Point spread function of an optical system with defocus and spherical aberration—analytical formulas

This work describes a procedure for an analytical calculation of the point spread function (PSF) of an optical system affected by defocus and spherical aberration. Explicit formulas are derived for the approximate calculation of the PSF of an optical system with spherical aberration up to the ninth order. Application of the derived formulas is performed on an example of optical systems with spherical aberration up to the third order.