In a previous survey, closed-form analytical solutions for four-spherical-mirror anastigmats were developed and used to map the solution space for such systems. In all cases, the systems investigated had objects at infinity, concave primary mirrors, and the primary mirror was always the element with the largest diameter. This survey includes systems with elements larger than the primary mirror. It also includes both new types of concave-primary-mirror systems and all of the convex-primary-mirror systems, which were previously excluded. Numerous systems are presented, including new forms of concentric-mirror systems and systems that have zero Petzval curvature. Also investigated are off-axis or schiefspiegler forms, which include systems excluded from the previous survey due to large central obstructions when considered as on-axis systems. The fact that closed-form solutions are used to map out all solutions over the relevant parameter space means that the systems presented here (together with an earlier survey) represent the full and final range of possibilities for four-spherical-mirror anastigmats for which at least one of the system imaging conjugates is infinite.
Andrew Rakich, Andrew Rakich,
"Four-mirror anastigmats, part 3: all-spherical systems with elements larger than the entrance pupil," Optical Engineering 47(3), 033003 (1 March 2008). https://doi.org/10.1117/1.2898557