General equations for combining obliquely crossed spherocylinders

Abstract

Faria e Sousa’s equations (1995) for solving a pair of crossed spherocylindrical lenses are certainly a very useful tool for solving crossed spherocylinders. Those equations have already been derived by us and are in our forthcoming book entitled The Eye and Visual Optical Instruments, which is currently in the production stages at Cambridge University Press. We derived the equations by a slightly different and more rigorous method. Faria e Sousa makes the assumption in his equation (1) that the sum of two crossed spherocylindrical lenses is also a spherocylinder. If one is rigorous, this assumption needs to be verified. Our derivation does so and is as follows.