Mathematical modeling of mirror collimator with impedance rolled edges

Compact range is a relatively small test stand, designed to generate a plane wave using a complicated reflecting system. Compact range consists of two main parts: an anechoic chamber and a collimator. The main role of the collimator consists in transforming a spherical wave from the radiation source into a plane one. With collimator one can perform experiments with plane wave diffraction on objects of the complicated shape indoor, inside the anechoic chamber. These experiments lack most of outdoor experiments' disadvantages, such as weather dependence and several systematic inaccuracies, and in the same time it reduces the experiments' costs. Mirror collimators are the most common ones; they have the shape of an asymmetrical cut of a parabolic surface with a radiation source situated in its focus. One of the most significant sources of measurement inaccuracy is the field diffraction on the edges of collimator. There are two main ways to reduce this negative effect. First of all, one can serrate the edge of collimator, to redirect the diffracted field out from quiet zone of the collimator. Another way of reducing the unwanted field irregularity consists in adding a rolled edge surface to a collimator to redirect the reflected field from the quiet zone [1]. In this work the problem of synthesis of an optimal shape for a mirror collimator with rolled edges is examined. As an example of a collimator an extended cylindrical mirror, which has a section, consisting of a parabolic segment, supplemented with two edge roundings and a round segment, closing the section in the shadow zone, is considered. To make even further improvement, one can cover the mirror's edges with a radioabsorbing material [2]. The scalar diffraction problem on a two-dimensional mirror is solved. As a functional of an inverse problem the net C-norm of the resulting field's deviation is used. The functional has several parameters, including geometrical values of the rolled edges as well as the properties of the radioabsorbing material and the parameters of covering. As a main method to solve the direct problem the integral equation technique is used. The equations obtained are solved with Krylov-Boglyubov's method, while the inverse problem functional is minimized with Nelder-Mead's method. Calculation results are presented.