Light Grasp of a Telescope
The primary function of a telescope is to gather light and funnel it into the
observer's eye. The larger the telescope, the greater the amount of light
captured. Light gathering ability is a function of the area of the
objective lens or primary mirror. Thus the
aperture, or diameter, determines the
light grasp of a telescope. Since for a circular aperture, Area =
πr2, as the aperture is increased, the
light grasp increases by the square of the aperture. This means an 8"
aperture collects 4 times as much light as a 4" aperture. The 8" aperture
has an area of 50 in2, while the 4" aperture has only 12.5 in2.
How much more light a telescope gathers compared
to the unaided eye is determined by the ratio between the light-gathering area
of the telescope and the light-gathering area of the eye. The aperture of
the eye is determined by the size of the pupil (see the section below on The
Human Eye for more details). In general, the average pupil will open up to
about 7mm in diameter. Note that this means if the beam of light coming
out of the telescope eyepiece is larger than the maximum size of the eye, the
eye becomes the limiting factor and effectively reduces the aperture of the
telescope. This is described more later. The light gathering area of
the 7mm pupil is then 0.06 in2. For the 8" telescope, this
gives a ratio of 50/0.06 = 833, meaning an 8" telescope gathers 833 times more light than the
Above: The difference in relative size between an 8" (200mm) mirror and the 7mm
opening of the human eye
This implies an object seen with the unaided eye
will appear more than 800 times brighter through an 8" telescope. However, the
situation is more complicated than that. While the previous statement is
true for point sources (stars) it is not true for extended objects (galaxies,
nebulae, planets). This is because the light from an extended object is
being spread out by the fact that the telescope is magnifying the image.
So magnification factors into the equation; light is lost in proportion to the
square of the magnification. There is a minimum magnification allowed by
the limiting size of the pupil as described above. This works out such
that the image through a telescope can never be brighter than the image as seen
with the unaided eye. This seems counterintuitive. However, with
optimum magnification (described below) the image not be significantly dimmer
and will be considerably larger and more detailed.
An additional advantage of aperture that comes
into play when magnification is considered is image brightness at a given
magnification. Through a given telescope, doubling the magnification
reduces the brightness of an extended object fourfold. Doubling the
aperture of a telescope makes the image four times brighter at the same
magnification, or allows twice the magnification to be used while retaining the
same image brightness.
The direct ratio between telescope brightness
and unaided eye brightness still holds for point sources. For this reason,
stars will appear brighter than they do with the eye, independent of
magnification. The magnitude scale used to describe the brightness of
stars is a logarithmic scale. Each magnitude is a difference of 2.5 in
brightness. A 1st magnitude star is 2.5 times brighter than a 2nd
magnitude star. A 2nd magnitude star is 2.5 times brighter than a 3rd
magnitude star. And the difference between a 1st magnitude star and 3rd
magnitude star is 2.5 x 2.5 = 6.25 times. A telescope which can make stars
appear 833 times brighter than the unaided eye will allow stars 7.3 magnitudes
fainter to be seen. If you can see 6th magnitude stars with the unaided
eye, you should be able to see 13th magnitude stars through an 8" telescope.
In actuality, fainter stars can be seen. This is because of the decrease
in brightness of the sky background seen through the telescope. Sky
brightness is also a function of magnification, the sky growing darker as the
power is increased. At a magnification of 100x, the sky background appears
2.7 magnitudes darker than without the telescope, which translates to an extra 2
magnitudes of reach, allowing 15th magnitude stars to be seen. A darker
sky which allows fainter stars to be seen with the unaided eye will of course
allow even fainter stars to be seen through the telescope.
Resolution of a Telescope
A telescope, even with theoretically perfect optics, cannot produce a point
image of a point source, such as a star. This is because of
which is caused by the wave nature of light. As light passes through the
telescope aperture, the waves interfere with each other, diffusing the point
source. Imagine a wave of water coming in off the ocean and meeting with a
break in a wall as shown below. The aperture causes secondary waves to be
created, which the interfere with each other. Where crests and troughs of
waves coincide, destructive interference cancels out the waves.
Above: Wave interference at an aperture
The effect of this in a telescope is that the light from a star does not drop
off smoothly at the edge of the star image, but in a rhythmic pattern of
interference. At certain points around the star image, destructive
interference causes rings of zero intensity.
Above: Diffraction pattern of a star image through a telescope and
profile of the image brightness
Just like the walls in the ocean wave example, an aperture, such as the edge
of a mirror, causes light waves to interfere. The diagram below shows the
two wave patterns that are set up by the edge of a mirror. Where the waves
cross, there is constructive interference and the light is amplified, producing
the bright rings of the diffraction pattern. Halfway between these spots,
waves cancel each other out, causing destructive interference and forming the
gaps in the diffraction pattern.
Above: How the edge of a mirror creates a diffraction pattern
The resulting effect, assuming no other aberrations, is for about 85% of the
light from a point source to be located within the bright central spot of the
diffraction pattern. This central spot is called the Airy disk. The
outer rings are progressively fainter and are difficult to see under normal
conditions. The first bright ring outside the Airy disk contains less than
2% of the light from the source, and the rest are dimmer still. The
effective resolution of a telescope can then be considered the size of the
central disk in the diffraction pattern.
The size of the Airy disk can be determined mathematically.
Specifically the angular diameter of the disk is A = 1.22λ/D
radians, where λ is the wavelength of the light. As will be described
later, the human eye is most sensitive to a wavelength of 550 nanometers (nm),
in the yellow-green part of the visual spectrum. Converting to the more
useful angular measure of arcseconds, this gives a simple equation: A =
5.45/D, for a telescope diameter in inches. It can be seen that the larger
the telescope aperture, the smaller will be the Airy disk and the greater the
resolution. As an example, the resolution of an 8" telescope is 0.68
arcseconds. A 12" telescope has a resolution of 0.45 arcseconds. For reference, Jupiter is about 45 arcseconds in diameter.
The effect of
central obstruction, such as that
caused by the secondary mirror in a Newtonian or Cassegrain telescope, is to
transfer more light from the Airy disk to the outer rings. An extreme
example would be a 50% central obstruction. This would cause the first
ring to become 4 times brighter while the central disk would drop in brightness by a
factor of 2. It also has the interesting effect of reducing the diameter
of the Airy disk to about 80% of its unobstructed size. However, instead
of the brightness difference between the disk and first ring being a factor of
50, it is reduced to only a factor of 10. Overall the image quality is
worse, despite the smaller Airy disk size.
To obtain the most detail out of your telescope, it is critical to choose the
right magnification for the object being observed. Some objects will
appear best at low power, some at high power, and many at a moderate
magnification. This section will describe why different magnifications
work better than others, and give information on how to choose the appropriate
power for your viewing.
There is a lowest useable magnification on a telescope. This is
determined by the exit pupil of the optical system
and the size of the observer's pupil. The exit pupil is the diameter of
the beam of light produced by the telescope/eyepiece combination. The
lower the magnification, the larger the exit pupil. Exit pupil is
calculated easily by dividing the telescope's aperture (in millimeters) by the
magnification. Thus, an 8" (200mm) telescope operating at 50x has an exit
pupil of 4mm. At 100x on the same telescope, the exit pupil shrinks to
2mm. The minimum magnification is limited by the size of the observer's
eye. If the observer's pupil is smaller than the exit pupil of the
telescope, the beam of light is cut off and the effective aperture of the
telescope is reduced.
Above: Decreasing magnification (or increasing aperture) increases exit pupil size. If the
exit pupil is too large (right), the observer's pupil will restrict the
effective aperture of the telescope.
On average, the pupil of the eye will open to a maximum of 7mm. This is
age-dependent, so observers in their teens and twenties may have pupils as large
as 7-8mm, while middle aged observers will have pupils in the 6-7mm range.
By age 80 the pupil opens only to 3.5-5mm. In general, a 7mm exit pupil is
assumed. To determine minimum magnification, calculate the magnification
that yields a 7mm exit pupil. This is simply the telescope's aperture in
millimeters divided by 7. The table below gives minimum useable
magnifications for different apertures.
This calculation assumes that the telescope is capable of a magnification
this low. There are a couple restrictions that might prevent this. A
telescope with a very long focal length may require a longer-focal-length
eyepiece than is possible. For example, an 8" SCT with a focal length of
2032mm requires a 70mm eyepiece to reach 29x. Eyepieces longer than 55mm
are very uncommon. Additionally, even if such an eyepiece were available,
telescopes with large central obstructions, such as SCTs, suffer from an effect
where very low magnifications allow the central obstruction to be seen in the
image. Refractors, having no central obstruction, do not suffer from this
effect and make excellent low-power, wide-field instruments.
The most common telescope myth is that more power is better. And while
this is usually untrue, there are some instances where a very high magnification
is useful. The important thing to bear in mind is that the highest useable
magnification is most often restricted by atmospheric turbulence. You will
normally run into the limit imposed by seeing conditions before reaching the
telescope's optical limit. On nights of excellent seeing, however, pushing
the limits of power can be useful for certain types of observation.
The obvious use of high power is viewing the planets. Magnifications
more than 30x the telescope's aperture in inches are usually impractical for
planetary observation. Most observers find this is sufficient to see all
available detail. More magnification makes the planet appear larger but
not necessarily more detailed. On an 8" telescope, 30x per inch of
aperture produces 240x. This would make Jupiter appear 3°
across, or six times the size that the full moon appears to the unaided eye.
The exception to this is smaller telescopes, which can be used at higher power
per inch, often 40x to 50x. The table below shows recommended
magnifications for viewing the planets with telescopes of different apertures.
Higher magnifications can be used for viewing
double stars and, as the next
section shows, some deep-sky objects. Very close double stars may allow
magnifications up to 50x or 70x per inch of aperture, as long as the separation
is above the resolution threshold of the telescope. An 8" telescope, for
example, has a resolution of 0.68", and empirical data show that double stars
can often be detected when their separation is about half the telescope's
theoretical resolution due to the nature of diffraction patterns. This
means an 8" scope should (in theory) be able to detect double stars as small as
about 0.4". This depends greatly on the quality of the optics,
collimation, seeing conditions, the observer, and the
magnitude difference between the stars.
Again, smaller telescopes can tolerate more power. The table below gives
the maximum theoretical magnification for various telescopes.
There are several ways to determine the ideal magnification
for viewing an object. One simple method is based on the resolution of the
telescope. The human eye can typically resolve objects with an apparent size of 1
arcminute. The magnification required to enlarge details at the
telescope's resolution to 1 arcminute is 13x the aperture in inches. For
an 8" telescope this is 104x. Empirical evidence suggests that an exit
pupil of 2mm produces very detailed views of most deep-sky objects. A 2mm exit pupil
requires a magnification of 12.5x per inch, confirming the above theory.
A more complex theory for the best deep-sky magnification is based on the
human eye's response to contrast. The contrast between the sky background
and a faint celestial object is critical for observation. An object whose
surface brightness is such that the contrast between it and the sky is below the
eye's detection threshold will be invisible. Observers have noted that
low-contrast objects are often easier to detect at higher magnifications.
It is often assumed that this is due to higher power increasing contrast, but
this is not true. The relative contrast between the object and the sky
background is unchanged by magnification (each is affected equally).
However, the eye is more sensitive to low-contrast objects when they appear
Above: As the apparent size of an object increases, the contrast
necessary to see it decreases. Adapted from Clark.
This feature of the eye's response to contrast implies that more
magnification should make an object easier to detect. This turns out to be
true, although there is an upper limit. At some point, the surface
brightness of the object starts to decrease faster than the eye's detection
threshold. There is an ideal magnification, determined by what Roger N.
Clark calls the "optimum magnified visual angle." In his excellent book
Visual Astronomy of the Deep Sky, Clark describes the optimum magnified
visual angle (OMVA) as "the maximum magnification that will help detection."
The value of the OMVA is a function of the sky conditions, the surface
brightness of the object, the size of the object, and the telescope aperture.
Clark dedicates a lengthy appendix in his book to describing the iterative
calculation procedure. Suffice to say for our purposes there are some
generalizations that can be made.
In general, a smaller telescope will require a higher magnification to detect
an object. This is an interesting result and should be kept in mind by
observers using smaller instruments. For many objects, the optimum
magnification for a 6" telescope is 40% greater than for an 8" telescope.
If using a smaller telescope and an object is not seen, trying a higher
magnification may reveal the object. This is counterintuitive to the idea
that lower power yields a brighter image. While this is true, the contrast
effects of the human eye actually allow faint objects to be seen better at
higher power even though this causes a loss of surface brightness.
For a given telescope, the following rules apply. For small objects
with low surface brightness (such as galaxies), use a moderate magnification.
For small objects with high surface brightness (such as
planetary nebulae), use
a high magnification. For large objects regardless of surface brightness
(such as diffuse nebulae), use low magnification, often in the range of minimum
magnification (as described above). Specific recommendations for various
telescopes are given in the table below.
The Human Eye
An understanding of how the human eye functions can give you an edge in
getting the best visual observations. The human eye is a very
sophisticated and quite impressive organ which can adapt to an amazing array of
conditions. We are capable of seeing in both sunlight and moonlight
despite the full moon being half a million times fainter than the sun.
This huge dynamic range allows us to see detail in the moon and planets as well
as subtle swirls and spiral arms in dim nebulae and galaxies. The workings
of the eye can be used to definite advantage, so some of the structures and
visual adaptations of the eye, and how they factor into observing, are related
Above: The inner workings of your most important observing tool
Rods and Cones
The eye can be thought of as analogous to a telescope. The lens focuses
light onto the retina, just as a telescope lens would focus light onto a
plane. Putting a camera at the telescope's focal plane captures the light
just as the eye's retina does. And like a digital camera or CCD, the
retina is divided into "pixels" made up of light-sensitive cells called
cones. The differences between these two types of cells determine how the
eye sees things, especially celestial objects.
Rods are sensitive only to black and white, while cones come in three types,
each sensitive to a different color: red, green, and blue. Cones are
concentrated in the center of the retina, while rods form the periphery of the
Above: Color-sensitive cones occur in the center of the retina, with
black-and-white rods surrounding them
An important distinction between rods and cones is that cones
are sensitive to high light levels but not to dim light. This has a significant effect
on what you can see through a telescope. Since most astronomical objects
are dim, the light from them does not stimulate the color-sensitive cones.
This is why most deep-sky objects appear black and white. While these
objects have color, as any deep-sky photograph will show, the color is too faint
to be detected by the human eye. Brighter objects such as the planets and
bright stars can easily stimulate the cones and appear in color.
Some deep-sky objects are bright enough to stimulate the cone cells.
However, the eye's sensitivity to color changes in low light levels. The
peak wavelength to which the eye is sensitive shifts toward the green part of
the spectrum. Also, red and blue sensitivity drop off dramatically.
The diagrams below show the sensitivity of the human eye in bright light and low
light. Bright light vision is termed photopic, and low-light vision
is called scotopic.
Above: Photopic--daylight--response of the human eye
Above: Scotopic--night--response of the human eye. Note the loss
of sensitivity to blue and red wavelengths.
This shift in color sensitivity means that even if an object is bright enough
to stimulate color receptors, the dominant color will be green. In fact,
the deep-sky objects that tend to show the most prominent color are planetary
nebulae. This is because planetaries emit 57% of their light from excited
oxygen atoms, which give off light in the green part of the spectrum to which
the eye is most sensitive. Most observers see planetary nebulae as
blue-green in color.
Another effect of the difference between rods and cones comes from both their
relative sensitivity to light and their placement within the retina. When dark
adapted, rods are nearly 40 times more sensitive to light than cones. This
allows them to see four magnitudes fainter than the cones. However, since
the cones are concentrated in the middle 10% of the retina and the rods are
almost exclusively outside this zone, the eye is least sensitive in the center
of its vision and more sensitive to light falling outside the middle of the eye.
Averted vision is a technique where the observer intentionally looks to the
side of an object rather than directly at it. This places the light from
the object onto the rods rather than the cones, increasing the ability to see
it. Most of the rods are concentrated just outside of the center of the
retina, the peak occurring about 20° off axis.
This implies the best view of an object will occur when it is slightly, but not
excessively, offset from the center of vision.
There is a blind spot in the eye, where the
optic nerve attaches. This blind spot sits about 15° to 20° away from the
center of the eye, in the direction of the ear. Observers should thus
avert their vision in the direction of the nose to avoid placing the light from
the object onto the blind spot.
Everyone is familiar with the effect of the pupil opening wider upon entering
a dark room. This change takes only a few seconds, as you can see using a
mirror, a dark room, and too much free time. The pupil opens from about
2mm to 7mm. This increases the light gathering ability of the eye only
about 12 times. This is certainly not sufficient to account for the huge
range of brightness the eye can accommodate.
In addition to the physical change of widening the iris to allow more light
in, there are chemical changes that take place to account for a
several-thousand-fold increase in sensitivity. A chemical called rhodopsin
is generated as the eye adapts to the dark. The greater the amount of
rhodopsin, the greater the sensitivity of the rods and cones. Most of the
chemical change occurs within half an hour. This amount of time should be
allowed by the observer for dark adaptation before trying to observe very dim
objects. Dark adaptation continues for as much as two hours. The
ability to dark adapt is affected by exposure to bright light beforehand.
Spending long periods of time outdoors in bright sunlight can hinder the ability
to fully dark adapt for as much as several days.
As mentioned above, the pupil can expand through a range of diameters, from
less than 2mm to as much as 8mm. As we age, the pupil's maximum size
decreases. The average adult observer will most likely have a maximum
pupil size of 7mm. Older observers may only have 4-6mm maximum pupil
Pupil size affects a number of aspects of observing. Foremost it
determines the size of the beam of light the eye can accept. If the beam
coming from the telescope (the exit pupil) is larger than the pupil of the eye,
some of the light is blocked and the effective aperture of the telescope is
reduced. (See the exit pupil diagram above.) For example, if an 8"
telescope is used at 25x, the exit pupil will be 8mm. If the observer only
has a pupil size of 6mm, the effective aperture of the telescope is reduced to
The image quality of the human eye (ignoring for now any
defects such as astigmatism, etc.) is determined by the diameter of the pupil.
A larger pupil diameter increases the aberrations present in the eye.
While there is little to be done to control the pupil size of the eye while
observing, what can be controlled is the exit pupil of the telescope. Even
if the observer's eye is opened to 7mm, if the exit beam from the eyepiece is
smaller, only that much of the eye is used, and the effect is the same as if the
pupil were actually opened to that size. For example, a 2mm exit pupil
uses only 2mm of the eye, even if the actual pupil size is much larger.
Significant aberrations such as astigmatism are very dependent on exit pupil size.
Since these types of aberrations tend to minimize as the eye's pupil shrinks,
using higher magnifications on a telescope has the effect of using a smaller
portion of the eye and thus reducing aberrations. For this reason, most
observers with astigmatism find they must wear their glasses (or use corrective
optics on the eyepiece) when viewing at low powers and correspondingly large
exit pupils. However, when viewing at high power, glasses may not be
required due to the reduction in apparent aberration thanks to the smaller exit
In a digital or CCD camera, the spatial resolution is a
function of the pixel size on the CCD chip. Similarly, the resolution of the
human eye is dependent on the size of the cells in the retina. At the
center of the eye--the fovea--the smallest and most concentrated cone cells are
located. The average size of these cells is 1.5 microns. Compare
this to the typical 5-10 micron pixel size of most CCD chips. This works
out to a theoretical resolution of about 20 arcseconds. However, under
dark adapted conditions the pupil is opened to its maximum size and is subject
to more aberrations. This limits the resolution of the eye to about 60
arcseconds, or 1 arcminute. This implies that an object, such as a lunar
crater, which is 1 arcsecond across, when magnified 60 times, should be just
visible to the eye. This assumes, of course, that the telescope is capable
of resolving the object to begin with. For example, an object 0.2
arcseconds in size, magnified 300 times, would appear 60 arcseconds across.
However, 0.2 arcseconds is below the resolution threshold of any telescope
smaller than 27 inches in diameter.
Certain objects, such as close double stars or thin linear
features, may be visible below the threshold of both the telescope optics and
the observer's eye, due to the effects of diffraction, the stimulation of larger
numbers of cones, reduction of pupil size when viewing bright objects, and
contrast effects. From personal experience, using a high quality
telescope, the author has seen a 0.6-arcsecond double star clearly defined in a
6" telescope, which has a theoretical resolution of only 0.9 arcseconds.
As contrast lowers, the resolution of the eye decreases, so planetary detail may
not be as finely resolved as stellar or lunar details. The same is true of
Observing with a