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An algorithm for solving the problem of local shape errors of optical surfaces correcting by a small-sized ion beam, based on the matrix representation is presented. The algorithm involves searching for points that rise relative to the average height on the surface, where exposure to an ion beam of a given shape will lead to a decrease in the RMS deviation of the surface shape from the calculated one. It is shown that the new approach makes it possible to significantly expand the range of spatial frequencies, in which the height of relief can be reduced using the given ion beam size, and provides better results than the method of minimizing the functional of convolution of the ion beam and the surface map. Moreover, the new approach does not lead to appearance of shape errors (concentric structure) defined by the ion beam size and scanning step. An experiment for minimizing of local surface shape errors based on an etching map calculated using new approach was done. Matrix algorithm allowed in one procedure to reduce surface shape errors for a concave spherical optical element made of fused silica with a diameter D = 100 mm and a radius of curvature R = −137.5 mm in the RMS by more than 3 times. The initial RMS was 4.5 nm, RMS after treatment is 1.36 nm. • Dwell time calculation for deterministic machining of X-ray mirror substrates is presented. • The main equations of new algorithm are given and described. • The inapplicability of the exact calculation method is discussed. • Experimental results of applying the described algorithm are presented. [ABSTRACT FROM AUTHOR]

Retroreflective films are often used to enhance ultrasonic motion sensing with laser Doppler vibrometry by increasing surface reflectivity of metallic and polymer structures. This study reveals that such a surface modification leads to undesirable effects, which manifest themselves in notable changes of observed structural elastodynamic properties. The provided analysis shows systematic changes in dispersion curves of fundamental and high order guided waves propagating in laminates and significant amplification of their attenuation. Therefore, to avoid mistakes and additional errors when interpreting results of such measurements, e.g., in application to ultrasonic material characterization, the presence of reflective films should be considered and properly quantified. • Glueing of retroreflective films on laminate surfaces modifies its dispersion characteristics. • The changes are frequency-dependent and become more significant with the increase of frequency. • The presence of reflective films should be considered and properly quantified during analysis. • Some examples of undesirable effects with notable changes of elastodynamic properties are shown. [ABSTRACT FROM AUTHOR]