Specification of surface figure and finish in terms of system performance

We describe methods of predicting the degradation of the performance of a simple imaging system in terms of the statistics of the shape errors of the focusing element and, conversely, of specifying those statistics in terms of requirements on image quality. Results are illustrated for normal-incidence, x-ray mirrors with figure errors plus conventional and/or fractal finish errors. It is emphasized that the imaging properties of a surface with fractal errors are well behaved even though fractal-power spectra diverge at low spatial frequencies.