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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 57, Iss. 5 — May. 1, 1967
  • pp: 630–638

Hamilton’s Mixed and Angle Characteristic Functions and Diffraction Aberration Theory

ARTHUR B. SHAFER  »View Author Affiliations


JOSA, Vol. 57, Issue 5, pp. 630-638 (1967)
http://dx.doi.org/10.1364/JOSA.57.000630


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Abstract

The use of Hamilton’s mixed and angle characteristic functions in wave and diffraction aberration calculations is theoretically examined. The relation of Hamilton's mixed and angle characteristic functions to a new wave-aberration function is shown. This aberration function is to be used in the Luneburg-Debye diffraction integrals. The mixed and angle characteristic functions as utilized in diffraction theory via the Luneburg-Debye integrals are examined. The mathematical and physical approximations are discussed. The use of the Luneburg-Debye diffraction integrals for image evaluation is examined and some difficulties are pointed out. It is concluded that the above methods should not be used for microwave and radio-frequency imaging systems; they are of limited validity for optical imaging systems.

Citation
ARTHUR B. SHAFER, "Hamilton’s Mixed and Angle Characteristic Functions and Diffraction Aberration Theory," J. Opt. Soc. Am. 57, 630-638 (1967)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-57-5-630

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