Calculation of point-spread function for optical systems with finite value of numerical aperture

The scalar theory is described for calculation of the point-spread function (PSF) of optical systems with a large numerical aperture. In our work, we introduced an analytic description of this phenomenon and we derived exact and simple approximate relations that enable to calculate the PSF for a diffraction-limited optical system with a finite value of numerical aperture. The derived relations convert to classical relations that are commonly described in literature for the case that the value of numerical aperture tends to zero. Our derived relation is a generalization of the classical relation for calculation of PSF in the case of a large numerical aperture.