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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.
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Max Reiss (1948) studied this question.
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