# Three-mirror anastigmat

Last updated

A three-mirror anastigmat is an anastigmat 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.

## Contents

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 off-axis 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, and the remaining astigmatism is symmetrical around the distorted objects, allowing astrometry across the wide field of view. However, the astigmatism 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.

## History

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.

### Paul

The first were proposed in 1935 by Maurice Paul. [1] 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). 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. [2] 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.

### Paul-Baker

Paul's solution had a curved focal plane, but this was corrected in the Paul-Baker design, introduced in 1969 by James Gilbert Baker. [3] The Paul-Baker design adds extra spacing and reshapes the secondary to elliptical, which corrects field curvature to obtain a flat focal plane. [4]

### Korsch

A more general set of solutions was developed by Dietrich Korsch in 1972. [5] A Korsch telescope is corrected for spherical aberration, coma, astigmatism, and field curvature and can have a wide field of view while ensuring that there is little stray light in the focal plane.

## Related Research Articles

A Ritchey-Chrétien telescope is a specialized variant of the Cassegrain telescope that has a hyperbolic primary mirror and a hyperbolic secondary mirror designed to eliminate off-axis optical errors (coma). The RCT has a wider field of view free of optical errors compared to a more traditional reflecting telescope configuration. Since the mid 20th century, a majority of large professional research telescopes have been Ritchey-Chrétien configurations; some well-known examples are the Hubble Space Telescope, the Keck telescopes and the ESO Very Large Telescope.

A reflecting telescope is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century, by Isaac Newton, as an alternative to the refracting telescope which, at that time, was a design that suffered from severe chromatic aberration. Although reflecting telescopes produce other types of optical aberrations, it is a design that allows for very large diameter objectives. Almost all of the major telescopes used in astronomy research are reflectors. Reflecting telescopes come in many design variations and may employ extra optical elements to improve image quality or place the image in a mechanically advantageous position. Since reflecting telescopes use mirrors, the design is sometimes referred to as a "catoptric" telescope.

A Schmidt corrector plate is an aspheric lens which corrects the spherical aberration introduced by the spherical primary mirror of the Schmidt or Schmidt-Cassegrain telescope designs. It was invented by Bernhard Schmidt in 1931, although it may have been independently invented by Finnish astronomer Yrjö Väisälä in 1924. Schmidt originally introduced it as part of a wide-field photographic catadioptric telescope, the Schmidt camera. It is now used in several other telescope designs, camera lenses and image projection systems that utilise a spherical primary mirror.

The Newtonian telescope, also called the Newtonian reflector or just the Newtonian, is a type of reflecting telescope invented by the English scientist Sir Isaac Newton (1642–1727), using a concave primary mirror and a flat diagonal secondary mirror. Newton's first reflecting telescope was completed in 1668 and is the earliest known functional reflecting telescope. The Newtonian telescope's simple design has made it very popular with amateur telescope makers.

In optics, the coma, or comatic aberration, in an optical system refers to aberration inherent to certain optical designs or due to imperfection in the lens or other components that results in off-axis point sources such as stars appearing distorted, appearing to have a tail (coma) like a comet. Specifically, coma is defined as a variation in magnification over the entrance pupil. In refractive or diffractive optical systems, especially those imaging a wide spectral range, coma can be a function of wavelength, in which case it is a form of chromatic aberration.

A toroidal mirror is a reflector whose surface is a section of a torus, defined by two radii of curvature. Such reflectors are easier to manufacture than mirrors with a surface described by a paraboloid or ellipsoid. They suffer from spherical aberration and coma, but do not suffer from astigmatism like a spherical mirror when used in an off-axis geometry, provided the angle of incidence is matched to the design angle. Because they are easier to manufacture, they are much cheaper than ellipsoidal or paraboloidal mirrors for the same surface quality.

A Schmidt camera, also referred to as the Schmidt telescope, is a catadioptric astrophotographic telescope designed to provide wide fields of view with limited aberrations. The design was invented by Bernhard Schmidt in 1930.

Bernhard Woldemar Schmidt was a Baltic German optician. In 1930 he invented the Schmidt telescope which corrected for the optical errors of spherical aberration, coma, and astigmatism, making possible for the first time the construction of very large, wide-angled reflective cameras of short exposure time for astronomical research.

A catadioptric optical system is one where refraction and reflection are combined in an optical system, usually via lenses (dioptrics) and curved mirrors (catoptrics). Catadioptric combinations are used in focusing systems such as searchlights, headlamps, early lighthouse focusing systems, optical telescopes, microscopes, and telephoto lenses. Other optical systems that use lenses and mirrors are also referred to as "catadioptric", such as surveillance catadioptric sensors.

The Maksutov is a catadioptric telescope design that combines a spherical mirror with a weakly negative meniscus lens in a design that takes advantage of all the surfaces being nearly "spherically symmetrical". The negative lens is usually full diameter and placed at the entrance pupil of the telescope. The design corrects the problems of off-axis aberrations such as coma found in reflecting telescopes while also correcting chromatic aberration. It was patented in 1941 by Russian optician Dmitri Dmitrievich Maksutov. Maksutov based his design on the idea behind the Schmidt camera of using the spherical errors of a negative lens to correct the opposite errors in a spherical primary mirror. The design is most commonly seen in a Cassegrain variation, with an integrated secondary, that can use all-spherical elements, thereby simplifying fabrication. Maksutov telescopes have been sold on the amateur market since the 1950s.

The Schmidt–Cassegrain is a catadioptric telescope that combines a Cassegrain reflector's optical path with a Schmidt corrector plate to make a compact astronomical instrument that uses simple spherical surfaces.

The Cassegrain reflector is a combination of a primary concave mirror and a secondary convex mirror, often used in optical telescopes and radio antennas, the main characteristic being that the optical path folds back onto itself, relative to the optical system's primary mirror entrance aperture. This design puts the focal point at a convenient location behind the primary mirror and the convex secondary adds a telephoto effect creating a much longer focal length in a mechanically short system.

A Schmidt–Newtonian telescope or Schmidt–Newton telescope is a catadioptric telescope that combines elements from both the Schmidt camera and the Newtonian telescope. In this telescope design, a spherical primary mirror is combined with a Schmidt corrector plate, which corrects the spherical aberration and holds the secondary mirror. The resulting system has less coma and diffraction effects than a Newtonian telescope with a parabolic mirror and a "spider" secondary mirror support. The design uses a 45° flat secondary mirror to view the image, as in a standard Newtonian telescope.

The Houghton telescope or Lurie–Houghton telescope is a catadioptric telescope. Houghton's original design was patented in 1944. Instead of the fairly hard to make Schimdt and heavy meniscus (Maksutov) corrector lenses, the corrector for the Houghton is relatively easy to make. It consists of two lenses: a positive and a negative, set at the front of the telescope which fixes the telescope's aperture. All lens and mirror surfaces are spheroidal, which eases construction. These lenses are relatively thin, though not as thin as the Schmidt corrector. With a good anti-reflective coating, light loss and "ghost" reflections are minimal.

In astrophotography, the Wright camera design, presented by Franklin Wright in 1935, just a few years after the introduction of the Schmidt camera, was his "short" alternative to the original arrangement.

An anastigmat or anastigmatic lens is a photographic lens completely corrected for spherical aberration, coma, and astigmatism. Early lenses often included the word Anastigmat in their name to advertise this new feature. All modern photographic lenses are close to being anastigmatic.

Albert A. Bouwers (1893–1972) was a Dutch optical engineer. He is known for developing and working with X-Rays and various optical technologies as a high-level researcher at Philips research labs. He is lesser known for patenting in 1941 a catadioptric meniscus telescope design similar to but slightly predating the Maksutov telescope.

A meniscus corrector is a negative meniscus lens that is used to correct spherical aberration in image-forming optical systems such as catadioptric telescopes. It works by having the equal but opposite spherical aberration of the objective it is designed to correct.

In optical apparatuses such as curved mirrors, lenses or prisms, chromatic aberrations, i.e., unintended separation of colors, may occur. However, when optical aberrations distort monochromatic light the effect is called monochromatic aberration. A convex lens can be simply considered angles of prism that has different refracting angles

## References

1. Paul, Maurice (May 1935). "Systèmes correcteurs pour réflecteurs astronomiques". Revue d'Optique Theorique et Instrumentale. 14 (5): 169–202.
2. Wilson, R. N. (2007). Reflecting Telescope Optics I. Springer. p. 227. ISBN   978-3-540-40106-3.
3. 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.
4. Sacek, V. (14 July 2006). "Paul-Baker and other three-mirror anastigmatic aplanats". Telescope-Optics.net. Retrieved 2013-08-13.
5. Korsch, Dietrich (December 1972). "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.
6. Content, D. A.; Goullioud, R.; Lehan, J. P.; Mentzell, J. E. (14 September 2011). "Optical design trade study for the Wide Field Infrared Survey Telescope [WFIRST]" (PDF). Conference Proceedings of the SPIE. 8146. doi:10.1117/12.898528.