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We present here aplanatic systems in 3D geometry as a limiting case of a SMS 3D design. We extend the basic formulations governing rotationally symmetric aplanatic systems to freeform aplanatic systems and provide a formal proof that a SMS 3D design in the limiting case of 3 coincident points leads to a freeform aplanatic system.
Miñano et al. (Tue,) studied this question.