Paraxial imaging and walk-off effects with birefringent media in refracting surfaces, lenses, and slabs

The paraxial theory of spherical refracting surfaces, spherical lenses, and slabs with one birefringent medium is investigated analytically: using walk-off effects in the paraxial domain, a number of relations between objects and images are deduced, along with cardinal elements, in the case where the optic axis is parallel to the optical axis. This method naturally shows that in some cases first-order astigmatism appears. An argument based on the wavefront (and phase) transformation shows that any spherical birefringent thin lens is stigmatic in the paraxial domain, because the first-order astigmatisms due to the two surfaces of such a lens compensate each other. This is a priori not the case with thick birefringent lenses -- but two such cases are detailed.