 6.

The function R(x) can be considered as a solution of Eq. (3) corresponding to the eigenvalue λ = 0. In what follows, however, we will mean by eigenvalues only the λ's that differ from zero.

F. Gori and G. Guattari, Opt. Commun. 7, 163 (1973).

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