Nonparaxial Diffraction of the Cartesian Oval

We study the nonparaxial diffraction of the well-known Cartesian oval in finite and infinite conjugate configurations. We started by expressing the refraction of the Cartesian oval by analytical closed-form equations. These equations are convenient to obtain the pupil apodization function of the Cartesian oval, which is needed to compute the diffraction pattern using Richard-Wolf theory. A comparison of the diffraction patterns of the Cartesian oval with finite/infinite objects, the aplanatic lens, and the parabolic mirror for radially polarized illumination is presented. From this comparison, we conclude that a Cartesian oval for a far object is not a good candidate for tight focusing and super-resolution applications and the performance of a Cartesian oval in a finite conjugate configuration is similar to the performance of an aplanatic lens and in some scenarios, it can perform better than the aplanatic lens. (c) 2022 Society of Photo-Optical Instrumentation Engineers (SPIE)