Encircled Energy Factor as a Point-Image Quality-Assessment Parameter

The most important corollary of the Point Spread Function ( ) PSF is the “Encircled Energy Factor” or the “Encircled Power”. It measures the fraction of the total energy in the PSF , which lies within a specified radius ‘δ ’ in the plane of observation or detection. It is one of the significant parameters which serve as an index of the performance of an optical system. The radial distribution of energy within the image, called the encircled power, is a classical measure of the quality of the optical system producing that particular image. We will designate this important parameter by the symbol EEF (δ ). EEF (δ ), obviously vanishes when δ is zero and approaches unity when δ becomes infinity. Lord Rayleigh (1). Was the first to point out the importance of the encircled energy factor to find the illuminations in the various rings of the diffraction pattern and presented a formula for calculating the same.