The Effects Of Surface Quality Upon The Performance Of Normal Incidence X-Ray/XUV Imaging Systems

Abstract

For metal-coated mirrors, the Fresnel reflection coefficient becomes significant at X-ray and XUV wavelengths only when the angle of incidence approaches ninety degrees. Hence, grazing incidence mirrors have traditionally been utilized in order to obtain adequate reflectance for X-ray and XUV imaging applications. Although very large optical surfaces are required to achieve modest collecting areas, one benefit of grazing incidence mirrors is that the image degradation effects of optical surface irregularities diminish as the cosine of the incident angle. Recent advances in multilayer optical coating technology have made the use of normal incidence X-ray/XUV mirrors feasible from a sensitivity or total reflectance standpoint for many applications of interest; however, the effects of optical fabrication errors upon image quality is not as well understood. By applying Fourier techniques and linear systems theory, we have derived an analytic expression for a generalized surface transfer function 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 (PSF) from which encircled energy characteristics or other image quality criteria can be predicted. This transfer function characterization allows parametric studies and sensitivity analyses to be performed which provide insight into the relative importance of surface irregularities in the various spatial frequency domains as a function of wavelength for both normal and grazing incidence configurations.