Source-function synthesis in the self-consistent problem of radiation

A new approach to a rigorous theory of aperture antennas is proposed, which is based on solution of the self-consistent problem of radiation. It is ascertained that this formulation of the problem leads to a system of homogeneous Fredholm integral equations of the second kind—i.e., a problem for eigenfunctions and eigenvalues that provides a basis for solving the problem of field generation in the open space. The passage to Fredholm integral equations of the first kind allows one to solve the task of synthesis of the source function for a given radiation field.