Ray Transfer Matrix for Onion-Type GRIN Lenses

Abstract

We present the computation of an ABCD matrix for onion-type GRIN lenses. By applying a differential approximation of the layer thickness, the matrix product of a high number of matrices is synthetized into a single matrix where the elements are integrals. The difference between this ABCD matrix and a homogeneous lens matrix is one integration term in element C, which is the GRIN contribution to the lens power. In the case of the crystalline lens, the analytical approximation to the GRIN lens power provides an accurate and concise solution in terms of Gaussian hypergeometric functions.