Estimating field-dependent nodal aberration theory coefficients from Zernike full-field displays by utilizing eighth-order astigmatism

When using freeform surfaces in optical design, the field dependence of the aberrations can become quite complex, and understanding these aberrations facilitates the design process. Here we calculate the field dependence of low-order Zernike astigmatism (Z5/6) up to the eighth order in nodal aberration theory (NAT). Expansion of NAT astigmatism terms to the eighth order facilitates a more accurate fit to the Zernike astigmatism data. We then show how this estimated field dependence can be used to quantitatively analyze a freeform telescope design. This analysis tool adds to the optical designer's arsenal when up against the challenge of designing with freeform optics.