The functional relationship between the total illuminance and transfer function is obtained for systems having rotationally symmetric aberrations. It is shown that the behavior of the transfer function at zero spatial frequency determines the asymptotic behavior of the total illuminance. In addition, the moments of the transfer function determine the behavior of the total illuminance in the vicinity of the origin. Typical numerical results are presented.
RICHARD BARAKAT and AGNES HOUSTON, "Reciprocity Relations between the Transfer Function and Total Illuminance. I," J. Opt. Soc. Am. 53, 1244-1247 (1963)