Matrix methods for the evaluation of lens systems with radial gradient-index elements

Matrix methods have been used to examine the paraxial performance of homogeneous systems. This method has been extended to include the presence of gradient lens elements in the optical array. To accomplish this, an inhomogeneous rotation-translation matrix is developed to describe the path of a ray through the lens elements with quadratic radial index gradients. The system matrix elements are then used to predict the paraxial properties of the array. Three examples are examined: the Wood lens, two thin lenses coupled to a radial gradient index rod, and a model of the human eye which contains a radial gradient index crystalline lens.