Leveraging confocality and Cartesian reflectors in freeform optical designs

Conical optics have a long, deep history in telescope design—Newtonian, Gregorian, Cassegrain, Schwarzschild, etc.—because of their ability to stigmatically image one point source to another point source. Many designs based on conical optics are confocal: the stigmatic foci of each mirror are aligned to those of the preceding and following mirrors so that the overall system preserves the stigmatic imaging property of the individual surfaces. Even if strict confocality is not enforced—for example, if aspheric or freeform departures are added onto the base conics—designs with surfaces that are nearly conical can still maintain some of the advantages of strict confocality. We discuss how some of these advantages can be achieved in the context of unobscured, off-axis designs with freeform surfaces.