OPTICAL TERMS AND
CHARACTERISTICS OF TELESCOPES

APERTURE (DIAMETER OF THE LENS OR MIRROR)

This is the single most important factor in choosing a telescope. The prime function of all telescopes is to collect light. At any given magnification, the larger the aperture, the better the image will be.

The clear aperture of a telescope is the diameter of the objective lens or primary mirror specified in either inches or millimeters (mm). The larger the aperture, the more light it collects and the brighter (and better) the image will be. Greater detail and image clarity will be apparent as aperture increases. For example, a globular star cluster such as M13 is nearly unresolved through a 4" aperture telescope at 150 power but with an 8" aperture telescope at the same power, the star cluster is 16 times more brilliant, stars are separated into distinct points and the cluster itself is resolved to the core.

Considering your budget and portability requirements, select a telescope with as large an aperture as possible.

The photos to the right demonstrate what increasing aperture will give you -- higher contrast, better resolution and a brighter image. Top to bottom with Celestron telescopes -- C5 (5" aperture), C8 (8" aperture), C14 (14" aperture).  All were taken using eyepiece projection photography at a focal ratio of f/90 for comparison. The effects are even more pronounced during visual observation.

  FOCAL LENGTH

This is the distance (in mm.), in an optical system, from the lens (or primary mirror) to the point where the telescope is in focus (focal point). The longer the focal length of the telescope, generally the more power it has, the larger the image and the smaller the field of view. For example, a telescope with a focal length of 2000mm has twice the power and half the field of view of a 1000mm telescope. Most manufacturers specify the focal length of their various instruments; but, if it is unknown and you know the focal ratio you can use the following formula to calculate it: focal length is the aperture (in mm) times the focal ratio. For example, the focal length of an 8" (203.2mm) aperture with a focal ratio of f/10 would be 203.2 x 10 = 2032mm.

RESOLUTION

This is the ability of a telescope to render detail. The higher the resolution, the finer the detail. The larger the aperture of a telescope, the more resolution the instrument is capable of, assuming the telescope optics are of high quality.

RESOLVING POWER

For telescopes this is referred to as "Dawes limit." It is the ability to separate two closely-spaced binary (double) stars into two distinct images measured in seconds of arc. Theoretically, to determine the resolving power of a telescope divide the aperture of the telescope (in inches) into 4.56. For example, the resolving power of an 8" aperture telescope is 0.6 seconds of arc (4.56 divided by 8 = 0.6). Resolving power is a direct function of aperture such that the larger the aperture, the better the resolving power. However, resolving power is often compromised by atmospheric conditions and the visual acuity of the observer.

CONTRAST

Maximum image contrast is desired for viewing low-contrast objects such as the moon and planets. Newtonian and catadioptric telescopes have secondary (or diagonal) mirrors that obstruct a small percentage of light from the primary mirror. Some of the literature on amateur astronomy would lead you to believe that image contrast is severely reduced with Newtonians or catadioptrics because of this obstruction, but this is not the case. (It would be if more than 25% of the primary mirror surface area was obstructed.)

To calculate the secondary obstruction, use the formula (pi)r² for the primary and secondary mirrors which gives you the surface area of each. Then calculate the percentage of obstruction. For example, an 8" telescope with a 2¾" secondary obstruction has an 11.8% secondary obstruction:

primary 8" = (pi)r² = (pi)4² = 50.27
secondary 2¾" = (pi)r² = (pi)1.375 = 5.94
percentage = 5.94 is 11.8% of 50.27

Seeing conditions (or air turbulence) is the single most important factor that adversely affects image contrast when seeking planetary detail through a telescope. Instrument problems that can also adversely affect contrast in order of decreasing importance are: optical figure, collimation, optical smoothness, baffling, and a small increase in central obstruction. Note that the increase in central obstruction is rated as the smallest contributor adversely affecting contrast.

LIGHT GATHERING POWER (LIGHT GRASP)

This is the telescope's theoretical ability to collect light compared to your fully dilated eye. It is directly proportional to the square of the aperture. You can calculate this by first dividing the aperture of the telescope (in mm) by 7mm (dilated eye for a young person) and then squaring this result. For example, an 8" telescope has a light gathering power of 843. ((203.2/7)² =  843).

AIRY DISK BRILLIANCE FACTOR

When you view a star in a properly focused telescope you are not going to see an enlarged image since stars, even at high power, should look like points of light rather than disks or balls. This is simply because stars are very, very far away. But, if you magnify a star's image by about 60x per inch of aperture and look carefully you may be able to see rings around the star. This is not the star's disk you are seeing but the effect of having a circular aperture in your telescope and due to the nature of light. Under close inspection, when the star is at the center of the telescope's field of view, this highly magnified star image will show two things; a central bright area called the airy disk, and a surrounding ring or series of faint rings called the diffraction rings.

The airy disk becomes smaller as you increase the aperture. Airy disk brilliance (the brightness of a point-source stellar image) is proportional to the fourth power of aperture. In theory, when you double the aperture of a telescope, you increase its resolving power by a factor of two and boost its light gathering ability by a factor of four. But more importantly, you also reduce the area of the airy disk by a factor of four resulting in a sixteen-fold gain in stellar image brilliance.

To illustrate this, we show a faint, one-second double star below -- as viewed through both a 4-inch and an 8-inch telescope. Note that at the same power the airy disks are 16 times more brilliant in the 8-inch telescope in addition to being well-separated. Also note that the larger telescope reveals a faint star that is completely obscured in the 4-inch telescope. In the illustration, a darker disk corresponds to increased brightness.

EXIT PUPIL

The exit pupil of a telescope is the circular beam of light that leaves the eyepiece being used and is measured in mm. To calculate exit pupil, divide the aperture (in mm) by the power of the eyepiece being used. For example, an 8" aperture telescope (203mm) used with a 20mm eyepiece is working at 102 power and has an exit pupil of 2mm (203/102 = 2mm). Or, you can calculate the exit pupil by dividing the focal length of the eyepiece (in mm) by the focal ratio of the telescope.

POWER (MAGNIFICATION)

One of the least important factors in purchasing a telescope is the power. Power, or magnification, of a telescope is actually a relationship between two independent optical systems – (1) the telescope itself, and (2) the eyepiece (ocular) you are using.

To determine power, divide the focal length of the telescope (in mm) by the focal length of the eyepiece (in mm). By exchanging an eyepiece of one focal length for another, you can increase or decrease the power of the telescope. For example, a 30mm eyepiece used on the C8 (2032mm) telescope would yield a power of 68x (2032/30 = 68) and a 10mm eyepiece used on the same instrument would yield a power of 203x (2032/10 = 203). Since eyepieces are interchangeable, a telescope can be used at a variety of powers for different applications.

There are practical upper and lower limits of power for telescopes. These are determined by the laws of optics and the nature of the human eye. As a rule of thumb, the maximum usable power is equal to 60 times the aperture of the telescope (in inches) under ideal conditions. Powers higher than this usually give you a dim, lower contrast image. For example, the maximum power on a 60mm telescope (2.4" aperture) is 142x. As power increases, the sharpness and detail seen will be diminished. The higher powers are mainly used for lunar, planetary, and binary star observations.

Do not believe manufacturers who advertise a 375 or 750 power telescope which is only 60mm in aperture (maximum power is 142x), as this is false and misleading.

Most of your observing will be done with lower powers (6 to 25 times the aperture of the telescope [in inches]). With these lower powers, the images will be much brighter and crisper, providing more enjoyment and satisfaction with the wider fields of view.

There is also a lower limit of power which is between 3 to 4 times the aperture of the telescope at night. During the day the lower limit is about 8 to 10 times the aperture. Powers lower than this are not useful with most telescopes and a dark spot may appear in the center of the eyepiece in a Catadioptric or Newtonian telescope due to the secondary or diagonal mirror's shadow.

LIMITING MAGNITUDE

Astronomers use a system of magnitudes to indicate how bright a stellar object is. An object is said to have a certain numerical magnitude. The larger the magnitude number, the fainter the object. Each object with an increased number (next larger magnitude number) is approximately 2.5 times fainter. The faintest star you can see with your unaided eye (no telescope) is about sixth magnitude (from dark skies) whereas the brightest stars are magnitude zero (or even a negative number).

The faintest star you can see with a telescope (under excellent seeing conditions) is referred to as the limiting magnitude. The limiting magnitude is directly related to aperture, where larger apertures allow you to see fainter stars. A rough formula for calculating visual limiting magnitude is: 7.5 + 5 LOG (aperture in cm). For example, the limiting magnitude of an 8" aperture telescope is 14.0. (7.5 + 5 LOG 20.32 = 7.5 + (5x1.3) = 14.0). Atmospheric conditions and the visual acuity of the observer will often reduce limiting magnitude.

Photographic limiting magnitude is approximately two or more magnitudes fainter than visual limiting magnitude.

DIFFRACTION LIMITED (RAYLEIGH CRITERION)

A diffraction limited telescope has aberrations (optical errors) corrected to the point that residual wavefront errors are substantially less than 1/4 wavelength of light at the focal point. It is then acceptable to be used as an astronomical telescope. In compound optical systems, the individual components must be better than 1/4 wavelength for the wavefront error at the focal point to be at least 1/4 wavelength. As the wavefront number gets smaller (1/8th or 1/10th wavelength), the optical quality is progressively better.

FOCAL RATIO (PHOTOGRAPHIC SPEED OR F/STOP)

This is the ratio of the focal length of the telescope to its aperture. To calculate, divide the focal length (in mm) by the aperture (in mm). For example, a telescope with a 2032mm focal length and an aperture of 8" (203.2mm) has a focal ratio of 10 (2032/203.2 = 10). This is normally specified as f/10.

Many people equate focal ratios with image brightness, but strictly speaking this is only true when a telescope is used photographically and then only when taking pictures of so-called "extended" objects like the Moon and nebulae. Whether a telescope is used visually or photographically, the brightness of stars (point sources) is a function only of telescope aperture-the larger the aperture, the brighter the images. When viewing extended objects, the apparent brightness seen in the eyepiece is a function only of aperture and magnification, it is not related to focal ratio. Extended objects will always appear brighter at lower magnifications. Telescopes with small (sometimes called "fast") focal ratios do, however, produce brighter images of extended objects on film, and thus require shorter exposure times. Generally speaking, the main advantage of having a fast focal ratio with a telescope used visually is that it will deliver a wider field of view. "Fast" focal ratios of telescopes are f/3.5 to f/6, "medium" are f/7 to f/11, and slow" are f/12 and longer. An f/8 system requires four times the exposure of an f/4 as an example.

NEAR FOCUS

This is the nearest distance you can focus the telescope visually or photographically for close terrestrial work.

FIELD OF VIEW

The amount of sky that you can view through a telescope is called the real (true) field of view and is measured in degrees of arc (angular field). The larger the field of view, the larger the area of the sky you can see. Angular field of view is calculated by dividing the power being used into the apparent field of view (in degrees) of the eyepiece being used. For example, if you were using an eyepiece with a 50 degree apparent field, and the power of the telescope with this eyepiece was 100x, then the field of view would be 0.5 degrees (50/100 = 0.5).

Manufacturers will normally specify the apparent field (in degrees) of their eyepiece designs. The larger the apparent field of the eyepiece (in general), the larger the real field of view and thus the more sky you can see. Likewise, lower powers used on a telescope allow much wider fields of view than do higher powers.

 To demonstrate the power and field of view of a telescope, the photo on the left was taken with a 50mm lens and the photo on the right was taken with a Celestron C90 (1000mm f/11) at the same distance.

Photos courtesy of Alan Hale

OPTICAL DESIGN ABERRATIONS
There are several optical designs used for telescopes. Remember that a telescope is designed to collect light and form an image. In designing optical systems, the optical engineer must make tradeoffs in controlling aberrations to achieve the desired result of the design.

Aberrations are any errors that result in the imperfection of an image. Such errors can result from design or fabrication or both. It is impossible to design an absolutely perfect optical system. The various aberrations due to a particular design are noted in the discussion on types of telescopes.

Below we will briefly describe specific telescope aberrations:

Chromatic Aberration -- usually associated with objective lenses of refractor telescopes. It is the failure of a lens to bring light of different wavelengths (colors) to a common focus. This results mainly in a faint colored halo (usually violet) around bright stars, the planets and the moon. It also reduces lunar and planetary contrast. It usually shows up more as speed and aperture increase. Achromat doublets in refractors help reduce this aberration and more expensive, sophisticated designs like apochromats and those using fluorite lenses can virtually eliminate it.

Spherical Aberration -- causes light rays passing through a lens (or reflected from a mirror) at different distances from the optical center to come to focus at different points on the axis. This causes a star to be seen as a blurred disk rather than a sharp point. Most telescopes are designed to eliminate this aberration.

Coma -- associated mainly with parabolic reflector telescopes which affect the off-axis images and are more pronounced near the edges of the field of view. The images seen produce a V-shaped appearance. The faster the focal ratio, the more coma that will be seen near the edge although the center of the field (approximately a circle, which in mm is the square of the focal ratio) will still be coma-free in well-designed and manufactured instruments.

Astigmatism -- a lens aberration that elongates images which change from a horizontal to a vertical position on opposite sides of best focus. It is generally associated with poorly made optics or collimation errors.

Field Curvature -- caused by the light rays not all coming to a sharp focus in the same plane. The center of the field may be sharp and in focus but the edges are out of focus and vice versa.

COLLIMATION

The proper alignment of the optical elements in a telescope. Collimation is critical for achieving optimum results. Poor collimation will result in optical aberrations and distorted images. Not only is the alignment of the optical elements important but even more important is the alignment of the optics with the mechanical tube-this is called opto/mechanical alignment.