ASYMPTOTIC-BEHAVIOR OF DIFFRACTION IMAGES

It is shown that the derivative of the real part of the optical transfer function of an incoherent imaging system with respect to the radial or rectangular spatial frequency evaluated at the origin is independent of the aberrations of the system, irrespective of the shape of its pupil. Simple derivations are given to show as a consequence that, up to first order, the asymptotic behavior of the point-spread function for rotationally symmetric pupil functions, and encircled energy for rotationally symmetric pupils, are independent of the aberrations. These results are applied to the case of obscured circular pupils and the expressions obtained are shown to be in agreement with those obtained directly from the diffraction-limited point-spread function. Similar results are obtained on the asymptotic behavior of image energy in the case of rectangular pupils.