Optimization of the Ritchey-Chrétien telescope for a discrete set of reference spheres

We propose a method to minimize the amount of aspherization required to produce hyperboloid mirrors for the widely used Ritchey-Chrétien telescope design. The approach is based on fine-tuning the telescope's geometry to precisely match a discrete set of high-precision etalons, which are used to control the polishing of the spherical substrates. We support this optimization technique with an open-source implementation in Python and demonstrate its effectiveness through several real-world examples, achieving improvements of up to more than an order of magnitude, with the telescope parameters adjusted by only a fraction of a millimeter. We also show that this method can be extended to several other reflecting telescope designs.