Starting point designs for freeform four-mirror systems

Abstract

Driven by the development of freeform four-mirror solutions, we review and compare analytical meth- ods to generate starting point designs with various states of correction, surface types, symmetry, and obscura- tion. The advantages and disadvantages of each are examined. We have combined several concepts and techniques from the literature to analytically generate unobscured freeform starting point designs that are corrected through the third-order image degrading aberrations. The surfaces in these starting point designs are described as base off-axis conics that image stigmatically for the central field point, also known as Cartesian reflectors, with an aspheric departure “cap” (quartic with the aperture) added to the Cartesian reflec- tors. Tilt angles are chosen to cancel field-asymmetric field-linear astigmatism and unobscure the system. Paraxial data from an equivalent on-axis system are used to solve a system of linear equations to determine the magnitude of the aspheric departure “caps” that are placed on top of the base Cartesian reflectors, in order to eliminate the remaining third-order image degrading aberrations. In this approach, each aspheric departure “cap” is centered about the intersection of the optical-axis-ray, also known as the base ray, with the base surface, rather than being centered about the axis of rotational invariance.