Abstract

Optical data-processing systems in which the vectorial nature of light has to be taken into account can be described adequately by a theory in which the point spread is a tensor. The well-known scalar theory and the Jones calculus are, as special cases, both incorporated into this theory. Some basic properties and restrictions that can be imposed upon the optical system will be introduced. A general reciprocity relation will be derived, and the restriction that the reciprocity relation imposes upon the optical system will be discussed. This discussion leads to the remarkable conclusion that a reciprocal optical system neither can be described exactly in terms of a scalar theory nor by a Jones matrix with constant coefficients.

© 1978 Optical Society of America

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  1. H. J. Butterweck, "A general theory of linear, coherent optical data-processing systems," J. Opt. Soc. Am. 67, 60–70 (1977).
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  3. R. C. Jones, "A new calculus for the treatment of optical systems," J. Opt. Soc. Am. 31, 488–503 (1941).
  4. Although this assumption is not necessary, it will simplify the description of the optical system.
  5. H. J. Butterweck, "Reciprocity in optical data-processing systems," Arch. Elektr. Ubertr. 31, 335–347 (1977).
  6. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  7. If not specified, all integrations extend from - ∞ to + ∞.
  8. The Fourier transform of a function will be denoted by a capital letter.
  9. Previously (see Ref. 1) two different Fourier transforms are introduced. This notation, which leads to more symmetric expressions in the spatial frequency domain, is not used in the present paper.
  10. We used this definition of losslessness to show the resemblance between expression (13) and the corresponding expression in the scalar theory. However this definition holds only in the paraxial approximation, while for more general cases this definition should be replaced by an equation using the Poynting vector.
  11. An optical element is a simple optical system, e.g. a lens, a transparency, or a polarizer. A general optical system consists, then, of one or several optical elements, placed in cascade.
  12. p. Beckmann, The depolarisation of electromagnetic waves (Golem, Boulder, Colorado, 1968).
  13. McGraw-Hill Encyclopedia of science and technology.
  14. Although these elements are not necessarily isotropic, it can be proved (see Ref. 5) that Eq. (24) is still valid.
  15. A. S. Marathay, "Realization of complex spatial filters with polarized light," J. Opt. Soc. Am. 59, 748–752 (1969).
  16. S. R. Dashiell and A. W. Lohmann, "Image substraction by polarization- shifted periodic carrier," Opt. Commun. 8, 100–104 (1973).
  17. D. R. Rhodes, Synthesis of planar antenna sources (Clarendon, Oxford, 1974).

1977 (2)

H. J. Butterweck, "Reciprocity in optical data-processing systems," Arch. Elektr. Ubertr. 31, 335–347 (1977).

H. J. Butterweck, "A general theory of linear, coherent optical data-processing systems," J. Opt. Soc. Am. 67, 60–70 (1977).

1973 (1)

S. R. Dashiell and A. W. Lohmann, "Image substraction by polarization- shifted periodic carrier," Opt. Commun. 8, 100–104 (1973).

1969 (1)

1941 (1)

Beckmann, p.

p. Beckmann, The depolarisation of electromagnetic waves (Golem, Boulder, Colorado, 1968).

Butterweck, H. J.

H. J. Butterweck, "A general theory of linear, coherent optical data-processing systems," J. Opt. Soc. Am. 67, 60–70 (1977).

H. J. Butterweck, "Reciprocity in optical data-processing systems," Arch. Elektr. Ubertr. 31, 335–347 (1977).

Dashiell, S. R.

S. R. Dashiell and A. W. Lohmann, "Image substraction by polarization- shifted periodic carrier," Opt. Commun. 8, 100–104 (1973).

Goodman, J. W.

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

Jones, R. C.

Lohmann, A. W.

S. R. Dashiell and A. W. Lohmann, "Image substraction by polarization- shifted periodic carrier," Opt. Commun. 8, 100–104 (1973).

Marathay, A. S.

Rhodes, D. R.

D. R. Rhodes, Synthesis of planar antenna sources (Clarendon, Oxford, 1974).

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Arch. Elektr. Ubertr. (1)

H. J. Butterweck, "Reciprocity in optical data-processing systems," Arch. Elektr. Ubertr. 31, 335–347 (1977).

J. Opt. Soc. Am. (3)

Opt. Commun. (1)

S. R. Dashiell and A. W. Lohmann, "Image substraction by polarization- shifted periodic carrier," Opt. Commun. 8, 100–104 (1973).

Other (12)

D. R. Rhodes, Synthesis of planar antenna sources (Clarendon, Oxford, 1974).

Although this assumption is not necessary, it will simplify the description of the optical system.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

If not specified, all integrations extend from - ∞ to + ∞.

The Fourier transform of a function will be denoted by a capital letter.

Previously (see Ref. 1) two different Fourier transforms are introduced. This notation, which leads to more symmetric expressions in the spatial frequency domain, is not used in the present paper.

We used this definition of losslessness to show the resemblance between expression (13) and the corresponding expression in the scalar theory. However this definition holds only in the paraxial approximation, while for more general cases this definition should be replaced by an equation using the Poynting vector.

An optical element is a simple optical system, e.g. a lens, a transparency, or a polarizer. A general optical system consists, then, of one or several optical elements, placed in cascade.

p. Beckmann, The depolarisation of electromagnetic waves (Golem, Boulder, Colorado, 1968).

McGraw-Hill Encyclopedia of science and technology.

Although these elements are not necessarily isotropic, it can be proved (see Ref. 5) that Eq. (24) is still valid.

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

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