Formation of the optical signal matched with spheroidal functions to transfer in lens system without distortions

Prolate angular spheroidal functions of zero order and their properties are considered. The calculation of spheroidal functions produced for different parameters. One-dimensional Gaussian beam decomposition into spheroidal functions is performed which allowed evaluate the distortion of the optical signal passing through the lens system. We demonstrate the possibility of the formation of the optical signal transmitted through a lens system without distortion when it is a superposition of spheroidal functions consistent with the parameters of the optical system.