Effects of surface scatter on the optical performance of x-ray synchrotron beam-line mirrors

The increased availability of advanced synchrotron radiation sources is resulting in a resurgence of activity in the field of x-ray and extreme ultraviolet imaging systems. However, scattering effects caused by residual optical fabrication errors frequently dominate geometrical design errors in the degradation of image quality at these very short wavelengths. Traditional optical design and analysis techniques (geometrical ray tracing) are therefore inadequate for predicting the performance of high-resolution synchrotron beam-line optics. A surface-scattering theory must be implemented to model the image degradation effects of residual surface irregularities over the entire range of relevant spatial frequencies. This includes small-angle scattering effects caused by mid-spatial-frequency surface errors that fall between the traditional figure and finish specifications. Performance predictions are presented parametrically to provide insight into the optical fabrication tolerances necessary to meet the requireme nts of a specific application.