Wave problems in acoustics and optics, although having different physical nature, are nevertheless described by practically identical governing equations. For this reason, the methods of solution in these two fields were developed in parallel and with close interconnection. In this paper, the problem of scattering of an incident wave by a relief boundary surface of periodic geometry is investigated. For simplicity, a scalar wave equation from linear acoustics is used, but it is considered in the frequency range more typical for optics problems, when the wavelength is one or two orders of magnitude smaller than the characteristic size of relief grains, i.e. in the short-wave range. The problem is of great practical importance, since the methods of irradiating surfaces with beams of light waves (including lasers) effectively work for non-destructive quality control of surfaces of products made of metals, composites, polymers and other materials. The problem in the harmonic time mode and in the two-dimensional approximation is reduced to a boundary integral equation, which after discretization is reduced to a system of linear algebraic equations. A number of examples of scattering by two types of boundary contours, with three different values of the amplitude of the elevation of relief grains, are considered. Important theoretical and practical conclusions are made based on the calculation results.
Sumbatyan et al. (Tue,) studied this question.