Surface finish requirements for soft x-ray mirrors.

We have examined the correlations between direct surface-finish metrology techniques and normalincidence, soft x-ray reflectance measurements of highly polished x-ray multilayer mirrors. We find that, to maintain high reflectance, the rms surface roughness of these mirrors must be less than ~ 1 Å over the range of spatial frequencies extending approximately from 1 to 100 µm(-1)1 (i.e., spatial wavelengths from 1 µm to 10 nm). This range of spatial frequencies is accessible directly only through scanning-probe metrology. Because the surface-finish Fourier spectrum of such highly polished mirrors is described approximately by an inverse power law (unlike a conventional surface), bandwidth-limited rms roughness values measured with instruments that are sensitive to only lower spatial frequencies (i.e., optical or stylus profileres) are generally uncorrelated with the soft x-ray reflectance and can lead to erroneous conclusions regarding the expected performance of substrates for x-ray mirrors.