Apodization theory is concerned with the determination of the distribution of light over the exit pupil of an optical system required in order to achieve a suppression of the side lobes of the diffraction pattern. Here analytic solutions are given to the problem of determining the distribution of light in the exit pupil to concentrate maximally the illuminance in a geometrically similar region of the image plane. Both slit and circular apertures are treated.
DAVID SLEPIAN, "Analytic Solution of Two Apodization Problems," J. Opt. Soc. Am. 55, 1110-1114 (1965)