Calculation of eigenfunctions for imaging two-lens system with axial symmetry

Eigenfunctions of the optical operator describing limited imaging system with two lenses are considered under axial symmetry. Resulting functions are analogous to the generalized spheroidal functions which are eigenfunctions of the zero-order Hankel transformation. The expression for eigenfunctions' calculation is obtained using operator representation of the optical system.
The influence of the spectrum width on the number of significant eigenvalues is investigated. Decomposition of circular, annular, and Gaussian beam by eigenfunctions is calculated and deviation from the original signals is estimated.