Transfer function characterization of grazing incidence optical systems.

By using Fourier techniques and linear systems theory we have derived an analytic expression for a generalized transfer function for grazing incidence optical systems operating at ultraviolet and x-ray wavelengths that includes the effects of optical fabrication errors over the entire range of relevant spatial frequencies. The Fourier transform of this transfer function yields the image distribution (or point spread function) from which encircled energy characteristics or other image quality criteria can be obtained. This transfer function characterization of grazing incidence optical systems allows parametric trade studies and sensitivity analyses to be performed as well as the derivation of fabrication tolerances necessary to satisfy a given image quality requirement.