Nodal aberration properties of coaxial imaging systems using Zernike polynomial surfaces

As a combination of the nodal aberration theory (NAT) and the freeform surface optical design, the nodal aberration properties of Zernike polynomial surfaces in a coaxial imaging system are analyzed in detail in this paper. The aberrations induced by the Zernike polynomial terms on either the reflective or the refractive surfaces in the system can be quantitatively calculated, which can be used to predict the surface figure or mount-induced errors, or as guidance for aberration correction and optimization during the freeform optical design. Specially, some new kinds of aberrations with complex field dependence can be generated by the Zernike polynomial terms, which further lead to the discovery of linear or multilinear nodes (cruciate nodes) in the aberration field. This linear nodal property will benefit the design of some kinds of freeform optical systems with a linear field of view. Furthermore, an iterative method based on the NAT is proposed to correct the field-constant aberrations.