Point spread function of linear polarized aspherical vector fields in high-NA optical systems

The Richards–Wolf diffraction integrals (1959) are fundamental for computing vectorial point spread function (PSF) in aberration-free high-NA microscopes with spherical wavefronts. However, their inherent limitation to perfect sphericity restricts the accurate modelling of real, aberrated systems. This paper utilizes a generalized diffraction integral to extend vectorial diffraction theory to aspherical wavefronts, arbitrary pupils and complex aberrations. We compute PSFs for aspherical wavefronts under linear polarization within microscopic systems. Numerical simulations reveal asymmetric focal distributions, reduced resolution and polarization effects due to aberrations.