An analytic expression for the field dependence of Zernike polynomials in rotationally symmetric optical systems

Abstract

Zernike polynomials have emerged as the preferred method of characterizing as-fabricated optical surfaces with circular apertures. Over time, they have come to be used as a sparsely sampled in field representation of the state of alignment of assembled optical systems both during and at the conclusion of the alignment process using interferometry. We show that the field dependence of the Zernike polynomial coefficients, which has to-date been characterized essentially by aperture dependence, can be introduced by association to the field dependent wave aberration function of H.H. Hopkins.