X-ray study of concave surface roughness

We propose to extend x-ray scattering method to the investigation of concave surface roughness. Our approach is based on the use of the whispering gallery effect, which consists in that an x-ray beam falling tangentially on to a concave surface slides along a surface due to successive total external reflections. During its propagation the beam gradually broadens because the scattering transfers some part of radiation to the range of larger glancing angles. Fitting of a simulated angular distribution of outgoing beam to a measure done enables the determination of statistical parameters of concave surface roughness. Possible experimental schemes are analyzed by using ray-tracing technique, radiation scattering by surface roughness being modeled by the Monte Carlo method. Results of experiments in x-ray spectral region are discussed. Carbon-coated cylindrical surfaces with the radius of curvature of 6 cm and the arc angle of 45 and 60 degrees are studied with soft x-rays. The measured angular distributions of outgoing radiation are shown to agree quantitatively with the theoretical calculations when the scattering of x-rays by the surface roughness are taken into account. The rms roughness and the correlation length of the studied surface are found to be about 1.2 nm and 0.3 micrometers , respectively. The possibility of the study of concave surface roughness with the use of hard x-rays is also discussed.