Generalized ABCD matrix of thin pure-phase transmittances: Application to thick spherically-aberrated lenses

Abstract

The behaviour of thin pure phase transmittances is represented by means of a generalized matrix, M, which can be handled as the ABCD-matrices associated with ordinary first-order optical systems. This formalism enables the application of generalized ABCD propagation formulae to cascaded optical systems containing pure phase transmittances. Matrix M is applied to thin and thick spherically aberrated lenses. In addition, the beam quality parameter of an incident Gaussian beam at the output plane of such lenses is investigated.