Freeform aplanatic reflective imaging systems with several stigmatic pairs

This manuscript introduces a method to design a freeform reflective optical system with the particularity of being aplanatic and having several stigmatic pairs. To achieve this goal the mathematical expressions in [Appl. Opt.63, 8068 (2024)APOPAI0003-693510.1364/AO.540494; Appl. Opt.62, 5260 (2023)APOPAI0003-693510.1364/AO.489061] are merged into a single set of expressions that leads to a system of differential equations that can be solved. The paper shows an illustrative example that explains how the method works. The resulting design is as expected by the theory proposed.