Modified Zernike Polynomials and Their Application to the Analysis of Fresnel Region Fields of Circular Apertures with Nonuniform and Nonsymmetric Illumination*

Modified Zernike polynomials and also a set of generalized functions Wmν(γ,u) are introduced. These polynomials and functions are then applied to the analysis of the Fresnel region field of circular apertures with nonuniform and nonsymmetric illumination. With m=0, the general result obtained in this paper reduces to the case of nonuniform but circular symmetric illumination obtained by the author in a previous paper. A general expression for the far field (Fraunhofer field) of circular apertures with general illumination is also derived. Finally, a simple example is given as an illustration.