Optical Telescopes
The optical configuration of a telescope is the first parameter to be decided on before any other decision concerning the telescope can be made. The choice of a telescope type is influenced by many factors. These include, cost, size, use, versatility, and mounting type. Finding a balance between conflicting requirements is never easy. The optical design is governed by all of these considerations and the type of astronomy to be carried out on the telescope. There are two basic types of optical telescopes, the refractor and the reflector. There are many variations of the two basic types of telescopes. Within the two basic types of optical telescopes there are advantages and disadvantages.
Refractor
The refractor is the classic telescope design. The refractor is the telescope that is most often associated with optical telescopes. The invention of the refractor is credited to Jan Lippershey in 1608. Galileo used Lippershey's invention to observe the sky in 1609 giving rise to the astronomical refractor, (Brown 1975). The first refractor was a simple positive lens for the objective with a simple negative lens as an eyepiece. Modern astronomical refractor objectives are more complex and consist of 2 or more lenses of different types of glass. There are two types of refractors based on the degree of color correction. The Achromat and the Apochromat. The general optical layout for the refractor is shown in figure 1

Figure 1. Optical lay out of the Astronomical refractor. The lens consists of two or more elements depending on the degree of color correction. Two colors are an Achromat while more than two colors are called an Apochromat.
The astronomical refractor typically suffers form an aberration known as Chromatic Aberration. Chromatic aberration is a result of refraction in glass. In a simple lens the colors are separated in an effect that is similar to the effect of a prism. The achromatic refractor was developed to correct chromatic aberration. An achromat corrects for two colors and an apochromat corrects for more than two colors.
A refractor can be inexpensive to construct in small sizes typically less than 10cm. A refractor in its simplest form requires two types of glass and four figured optical surfaces. This means that an astronomical refractor objective in the range of 50 cm is very expensive and difficult to construct. Constructing a refractor is usually beyond the patients of the average amateur. The astronomical refractor is also of f10 or longer which results in a long tube assembly so mounting is a bit more difficult than the shorter reflector. For these reasons the astronomical refractor becomes impractical to construct above 15 cm for a reasonable cost.
Reflectors
The reflecting telescope is less known that the refractor among the general public even though it is much more popular among amateurs. The reflecting telescope replaces the objective lens of the refractor with a mirror to reflect the light to a focus. The reflector is the preferred telescope for both amateur astronomers and professional astronomers for two reasons. 1) Reflectors are much less expensive for a given aperture than a refractor. 2) Reflectors can be made much larger than a refractor. A practical limit for a refractor is around 1 meter where as the limit on size of a reflector has not been reached. Reflectors are being proposed with apertures of 100 meters. (2) There are many types of reflecting telescope designs and many variants within each major category. A partial list of the different types of reflecting telescopes is given for reference.
The Newtonian telescope was invented by Sir Isaac Newton in 1672, (Brown, 1975). Because of its simplicity and ease of construction, the Newtonian telescope has become the standard optical system for amateur and many professional telescopes. The Newtonian telescope consist of a single parabolic mirror and an optical flat to redirect the image to the outside of the optical tube, Figure 2

Figure 2. Optical lay out for a Newtonian telescope. The primary mirror is locate at the end of the optical tube assembly. Light is reflected off of the primary mirror to a flat secondary mirror where it is directed outside of the optical tube assembly where the image can be viewed.
In large professional telescopes the diagonal is not used rather the astronomer and instruments ride directly at the focus. This arrangement is called the prime focus.
Cassegrain
The Cassegrain telescope was invented by Guillaume Cassegrain in 1672, (Brown, 1975). The Cassegrain has been very popular among amateurs and professionals alike. The three primary types of Cassegrains Classical, Dall Kirkham, and Ritchie Chretien. The optical layout of each type of Cassegrain is identical. Only the figure on the optical surfaces differs between the different type of Cassegrains, Figure 3. The Classical and Ritchie Chretien are both widely used among professional and the Dall Kirkham is popular among amateur telescope makers. Each Cassegrain has the same optical lay out that consists of a concave primary and a convex secondary.

Figure 3. The optical lay out of the Cassegrain. All Cassegrain telescopes have the same optical layout. A perforated primary mirror is located at the end of the optical tube assembly. The secondary mirror reflects the light back through a the hole in the primary where the image is formed.
Classical
The Classical Cassegrain consists of a parabolic primary mirror and a convex hyperbolic secondary mirror. The Classical Cassegrain is often used in conjunction with a Newtonian. A Newtonian reflector can be converted to a Cassegrain by changing the secondary mirror form the optical flat of the Newtonian with the hyperbolic secondary of the Classical Cassegrain. Even though the classical Cassegrain has a difficult to figure secondary it suffers from less coma than does the Dall-Kirkham, (Rutten and VanVenrooij, 1988). Moderate coma and the ease of converting an existing Newtonian to a Classical Cassegrain make it a logical choice for a second focus on a telescope.
Dall-Kirkham
The Dall-Kirkham is popular among amateur
telescope
makers. The Dall-Kirkham consists of a spherical secondary mirror and
an
elliptical primary. The spherical secondary is much easier to fabricate
than the steep hyperbolic secondary of the Classical Cassegrain. The
elliptical
primary is also fairly easy to fabricate. Despite the fact that the
Dall-kirkham
is easier to fabricate it suffers form more sever coma in shorter focal
lengths, (Rutten and VanVenrooij, 1988). This and the inability to
convert
the optical path to a Newtonian make the Dall-Kirkham less desirable
than
a Classical Caesarian.
Ritchie-Chretien
The Ritchie-Chretien is very popular among
professional
astronomers because of its optical properties. The Ritche-Creitien
telescope
consists of a hyperbolic primary and secondary. Both of these optical
surfaces
are difficult to fabricate which accounts for not being popular in the
amateur community. Even though the Ritche-Creitien optics are harder to
make the Ritche-Creitien has advantages over both the Classical
Cassegrain
and Dall-Kirkham. The Ritche-Creitien does not suffer from coma, thus
it
can be made in shorter focal ratios and is well suited to photography,
(Rutten and VanVenrooij, 1988). However, the star images at the edges
of the field are enlarged. The Ritchie-Chretien cannot be
converted
to another focus like the Classical Cassegrain.