Vector diffraction of aspherical wavefronts with azimuthal polarization in microscope objectives

The Richards-Wolf integral models electromagnetic fields in high-NA optical systems like microscopes, capturing polarization effects of azimuthally polarized beams, but is limited to spherical wavefronts, failing to account for aberrations or aspherical surfaces. A novel, to our knowledge, generalized diffraction integral [Appl. Opt.64, 6036 (2025)10.1364/AO.568541] extends this framework to handle freeform vectorial fields and aberrations, reducing to the classical form for spherical cases. We apply this method to compute the point spread function (PSF) of microscopes with aspherical wavefronts and azimuthal polarization, analyzing aberration impacts. Our results show improved PSF accuracy, enhancing super-resolution imaging and optical trapping and thus advancing polarization-sensitive microscopy design.