Encircled energy calculations show the effects of focus errors, spherical aberration, and a central stop on image contrast. The complementary quantity (excluded energy) gives the illumination at the center of a dark spot on an incoherent background and is useful in some photometric situations. A simple formula is given for the approximate calculation of the excluded energy at large distances from the center of the diffraction pattern.
A. T. Young, "Photometric Error Analysis, X: Enriched Energy (Total Illuminance) Calculations for Annular Apertures," Appl. Opt. 9, 1874-1878 (1970)