From the Monthly Notes of the Royal Astronomical Society (1984) Vol. 210 pp 597-609
The Mersenne-Schmidt: a three-mirror survey telescope. Accepted 1984 March 20, Received 1984 February 10.
2. Three-mirror telescopes; previous work
      The first well-corrected telescopes using three curved mirrors were proposed by Paul (1935). In one of these designs the light focused by a paraboloidal primary mirror falls on a spherical convex secondary mirror and is made approximately parallel. It is then refocused by a spherical concave tertiary mirror, with the same numerical radius of curvature as the secondary, and with its center of curvature at the pole of the secondary. This system is corrected for Seidel spherical aberrations, coma and astigmatism. Paul discarded it because the considered the central obstruction too large. Baker (1969) independently discovered its properties, and showed that two spherical mirrors could be used to give the Palomar 5.08m (200 inch) telescope an extended field of good definition. Baker also showed that the field could be flattened by making the radius of curvature of the tertiary mirror longer than that of the secondary, and making the secondary ellipsoidal. the larges set of secondary mirrors proposed by Baker would have provided a beam of parallel light 1.27m (50 inch) in diameter, and covered a field 0.92º in diameter. The image quality could be improved by giving the secondary convex mirror a slight turned-down edge superimpose on its ellipsoidal figure, resulting in images under 0.3 arcsec in diameter at F/4.40.

      Baker (1969) also reviewed existing designs of corrector lenses and mirrors up to that date. Rumsey (1971) showed that there were two other forms of corrector for a paraboloid which used two spherical mirrors, but these had larger central obstructions than the Paul-Baker version. Korsch (1977) described a telescope with three curved mirrors (two concave ellipsoids and one convex hyperboloid) which also needed a small plane mirror to bring the focus to an accessible position, and gave images not more than 0.07 arcsec (rms) in diameter at the edge of a field 1.5º in diameter while working at F/12. The first two mirrors superficially resemble a Cassegrain combination, and the third mirror refocuses the light after it has passed through an imperfect intermediate image. Near the edge of the field the light strikes the focal plane at more than 20º to its normal, having passed through a small exit pupil close to the focus; this feature might be inconvenient if optical fibers were used, as some losses might occur if any detector with a fiber-optic face plate were used. Near the center of the field where these problems are minimized there is a small area which is partially vignetted by the folding flat mirror required to bring the final focus to an accessible position. The good performance of this telescope is remarkable as it uses three mirrors each of which is either an ellipsoid or an hyperboloid, without extra figuring.

      Robb (1978) described a rather general method of designing three-mirror telescopes, and gave as an example one with images smaller than 0.058 arcsec (rms) diameter over a flat field of 2.3º when working at F/5. This had a perforated primary mirror and converging light between the second and third mirrors. However it would need a substantial baffle around the secondary mirror to prevent stray light from the sky reaching the focus after a single reflection in the tertiary mirror, and the plateholder diameter required to cover the whole field is 0.8 of the diameter of the beam of light passing it on the way from the secondary to the tertiary mirror, the plateholder alone obstructs 64 % of the area of the primary mirror on and close to the axis, and with the sky fog baffle as well the loss is the same as the edge of the field and slightly more than 66% at some intermediate angles. It therefore works effectively at F/8.33.

      Angel, Woolf and Epps (1982) designed a Paul-Baker system with an F/1 primary mirror, F/2 final focus, and a (concave) curved field 1º in diameter in which 80% of the light falls within a diameter of 0.13 arcsec at the center of the field, and 0.19 arcsec at the edge.

      Yamashita and Nariai (1983) have recently examined the general properties of three-mirror telescopes within the limitations of third-order optical theory. Epps and Takeda (1983) have optimized some of their designs, obtaining rms image spreads as small as 0.01 arcsec over a field 1º in diameter at F/4. One design shows a perforated primary mirror with the tertiary mirror a very short distance behind it.

      Neither Paul no Baker appears to have considered perforating the primary mirror and placing the third mirror behind it; this is probably because they regarded the second and third mirrors as a corrector system for an existing paraboloidal mirror which would continue to be used, at other times, in prime focus, Cassegrain or coude configurations.