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One Mirror
Two Mirror
Coma Corrector

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The second method of focussing light is to reflect the rays off of the surface of a curved mirror, producing a type of telescope called a reflector.

Before the introduction of achromatic objectives, telescopes with a single-lens objective were severely affected by chromatic aberration. After some theoretical attempts—primarily by Marin Mersenne several authors, beginning in the 1660s, advocated the use of mirrors to compensate for that drawback. When reflecting surfaces are used, light rays are not refracted, so the images they produce are effectively free of chromatic aberration. Moreover, by choosing appropriate surface forms, one can even eliminate geometrical aberrations and thus obtain optically correct images. Reflecting telescopes, also called reflectors, use as an objective a concave mirror called primary mirror (to form a "real" image, the objective of any optical instrument must always be converging; convex mirrors are diverging) and one or more smaller, suitably shaped mirrors called secondary mirrors. The most common types of reflector use a parabolic-section primary, which, being free of spherical aberration and other geometrical aberrations, provides chromatically and geometrically perfect images.

The most common reflectors in use today are called Newtonians because this design was pioneered by Isaac Newton. A mirror is made by coating the front surface of a concave piece of glass with a reflecting material. Light rays entering the telescope reflect off of the mirror and since they never pass through the glass no false colour is produced. The surface of the mirror of a high focal ratio reflector can be shaped or figured to that of the surface of a sphere. This works for small reflectors and those with focal ratios of f/9 or higher. However, with large reflectors and those with focal ratios of f/8 or lower, these spherical mirrors do not bring all of the light rays to the same focal point. The rays from the mirror's perimeter are focussed at a different point from it's centre, resulting in an image which lacks contrast due to spherical aberration. To overcome this defect, mirror surfaces are shaped during polishing to a paraboloidal shape which focuses all of the light rays to the same point.

Since the light rays are reflected back up the optical tube by the primary mirror, they must be redirected in order to be viewed. A secondary mirror, which has a flat surface is mounted at a 45 degree angle in the centre of the tube to reflect the rays to the focal point. The secondary is usually oval in shape because this presents a circular shape when viewed from a 45 degree angle. Obstructions, such as secondary mirrors, have a limited visual effect when placed in the path of the light entering the telescope. They modify the diffraction patterns, which can cause a slight loss of contrast, and they reduce the amount of light reaching the focal point. However, they are not seen in the focussed image presented through the eyepiece.

Since the eyepiece is near the front of the tube, reflectors can be mounted lower to the ground giving more convenient viewing and greater stability. Only two surfaces need to be shaped, polished and coated and these can be tested separately. This makes them less expensive to produce than other telescope designs. On the negative side, a long optical tube Newtonian on a German equatorial mount can be more susceptible to wind vibrations than shorter designs. Collimation of both mirrors is part of the regular maintenance for reflectors.

The form of reflecting telescope suggested by James Gregory (1638-1675) predates the familiar form of reflector which Isaac Newton (1642-1727) first designed and made in 1668. The problem with the reflecting telescope is how to view the image formed by the primary mirror. With a single concave mirror, this image is formed on the optical axis, and the head of the observer then gets in the way. Newton solved the problem by using a small diagonal mirror to deflect the image to the side, where it may be viewed through the eyepiece. Gregory's solution was to place a small, short focal length, concave mirror along the optical axis. The rays reflect back toward the primary mirror and pass through a small hole in its center. The resulting image is then viewed with the aid of the eyepiece.

Utilizing a (usually) perforated primary mirror, other configuration was initially developed in 1672 by the frenchman Cassegrain. Although he designed the system, it's unlikely that any actual Cassegrain telescopes were built, since the aspheric (not spherical) surfaces required by the design were yet to be achieved by opticians. A Cassegrain can be thought of as a Newtonian where, instead of exiting the tube at a right angle, the light path is directly folded back through the hole in the center of the primary mirror. The classical Cassegrain system uses a paraboloidal primary and a hyperboloidal secondary. Primary advantages of this design include a flat field and (other than coma), good image correction. Plus, with the folded optical path, the physical length of the telescope can be remarkably short, even for larger, long focal length instruments.

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