2. Reducing Inverse Problem of the Short-Wave Diffraction to Minkowski Problem

As follows from Eq. (6.120), the far›eld scattered amplitude in a direct diffraction problem for convex obstacles is expressed in terms of the Gaussian curvature. Therefore, in practical (inverse) reconstruction problems, when the scattered amplitude is usually known for a set of observation angles being received in a far zone, we arrive at the inverse problem which coincides with the classical Minkowski problem well known in differential geometry (see, for example, Blaschke, 1930; Pogorelov, 1973, 1978). This problem can be formulated in the following way.