Calculation of Encircled Energy as Optical Quality Assessment Parameter for Image System

Abstract

Abstract In this paper a theoretical investigation of the Encircled Energy of an annular pupil (with different obscuration ratio ε = 0.25, 0.5, 0.75) for diffraction limited and defocus (optical system suffers from focal shift) optical system. The numerical evaluation was carried out using pupil function technique in Cartesian coordinates which has the advantage of introducing any kind and amount of aberration in the optical system. Another quality criterion for measuring the efficiency of optical systems is the Gradient determination. The maximum gradient value is near the center of the Encircled Energy curve in the image plane and will be decreases when the wave front aberration increases in the image plane. The presented results shows beater information when the optical system has a large amount of focal shift, and shows a clear reduction in the Encircled Energy values with increasing obscuration ratio This indicates that the central spot in the central ring group contains only a fraction of the total energy, so the whole set of central rings considered as the Effective Image Element.