Abstract

The application of optical transfer theory to the process of image formation requires that the image-forming system be linear and space invariant. In a space-invariant system, the point image retains its shape while the point source explores the object plane. The purpose of this paper is to investigate image-forming systems which are linear but space variant. Such systems may exceed performance limitations which are inherent in linear space-invariant systems. A method for experimentally determining space variance is devised. The degree of space invariance is defined and evaluated for several examples of space-variant systems.

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  1. R. V. Pole (Thomas J. Watson Research Center, Yorktown Heights, New York) proposed the term "space invariance" instead of the formerly used "stationarity." The term "nonisoplanatism" which has been used in this context, refers traditionally to the space variance caused by aberrations only.
  2. P. Lacomme, Opt. Acta 1, 33 (1954).
  3. H. Wolter, Physica ′24, 457 (1958).
  4. J. W. Menter, Advan. Phys. 7, 299 (1958).
  5. E. Lau, Physik. Z. 38, 446 (1937); A. Lohmann and D. Paris, Optik 22, 226 (1965).
  6. A. Lohmann, Hausmitteilungen J. Schneider und Co. 14, 52 (1962).
  7. Integrals without limits of integration are here and henceforth to be taken from - ∞ to + ∞.
  8. H. Wolter, Arch. Elek. Übertragung 13, 393 (1959); Opt Acta 7, 53 (1960).
  9. Unfortunately, this term implies that "invariance" can have a variable degree, while really something is either invariant or it is not. However, so far we were unable to find a more appropriate term.
  10. p. B. Fellgett and E. H. Linfoot, Phil. Trans. Roy. Soc. London A247, 369 (1955).

Fellgett, p. B.

p. B. Fellgett and E. H. Linfoot, Phil. Trans. Roy. Soc. London A247, 369 (1955).

Lacomme, P.

P. Lacomme, Opt. Acta 1, 33 (1954).

Lau, E.

E. Lau, Physik. Z. 38, 446 (1937); A. Lohmann and D. Paris, Optik 22, 226 (1965).

Linfoot, E. H.

p. B. Fellgett and E. H. Linfoot, Phil. Trans. Roy. Soc. London A247, 369 (1955).

Lohmann, A.

A. Lohmann, Hausmitteilungen J. Schneider und Co. 14, 52 (1962).

Menter, J. W.

J. W. Menter, Advan. Phys. 7, 299 (1958).

Pole, R. V.

R. V. Pole (Thomas J. Watson Research Center, Yorktown Heights, New York) proposed the term "space invariance" instead of the formerly used "stationarity." The term "nonisoplanatism" which has been used in this context, refers traditionally to the space variance caused by aberrations only.

Wolter, H.

H. Wolter, Arch. Elek. Übertragung 13, 393 (1959); Opt Acta 7, 53 (1960).

H. Wolter, Physica ′24, 457 (1958).

Other (10)

R. V. Pole (Thomas J. Watson Research Center, Yorktown Heights, New York) proposed the term "space invariance" instead of the formerly used "stationarity." The term "nonisoplanatism" which has been used in this context, refers traditionally to the space variance caused by aberrations only.

P. Lacomme, Opt. Acta 1, 33 (1954).

H. Wolter, Physica ′24, 457 (1958).

J. W. Menter, Advan. Phys. 7, 299 (1958).

E. Lau, Physik. Z. 38, 446 (1937); A. Lohmann and D. Paris, Optik 22, 226 (1965).

A. Lohmann, Hausmitteilungen J. Schneider und Co. 14, 52 (1962).

Integrals without limits of integration are here and henceforth to be taken from - ∞ to + ∞.

H. Wolter, Arch. Elek. Übertragung 13, 393 (1959); Opt Acta 7, 53 (1960).

Unfortunately, this term implies that "invariance" can have a variable degree, while really something is either invariant or it is not. However, so far we were unable to find a more appropriate term.

p. B. Fellgett and E. H. Linfoot, Phil. Trans. Roy. Soc. London A247, 369 (1955).

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