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
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.
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 =
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.
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.
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
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
primary 8" = (pi)r² = (pi)4² = 50.27
secondary 2¾" =
(pi)r² = (pi)1.375 = 5.94
percentage = 5.94 is 11.8% of
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
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.
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
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
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
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
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
This is the nearest distance you can focus the
telescope visually or photographically for close terrestrial work.
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 =
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
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
-- 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.
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
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.
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.
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