Scalar analytical expressions for the field dependence of Zernike polynomials in asymmetric optical systems with circular symmetric surfaces

In this paper we derive scalar analytical expressions describing the full field dependence of Zernike polynomials in optical systems without symmetries. We consider the general case of optical systems constituted by arbitrarily tilted and decentered circular symmetric surfaces. The resulting analytical formulae are inferred from a modified version of the full field dependent wavefront aberration function proposed in the Nodal Aberration Theory (NAT). Such formula is modified with the scope of solving few critical points arising when primary and higher order aberrations are both present in an optical system. It is shown that when secondary aberrations are taken into account in the wavefront aberration function, the final effect is a perturbation to the symmetry of the field dependence of the Zernike polynomials. In particular, the centers of symmetry of the Zernike polynomial field dependences are shifted with respect to the locations predicted using the NAT equations as a consequence of the presence of higher order aberrations. The retrieved analytical expressions are verified through surface fitting to real ray-trace data obtained for a simple optical system. (c) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement