Four-mirror flat-field anastigmat aplanat telescopes with simple closed-form solutions.

A four-mirror anastigmat aplanat telescope can be constructed using a Gregorian-form Mersenne afocal telescope as a feeder for a concentric spherical Schwarzschild objective. A flat image field can be obtained by adjusting the ratio of the radii of the mirrors. With the tertiary at the image of the aperture stop (the primary) the primary's conic K1 can be varied, using the tertiary's conic K3 to cancel the primary's spherical aberration without affecting the system's coma or astigmatism. For a spherical primary, the tertiary is an oblate ellipsoid (K3 >0). The minimum obscuration ratio is 44.7% (20% by area).