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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 38, Iss. 11 — Nov. 1, 1948
  • pp: 980–986

Notes on the Cos4 Law of Illumination

MAX REISS  »View Author Affiliations

JOSA, Vol. 38, Issue 11, pp. 980-986 (1948)

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The formulae for the distribution of illumination in the focal plane of a lens system without and with distortion are derived. These formulae are applied to some extreme wide-angle lenses, and a numerical example is included. Special attention is given to the distortion of the pupils and the importance of stop position for illumination. The formula for the illumination distribution in a monocentric system is derived.

MAX REISS, "Notes on the Cos4 Law of Illumination," J. Opt. Soc. Am. 38, 980-986 (1948)

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  1. G. Slussareff, J. Phys. U.S.S.R. 4, 537 (1941).
  2. M. Reiss, J. Opt. Soc. Am. 35, 283 (1945).
  3. I. C. Gardner, J. Research Nat. Bur. Stand. 39, 213 (1947).
  4. I. C. Gardner and F. E. Washer, J. Opt. Soc. Am. 38, 421 (1948), published while this paper was in print.
  5. W. N. Bond, Phil. Mag. 44, 999 (1922).
  6. 5 R. Hill, "A lens for whole sky photography," Proc. Opt. Conv. 2, 878 (1926).
  7. The entrance pupil of the axial beam is 0.302752 (distortion of the entrance pupil of the oblique beam).
  8. We should strictly use the formula E=(B/e′2)∫dS′ •cos1ω′, but as Gardner as shown (see reference 3) this makes little difference for small apertures.
  9. Obviously the Gauss points coincide with the center C and the distance A C=ƒ.

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