Line Spread Function and Cumulative Line Spread Function for Systems with Rotational Symmetry

The line spread function and the cumulative line spread function for a circular aperture having rotationally symmetric aberrations are determined by integrals involving the transfer function of the system. Asymptotic expansions of the line spread function and the cumulative line spread function are obtained from a knowledge of the transfer function and its derivatives evaluated at zero spatial frequency. The moments of the transfer function determine the behavior of the line spread function and the cumulative line spread function for small values of the argument. Typical numerical results are also presented.