Many types of telescopes have been invented since the early 1600’s when they were first used. The first telescopes were made with only lenses. Since lenses refract light, these telescopes are referred to as refractors. By the 1700’s, the astronomer’s desire for bigger telescopes exceeded the ability of glass manufacturers to make large pieces of glass. They solved this problem by using telescopes made with large curved mirrors, which are known as reflectors. When mirrors and lenses are combined, you get optical systems that are known as catadioptric.
Refractor Types
Galilean
The Galiean telescope is made of two lenses, a plano-convex objective and a plano- or bi-concave eyepiece. It is very simple, but it suffers from a limited field of view and chromatic aberration (light of different colors does not all focus at the same place).
Achromatic Doublets
To correct the chromatic aberration of the Galilean telescope, the objective is changed to an achromatic doublet. This is a lens made of a strong biconvex lens made of crown glass with a nearly plano-concave lens made of flint glass either glued to it (for small diameters) or with a small air space between them. The images are significantly improved because red and blue light are brought to focus at the same place. This leaves green and yellow light still slightly out of focus, but the improvement over a single lens is dramatic. While the types of glass are chosen to reduce the chromatic aberration, the curvatures of the surfaces can be optimized to reduce spherical aberration and coma, giving sharp images over at least a 0.5° field of view. Achromatic doublet objectives are commonly used in binoculars.
Apochromats
The best refracting telescopes available are based on apochromatic objectives. The glasses for these objectives are very special (and expensive), and are chosen so that red, green and blue light come to focus at the same place. Spherical aberration and coma are very well corrected, so the image is superb over the field of view of an eyepiece.
Reflector Types
Newtonian (parabolic)
Isaac Newton figured out that a concave parabolic mirror could be used to bring light of all colors to focus at the same place. This was decades before achromatic doublets were discovered, so Newtonian telescopes were the best available for a long time. Mirrors could also be made much larger than lenses, so most astronomical telescopes have Isaac Newton to thank for their existence. The parabolic form of the mirror eliminates spherical aberration, so the center of the image is excellent. Unfortunately, there are no more free variables available to correct coma or astigmatism, so the image deteriorates fairly quickly, especially for faster (lower) f/numbers. In this type of telescope, as well as the ones below, the largest mirror, called the primary mirror, takes the place of the objective in refracting telescopes.
Classical Cassegrain
A telescope with a large concave primary mirror with a short focal length and a convex secondary mirror to reimage the light to a point behind the primary is called a Cassegrain after Laurent Cassegrain, even though he was not the first to invent it (see the Wikipedia article). In the classical form, the primary mirror is parabolic and the secondary is hyperbolic. This corrects for spherical aberration, but does not attempt to correct any other aberrations.
Ritchey-Chretien
The Ritchey-Chétien telescope was invented by George Willis Ritchey and Henri Chrétien in the early 1910s. It replaces the parabolic primary with a slightly hyperbolic one, and adjusts the conic constants of the primary and secondary to eliminate both spherical aberration and coma. This give it a much larger useful field of view. The Hubble telescope was initially intended to be of this form. The appearance is very similar to a classical Cassegrain.
Three Mirror Anstigmat
For reflecting telescopes, the three major aberrations that need to be corrected are spherical aberration, coma and astigmatism. Since there are three aberration, the minimum number of mirrors needed to correct them (ignoring symmetry) is three. That is the reason three-mirror anastigmats exist. The challenge for this type of telescope is keeping the mirrors out of each other’s way. This, along with the difficulty of fabricating and aligning three mirrors, has restricted use of these telescopes to military applications. In the early 2010’s, an design method was developed that enabled the use of freeform mirrors. At the same time, machining methods for optical surfaces reached a point where very smooth freeform surfaces could be machined. These two achievements, when combined with test methods that are in development could lead to practical three mirror anastigmat telescopes with wide fields of view and fast F-numbers.
Catadrioptric Telescopes
The name “catadioptric” comes from the Greek “kata”, meaning against (reflecting), and “dio”, meaning through (refracting). Hence catadioptric telescopes contain both reflecting and refracting elements. The refracting elements generally have very long focal lengths, so they introduce negligible amounts of chromatic aberration, but they are quite useful in eliminating other aberrations.
Schmidt Camera
The Schmidt camera was invented by Bernhard Schmidt in 1930. It consists of a short focal length, spherical primary mirror and an aspheric corrector plate located at its center of curvature. The image is formed halfway between the two, and lies on a sphere with a radius equal to half that of the primary mirror. The aspheric corrector plate eliminates the spherical aberration of the primary mirror, and the symmetry about the primary’s center of curvature reduces the other aberrations to such an extent that this camera (it’s not really a telescope!) can take amazing pictures of a very wide field view at a fast F-number.
Schmidt-Cassegrain
If you start with a Schmidt camera and add a secondary mirror to make it work like a Cassegrain, you get what is called a Schmidt-Cassegrain. For practicality, the aspheric corrector plate is often brought closer to the primary mirror. This reduces the useful field of view, but you can’t get a large image through the hole in the primary mirror, so the tradeoff is acceptable. An American company named Celestron developed a practical way to make these telescopes in large volumes, so they have become very popular.
Maksutov-Cassegrain
Aspheric surfaces are difficult make accurately, so Dmitri Dmitrievich Maksutov came up with an alternative corrector made with almost concentric spherical surfaces. The image can be well corrected over a field of view covering most of a 35mm format. Unfortunately, the concentric corrector is still difficult to make, so this type of telescope is not extremely popular.