The algorithm for solving the problem of local surface shape errors correction by small-size ion beam is proposed in the paper. The algorithm involves a sequential search of heights relative to the average value with the aim to find the most optimal etching point that satisfies the criterion - reducing the sum of the modules of the derivatives on the etching spot. It is shown that the new approach makes it possible to significantly expand the range of spatial frequencies that can be influenced at a given size of the ion beam.

We studied the use of morphometric variables (maximal curvature, minimal curvature, mean curvature, topographic index, etc.) for study of the surface of X-ray optical elements. We performed calculations on digital elevation models of a spherical concave substrates: primordial and smoothed digital elevation models, before and after technological operations (mechanical lapping, axisymmetric surface shape correction, ion beam figuring). We have demonstrated a visual display of weakly expressed topography inhomogeneities, incl. which are not displayed on the maps of the original digital elevation models. The consideration included the study of both the measured samples and the errors in the formation of the digital elevation model (artifacts from the recording system and from the inhomogeneity of the medium), as well as the features of scale decomposition when using the universal spectral-analytical method.