Calculation and research of point spread function of apodized optical system in order to compensate for defocusing

It is known that image quality deteriorates noticeably when defocusing or shifting the detection device from the plane of sharpness. One way to increase the depth of focus of the optical system and reduce the negative consequences of blurring defocused images is to phase apodize the system, for example, with a cubic phase function. However, apodization is accompanied not only by positive effects (increasing the depth of focus), but also by a significant change in the structure of the point scattering function and the growth of side lobes. Digital post-processing can be applied to eliminate the negative effect, but at the same time it is desirable to perform some optimization of the apodizing function, compromising between increasing the depth of focus and distortion of the point scattering function. In this paper, we performed a calculation and comparative study of the properties of the point spread function during apodization of the optical system by a phase power function of various powers (from the third to the fifth). The research results showed that the depth of focus increases by several tens of times compared with the unapodized lens. The distortion of the point spread function, which occurs in this case, can be reduced by increasing the degree of the apodizing function. Since an increase in the depth of focus and a decrease in the size of the light spot are competing criteria, a compromise is possible with a solution.