Encircled energy can be easily estimated for imaging systems with oddly shaped apertures using a simple asymptotic approximation formula. A useful tool for the optical system designer, it linearly relates the encircled energy to the perimeter-to-area ratio of the aperture. Comparisons made with numerical calculations show that it is usefully accurate for circles in the focal plane as small in radius as λƒ#.
© 1984 Optical Society of America
Peter P. Clark, James W. Howard, and Edward R. Freniere, "Asymptotic approximation to the encircled energy function for arbitrary aperture shapes," Appl. Opt. 23, 353-357 (1984)