The Relationship of Point Spread Functions of Aberration and Diffraction Limited Lens of Matrix Imagers

Abstract

Background. Thermal imagers are widely used in many areas, but the priority is to use them for military purposes where the primary goal is focused on the identification and recognition of objects in difficult weather conditions. The quality of thermal imaging is estimated by the modulation transfer function (MTF), which is obtained by Fourier transform of the point spread function (PSF). Objective. The aim of the paper is to get the ratio, which would have established a relationship between the PSF aberration and diffraction limited lens matrix imagers.Methods. An approximation of the PSF in the form of a Gaussian function was proposed to consider as PSF limited lens aberration. Results. Based on the analysis of functions of energy concentration, the relationship between the PSF for the aberration and diffraction limited lens was established. The formula, which summarizes all the formulas with correspondingly different conditionally selected levels, which determine the radius of the circle scattering PSF aberration of an optical system (AOS) was obtained. Conclusions. Analysis of the resulting relationship for PSF aberration and diffraction-limited lens showed that produced by PSF luminance highs differ in 2 times, on condition that the radius of the circle scattering AOS is minimum. The formula for calculating the minimum radius of the circle of confusion, in which AOS is considered diffraction limited, is obtained.