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)