Properties of an Image
The image formed by either a lens or a mirror has certain properties that depend on the diameter of the objective, or aperture a, and focal length f. One property is the size of the image or plate scale.
Since the image of a star is a point, size is not an important consideration.
But for an extended object, such as a planet or a galaxy, the image size depends on the angular size of the galaxy on the sky and on the focal length of the objective.
The brightness of the image is important because it determines whether the object can be seen and how long it will take to photograph. The brightness of an image of a star depends on how much light is intercepted by the objective and how much the light is spread out in the image plane (the scale). Hence, image brightness is proportional to the area of the objective or to the square of the aperture and inversly proportional to the focal length squared (a/f)2. Doubling the aperture but leaving the focal length the same increases the area of the objective or its light-gathering power four times, concentrating four times as much light into the same-size image.
When photographing a galaxy, the image brightness depends on the amount of radiant energy per unit area of the image. The objective's area (or the square of its aperture) still determines the total amount of energy collected, but the total energy is distributed over an extended image. Thus the larger the image's area, the smaller the energy per unit of area. The image size of a galaxy increases in proportion to the focal length, so for a given telescope aperture the surface brightness of the image decreases as the focal length is made longer.
How well a telescope can discriminate between two objects close together on the sky or can bring out fine details in an extended object is called its resolving power. Because of the wave nature of light, the image of a star is actually a diffraction pattern; it appears as a bright central spot, called a diffraction disk, surrounded by progressively fainter rings. When the diffraction patterns of two stars that are close together no longer overlap, we can see separate stellar images. The larger the telescope's aperture, the smaller the diffraction disk of each image. A large aperture therefore improves the resolution of closely adjoining features by making the diffraction effect of adjacent objects overlap less. We define resolving power as the smallest angle between two close objects whose images can just be separated by a telescope. This critical angle is directly proportional to the wavelength of the observed radiation and inversely proportional to the aperture of the objective: smallest resolvable angle goes as aperture/wavelength.
Telescopes that use lenses for the objective are known as refracting telescopes or "refractors" and those which employ a mirror are called reflecting telescopes or "reflectors". The objective lenses of early refracting telescopes could not form sharp images because single lenses failed to bring all colors to a common focus, a condition known as chromatic aberration. In addition, since the lens shape was (and usually still is) spherical rather than a complicated difficult to manufacture "correct" figure, tle lens suffered from spherical aberration. These conditions can now be reduced by using a compound achromatic lens, two lenses of different types of glass, as the objective in refracting telescopes.
See how to make an achromat...
Spherical aberration also occurs in reflecting telescopes. If the surface of the mirror is parabolic rather than spherical the spherical aberration is eliminated, although off-axis aberrations (coma and astigmatismstill remain.
Why are the big modern telescopes of the reflecting type? Reflecting telescopes have many advantages over refractors: The reflecting telescope is free from chromatic aberration, making it ideal for all-purpose photography and spectroscopy. Also, since a lens must be supported by its edges, there is a limit to the size of a lens that will not strain from its own weight. But a mirror can be supported both at its edges and from the back, and such a means of support allows much larger mirrors to be built than lenses. The largest refractor has an aperture slightly over 1 m, but the largest reflector is 10 m in diameter.
There are other advantages to reflectors: The glass for the mirror in a reflecting telescope need not be so optically pure as that required for a large lens because the light reflects off the front surface and does not pass through the mirror, as it does through a lens. In addition, a mirror has only one surface that must be painstakingly ground--a compound lens has four. To counter changes in temperature that would affect the focal length of the reflector, large mirrors are constructed of fused silica or of a zero-expansion pyroceramic material. The mirror's surface is coated with a thin layer of highly reflecting aluminum that is replaced many times during the life of the telescope.
Reflecting telescopes can be designed for many kinds of astronomical work through choice of the focal arrangement to suit the type of observation. For photography, photometry, and spectroscopy of faint objects, the prime focus is best because its short focal length (bright image) lessens the exposure time required.
The Newtonian focus, most useful for small telescopes and often used by amateur astronomers, is little used by professional astronomers. In both these arrangements, the observer works at a considerable distance above the observatory floor, since both focal positions are near the entrance of the telescope.
In the Cassegrain focal arrangement, a conves secondary mirror near the entrance of the telescope is used to slow the rate at which light rays converge after reflecting off the objective mirror, effectively increasing the telescope's focal length. The secondary mirror reflects the converging rays to the bottom of the telescope and through a hole in the objective mirror to a focus behind the objective. This is a much more convenient observing position since it is near the floor and behind the telescope. Of all the observations made with the 5-m Hale telescope on Palomar Mountain, 75 percent are from the Cassegrain focus.
One might think that putting the secondary mirror and its supports or the observer's cage for the prime focus into the path of the light rays would obscure part of the image, but the only effect is to cut down the amount of light reaching the objective. The loss is small, and the quality of the image is not terribly affected.
Equipment that is too heavy and bulky to be attached to the back of the primary mirror or is sensitive to changes in gravity as the telescope moves can be placed in a room below the observatory floor. Through the use of an auxiliary flat mirror, the long converging beam from the primary mirror can be diverted down the hollow polar axis around which the telescope rotates and into the room below. With this coude focal arrangement, the focal position always remains the same no matter which way the telescope points. More recently, with alt-azimuth mountings becoming popular, the Nasmyth focus, wherein the light from the Cass secondary is picked off by a Newtonian flat and directed through the azimuth axis, is becoming popular. Though not stationary, fairly heavy equipment can be located at this focus and the Newtonian flat can switch from one side of the azimuth axis (instrument) to the other (a second instrument) within seconds.
An optical telescope, in order to follow an object as the Earth's rotation carries it across the sky, must be free to move. In order to track stars accurately and to permit a telescope to be pointed in any direction, an equatorial mounting system is used for most telescopes. This system has two axes of rotation: The telescope can be made to rotate in an east-west sense (hour angle) around its polar axis, which is aligned with the Earth's axis of rotation; The declination axis, which is perpendicular to the polar axis, is used to rotate the telescope in a north-south sense (decination).
Large telescopes are usually pointed by a computer from an operating console and guided thereafter with hand controls. Once a large telescope is properly pointed, the computer operates as a clock to slowly turn the telescope westward around its polar axis at the same rate as the Earth turns eastward, thereby keeping the area of interest always in the telescope's field of view. The great simplicity in an equatorial mounting is that tracking requires continuous motion about only one of its two axes. The disadvantage, which applies only to the largest telescopes now in operation and planned for the future, is that the polar axis is inclined in the Earth's gravitational field and must rotate on one edge of its end. In this position, gravity creates a large mechanical stress on the polar axis that presents a very difficult engineering problem.
One means of preventing some of the mechanical stress on the polar axis is to align it with gravity. Such a mounting is known as altazimuth mounting; with it a telescope rotates about a vertical axis and about a horizontal axis. This mounting's disadvantage is that unlike the equatorial mounting, it must turn continuously about both axes at the same time in order to track a star. When the telescope approaches the area of the sky directly overhead, continuous tracking becomes virtually impossible. Even with this disadvantage, the altazimuth mounting will be the primary mounting for very large telescopes to be constructed in the future.
The geographic location of an observatory are important in order to obtain all the capability built into the telescope and its mounting. An ideal site for an optical observatory is a mountaintop where turbulent motions in the atmosphere are minimal, the air is dry and transparent, and the sky is dark. The southwestern part of the United States or spots along the West Coast are satisfactory locations, in addition to having many clear days and nights. Kitt Peak National Observatory is located in such a site, on a mountaintop, about 65 miles southwest of Tucson, Arizona.
The principal problems in building very large telescopes on the Earth's surface today are cost and construction time. A new 5-m Hale telescope would now cost about $25 million and take 10 years to build, while a 10-m telescope would cost $200 million and take 20 years to build and a 25-m telescope would cost about $3 billion and take 50 years to build. Clearly some dramatic changes in design are needed to lower cost and construction time.
A new telescope design, called the Multiple-Mirror Telescope has been installed by the Smithsonian Institution and the University of Arizona in southern Arizona. It uses a mosaic of independent mirrors of small size coordinated by laser beams to collect and focus light in order to simulate the collecting ability of a large-aperture single mirror. The telescope consists of a circular array of six identical 1.8-m mirrors on an altazimuth mounting; the array has light-gathering power equivalent to that of a 4.5-m single mirror. The six mirrors are not thick solid ones but are of a new lightweight design, as shown in Figure 12. They are partially hollow, which requires a smaller mechanical structure to move them. Thus the cost of the Multiple-Mirror Telescope was about one-third that of a conventionally designed telescope, and it required less time to build. This instrument has been successful in demonstrating the practicality of the multiple-mirror concept.
The Multiple-Mirror Telescope is not the only new design; others are displayed in Figure 16, which presents artist conceptions of new designs for future large telescopes. One new design that will definitely be built is the University of California's 10-m segmented-mirror telescope, which will hopefully go into operation in the early 1990s atop Mauna Kea, Hawaii. Using the multiple-mirror design, a second very large telescope, known as the 15-m National New Technology Telescope, has been proposed and will begin construction in fiscal year 1988 if funded. Although it has been argued that the success of Space Telescope, a 2.4-m reflecting telescope that is to be put into orbit in early 1988, will lessen the need for a mammoth new telescope on the ground, the reverse is probably true--it will increase the need. Since Space Telescope will not be limited by light losses produced by the atmosphere, it will primarily operate at shorter wavelengths than the visible. Hence it would be desirable to have a very large telescope on the ground working in conjunction with Space Telescope to observe in the visible region of the spectrum.