Aberration-based design example for freeform optical designs with base off-axis conics

In this paper, we show, via a design example, how to leverage the parameters of a base off-axis conic to design freeform optical systems using the full-field display driven aberration-based design method discussed in [1]. Off-axis conic sections are often considered when designing unobscured or non-axisymmetric systems, including as base surfaces for freeform optics [2-8]. Likewise, design methods that use nodal aberration theory and full-field displays to gain insight into the aberrations of freeform systems have been demonstrated to be effective at generating starting points and performing designs (e.g., [1, 9-11]). However, in these aberration-based design methods, a central consideration is the correction of coma and astigmatism, which often involves the introduction of orthogonal polynomial astigmatism and coma terms (i.e.,, Z5/Z6 and Z7/Z8 for the Fringe Zernike polynomials). These terms are often major contributors to freeform departures, thus reducing or eliminating the need for orthogonal polynomial astigmatism and coma may improve interferometric testability estimates based on the magnitude of freeform departures. Consequently, in this paper, we leverage the parameters of base off-axis conics to follow the aberration-based design method without the use of additional orthogonal polynomial astigmatism and coma terms. While an off-axis conic is not exactly equivalent to a sphere plus astigmatism and coma, it is shown via a design example that re-designing with base off-axis conic parameters from the start can yield a new design that achieves equivalent optical performance without orthogonal polynomial astigmatism and coma. When these design methods are coupled with design methods aimed at reducing surface departures, significant improvements in interferometric testability estimates can be achieved, including when compared to fitting freeform surfaces designed with base spheres with the best-fit off-axis conic after optimization. For comparison, the design study in this paper is conducted twice: once using base off-axis conics with Fringe Zernike sag departure terms (excluding Zernike astigmatism and coma), and once using base spheres with Fringe Zernike sag departure terms (including Zernike astigmatism and coma).