A semi-analytic approach to calculating the Strehl ratio for a circularly symmetric system. Part 1: static wavefront

Close-form expression for the Strehl ratio calculated in the spatial frequency domain of the optical transfer function (SOTF) is considered for the case of an optical system that has circular symmetry. First, it is proved that the SOTF for the aberration-free diffraction limited optical system is equal to one. Further, a semi-analytic solution for the SOTF for a system described by the second (defocus) and the fourth (spherical) order aberrations is provided. It is shown that the proposed semi-analytical solution is of an order of a magnitude computationally more efficient than the commonly used approach based on the discrete Fourier transformation