Asymptotic approximation to the encircled energy function for arbitrary aperture shapes

Abstract

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 λf #.