A three-mirror anastigmat is a telescope built with three curved mirrors, enabling it to minimize all three main optical aberrations - spherical aberration, coma, and astigmatism. This is primarily used to enable wide fields of view, much larger than possible with telescopes with just one or two curved surfaces.
A telescope with only one curved mirror, such as a Newtonian telescope, will always have aberrations. If the mirror is spherical, it will suffer from spherical aberration. If the mirror is made parabolic, to correct the spherical aberration, then it must necessarily suffer from coma and astigmatism. With two curved mirrors, such as the Ritchey–Chrétien telescope, coma can be eliminated as well. This allows a larger useful field of view. However, such designs still suffer from astigmatism. This too can be cancelled by including a third curved optical element. When this element is a mirror, the result is a three-mirror anastigmat. In practice, the design may also include any number of flat fold mirrors, used to bend the optical path into more convenient configurations.
Paul and Paul-Baker designs
As shown by Korsch, many combinations of the three mirror figures can be used to cancel all primary aberrations. In general these involve solving a fairly complex set of equations. A few configurations are simple enough, however, that they could be designed starting from a few intuitive concepts. Paul discovered the first of these in 1935. His solution had a curved focal plane, and this was remedied in the Paul-Baker design.
The basic idea behind Paul's solution, and Schmidt telescopes in general, is that spherical mirrors, with an entrance pupil at the focal length, have only spherical aberration - no coma or astigmatism. So if the spherical aberration can be corrected, a very wide field of view can be obtained. The conventional Schmidt does this with a refractive corrector plate which also defines the entrance pupil.
Paul's idea was to start with a Mersenne style beam compressor, which looks like a Cassegrain made from two (confocal) parabaloids. The compressed input beam is then directed to a spherical tertiary mirror, which of course then results in traditional spherical aberration. Paul's key insight is that the secondary can then be converted back to a spherical mirror. This induces the exact inverse of the final mirror's spherical aberration, if the secondary has same radius of curvature as the spherical tertiary mirror and the spacing is correct. The two spherical aberrations then cancel, and detailed analysis shows all other aberrations are removed as well. In addition the secondary is now easier to fabricate. This design is also called a Mersenne-Schmidt, since it uses a Mersenne configuration as the corrector for a Schmidt telescope.
Baker extended this idea by adding extra spacing, and reshaping the secondary to elliptical, in order to obtain a flat focal plane.
- The James Webb Space Telescope is a three-mirror anastigmat.
- The Large Synoptic Survey Telescope is a modified three-mirror anastigmat of Paul-Baker design.
- The KH-11 Kennan (or perhaps the now cancelled Future Imagery Architecture) telescopes may be a three-mirror anastigmat, since the spare telescopes given to NASA by the National Reconnaissance Office are of this form.
- The European Extremely Large Telescope will be a three-mirror anastigmat design, with two additional flat fold mirrors.
- Paul, M. (1935). "Systèmes correcteurs pour réflecteurs astronomiques". Revue d'Optique Theorique et Instrumentale 14 (5): 169–202.
- Baker, J.G. (1969). "On improving the effectiveness of large telescopes". IEEE Transactions on Aerospace and Electronic Systems. AES-5 (2): 261–272. Bibcode:1969ITAES...5..261B. doi:10.1109/TAES.1969.309914.
- Sacek, V. (14 July 2006). "Paul-Baker and other three-mirror anastigmatic aplanats". Telescope-Optics.net. Retrieved 2013-08-13.
- Korsch, D. (1970). "Closed Form Solution for Three-Mirror Telescopes, Corrected for Spherical Aberration, Coma, Astigmatism, and Field Curvature". Applied Optics 11 (12): 2986–2987. Bibcode:1972ApOpt..11.2986K. doi:10.1364/AO.11.002986.
- Wilson, R. N. (2007). Reflecting Telescope Optics I. Springer. p. 227. ISBN 978-3-540-40106-3.