Three-mirror anastigmat

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.

Many combinations of three mirror figures can be used to cancel all third-order aberrations. In general these involve solving a relatively complex set of equations. A few configurations are simple enough, however, that they could be designed starting from a few intuitive concepts.

The first were proposed in 1935 by Maurice Paul. The basic idea behind Paul's solution is that spherical mirrors, with an aperture stop at the centre of curvature, have only spherical aberration - no coma or astigmatism (but they do produce an image on a curved surface of half the radius of the spherical mirror, for a mirror in air). So if the spherical aberration can be corrected, a very wide field of view can be obtained. This is similar to the conventional Schmidt design, but the Schmidt does this with a refractive corrector plate instead of a third mirror.

Paul's idea was to start with a Mersenne beam compressor, which looks like a Cassegrain made from two (confocal) paraboloids, with both the input and output beams collimated. The compressed input beam is then directed to a spherical tertiary mirror, which results in traditional spherical aberration. Paul's key insight is that the secondary can then be converted back to a spherical mirror. One way to look at this is to imagine the tertiary mirror, which suffers from spherical aberration, is replaced by a Schmidt telescope, with a correcting plate at its centre of curvature. If the radii of the secondary and tertiary are of the same magnitude, but opposite sign, and if the centre of curvature of the tertiary is placed directly at the vertex of the secondary mirror, then the Schmidt plate would lie on top of the paraboloid secondary mirror. Therefore the Schmidt plate required to make the tertiary mirror a Schmidt telescope is eliminated by the paraboloid figuring on the convex secondary of the Mersenne system, as each corrects the same magnitude of spherical aberration, but the opposite sign. Also, as the system of Mersenne + Schmidt is the sum of two anastigmats: the Mersenne system is an anastigmat, and so is the Schmidt system, the resultant system is also an anastigmat, as third-order aberrations are purely additive. 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.

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