The Effect of a Parabolic Apodizer on Improving the Imaging of Optical Systems with Coma and Astigmatism Aberrations

We present the results of improving resolution in the imaging of two closely spaced point sources with an optical system under the influence of apodization and different types of aberrations. In particular, we consider the effect of coma and astigmatism, which are well-known aberrations that can deteriorate the resolution of an optical imaging system. Furthermore, a parabolic apodizer was included in an optical system to improve its imaging capabilities. We found that the two-point imaging performance of an optical system with a parabolic apodizer strongly depends on the coherence conditions of incident light. Furthermore, to analyze the efficiency of the parabolic apodizer, we compared the results of two-point imaging obtained with apodized and unapodized optical systems for distances between the two-point sources, less than or equal to the diffraction limit of an optical system. Moreover, the results of imaging the USAF chart with a parabolic apodizer are presented to show the apodizer's efficacy in single-object imaging. Our results can be applied to the imaging of closely moving structures in microscopy, resolving dense spectral lines in spectroscopy experiments, and developing systems useful for resolving the images of closely associated far-distance objects in astronomical observations.