V.V. Akhiyarov

The analytical solution for the diffraction problem on thin perfectly conducted disk in oblate spheroidal coordinate system is considered. In this case the scalar Helmholtz equation is separable and its solution is determined by the oblate angular and radial spheroidal functions, which depends only on one coordinate. The main difficulty in spheroidal functions calculating is to define separation constants and expantion coefficients. As a rule, in order to solve this problem the theory of continued fractions is applied, which limits the range of calculations. However, currently there are methods for high-precision determination of spheroidal functions based on the representation of the separation constants and expantion coefficients as eigenvalues and eigenvectors of some tree-diagonal matrix. Then the problem of determining the expansion coefficients can be solved very simply, since the calculation of eigenvalues and eigenvectors is a standard mathematical procedure. The considered algorithm for calculating the angular and radial oblate spheroidal functions allows to solve the scattering problem of a plane electromagnetic wave on the thin disk. In this work all necessary formulas for far field scattering calculation are presented. Using these formulas radar cross section diagrams for the backscattering and bistatic scattering were obtained.