Field aberrations in terms of the Q-polynomial basis and its relationship to the Zernike basis

Abstract

The aberrations generated at the image plane of an optical system that includes freeform surfaces described through Q-polynomials can be calculated using nodal aberration theory. By analyzing the definition of each Q-polynomial, they can be compared with Zernike polynomials allowing a relationship between the two bases. This relationship is neither simple nor direct, so a fitting must be made. Once established, the contribution to the aberration field map generated by each surface described through the Q-polynomial can be calculated for any surface that is not at the stop of the system. The Q-polynomials are characterized by their orthogonality in the gradient instead of the surface, which represents an opportunity to restrict the changes in the slope in a simple way and facilitate the manufacturing process. The knowledge of the field aberrations generated by each Q-polynomial allows selecting that which of them are necessary to be introduced as variables in the optimization process for an efficient optimization.