Encircled energy factor in impulse response functions of optical systems with first-order parabolic filters

The encircled energy EEF ( δ ) measures the fraction of the total energy contained within a circle of specified radius ‘δ ’ in the image plane, centered on the diffraction head. This is one of the important parameters in the study of a diffraction image. LORD RAYLEIGH [1] first pointed out the importance of the studies on the encircled energy in the diffraction pattern as an image quality assessment parameter. Although the encircled energy is a good test for the quality of an optical system, it has not been used much in the early years, because, of the difficulties in its calculations. To overcome this difficulty, LANSRAUX and BOIVIN [2] introduced computing techniques for the numerical evaluation of the encircled energy in the diffraction pattern of an optical system having aberrations. The image structure of selfluminous or incoherently illuminated objects, formed by optical instruments like astronomical telescopes and cameras used in aerial photography is determined by the diffraction studies. The Fractional Encircled Energy gives an idea of the effective spread of the diffraction pattern. This spread will determine the resolution as in the astronomical imagery like imaging of distant point objects through a random stationary atmosphere. In what follows now, we will present a brief review of the previous works done on the EEF by various authors.