High-precision analysis of aberration contribution of Zernike freeform surface terms for non-zero field of view.

Clarifying the aberrations arising from freeform surfaces is of great significance for maximizing the potential of freeform surfaces in the design of optical systems. However, the current precision in calculating aberration contribution of freeform surface terms for non-zero field of view is insufficient, impeding the development of freeform imaging systems with larger field of view. This paper proposes a high-precision analysis of aberration contribution of freeform surface terms based on nodal aberration theory, particularly for non-zero field points. Accurate calculation formulas of aberrations generated by Zernike terms on freeform surface are presented. Design examples illustrate that the calculation error of the provided formulas is 78% less than that of conventional theoretical values. Building upon high-precision analysis, we propose an optimization method for off-axis freeform surface systems and illustrate its effectiveness through the optimization of an off-axis three-mirror system. This research extends the applicability of nodal aberration theory in aberration analysis, offering valuable insights for the optimal design and alignment of optical freeform systems.