Orthogonal polynomials describing polarization aberration for rotationally symmetric optical systems

Optical lithography has approached a regime of high numerical aperture and wide field, where the impact of polarization aberration on imaging quality turns to be serious. Most of the existing studies focused on the distribution rule of polarization aberration on the pupil, and little attention had been paid to the field. In this paper, a new orthonormal set of polynomials is established to describe the polarization aberration of rotationally symmetric optical systems. The polynomials can simultaneously reveal the distribution rules of polarization aberration on the exit pupil and the field. Two examples are given to verify the polynomials.