Under certain circumstances, a system of two mirrors can be corrected to eliminate Seidel spherical aberration, coma, and astigmatism. Schwarzschild investigated the case of such a system with a flat field and an object at infinity. This paper considers the full range of solutions for different magnifications and field curvatures, with positive or negative powers and two real, one real and one virtual, and two virtual conjugates. If aspherical terms of higher than the fourth order in aperture are used, highly corrected systems of large relative aperture, covering extended field sizes, are possible. A numerical example is given of an f/0.7 system covering ±0.10 radians.

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