Investigation of an analytic aberration description for Alvarez-Lohmann type phase plates

Alvarez Lohmann lenses consist of two equal phase plates with cubic profile which are aligned, that their combined phase functions generate an offset like a parallel plate. By a displacement of the plates the combined phase function becomes proportional to the first derivative of the single elements profile. Alvarez and Lohmann independently used this thin element model to describe varifocal lenses. This principle can be applied to generate a variety of different functionalities. In realistic systems with finite distances and thicknesses those elements are prone to aberrations. Because of their free-form character aberrations are induced which cannot be distinguished into field and pupil aberrations in the same way as in classical optics. In 1999 Palusinski proposed an analytical method to investigate aberrations in such systems. From the slope of the element surfaces and distance between two phase plates the intersection points of the wave front with the second element are calculated for the whole wave front at once. We apply this method to Alvarez Lohmann lenses and similar phase plate pairs. The results are compared to ray tracing and common wave front propagation simulations.