This is a tool for the telescope user based
on JavaScript software, which will compute the values of a number of paramaters
for any telescope and eyepiece combinations. It starts off with some basic
information every telescope user should know for their equipment, and continues
into some more complex calculations.
Insert data in the white field, then press the "Enter
Diameter" button for whichever measurement system used. The computed
values will appear in the other boxes. To try different eyepieces, enter
their info in the Eyepiece Specifications field(s), and use the adjacent
buttons to re-compute the outputs.
Objective Diameter: the size of the main
light-gathering ("primary") lens or mirror of telescope (also
called the telescope's "aperture").
Focal Length: the effective Focal Length
of telescope is important to know; it is often listed on a label right
on the telescope, sometimes as Fl, and usually in millimeters. It is equal
to the Focal Ratio (f number) times the Objective Diameter.
f Ratio: the Focal Ratio (f number) is
the Focal Length divided by the Objective Diameter. Just as in camera lenses,
telescopes with lower "f numbers" are "faster"; they
form brighter (but smaller) images than telescopes of the same diameter
with with higher f numbers.
Eyepiece Focal Length: this determines
the "power" an eyepiece delivers on a given telescope; the shorter
the focal length, the higher the magnification. Usually noted as a number
on the eyepiece itself, normally measured in millimeters.
Eyepiece Apparent Field: when you put
your eye up to an eyepiece, this is the angular diameter (in degrees) of
the circle of view you see through it. It can vary from less than 50° to
more than 80°, depending on the eyepiece design. Find this out from
the manufacturer or seller of the eyepiece. If that is not possible, Apparent
Field can be approximately computed by measuring the diameter of the Field
Stop in the eyepiece; it is the aperture (opening) usually located up inside
the eyepiece barrel on the telescope side of the eyepiece (but may be internal
and not accessible in some wide-field eyepieces). Here is the approximate
Field Stop diameter for your eyepiece, based on the Apparent Field entered
above; if you replace this number with an actual measurement and click
the Enter Measured FS button, we'll recompute your Apparent Field based
on this measurement.
Magnification (power): how many times larger
(in angular size) an object looks through the telescope than it would look
to the unaided eye. For example, at 50x (fifty power, fifty times magnification),
the Moon (or whatever you're looking at) looks fifty times bigger across
than it does to the naked eye.
Exit pupil: the diameter of the beam of
focused light shining out of the eyepiece. This figure is important, because
if the beam is larger across than the pupil (the dark window) into the
eye, some of the light from the telescope won't make it in for You to see
it. In that case, the telescope would be performing like a smaller telescope
(sometimes much smaller). See the section below for more information on
your pupil size.
True Field: the angular diameter of the
part of the sky you can observe through the telescope. In other words,
if the Moon is one-half degree across, it will just fill the view through
a telescope/eyepiece combination which delivers a true field of 0.5°.
Can be measured in Degrees or Minutes of Arc (arc-minutes).
Field Transit Time: a product of the True
Field, this is how long it will take a star, located near the celestial
equator, to drift across the center of the field from one edge to the other
(when the telescope is not clock driven to follow the sky). This gives
some idea of how fast something will drift to the edge from the center
of the field (half of the full Field Transit Time).
The above computations are a good start to exploring the
properties of various telescope/eyepiece combinations, and are especially
important to make when you are selecting new eyepieces for a telescope
(to make sure the resulting system will really be useful). To go beyond
the basics, and explore what you should be able to see through your telescope,
continue on below.
It is important to note that there are a number of factors
which effect what one will actually see through a telescope, including:
the condition of the atmosphere as far as its clarity (transparency) and
steadiness (seeing); the amount of light pollution in your sky and in your
immediate neighborhood; the quality of the optics in your telescope, eyepiece,
and indeed, those in your eye itself. These variables cannot all be accounted
for here, but you may find some of these theoretical calculations helpful.
Please, be sure the telescope and eyepiece information is filled correctly
above.
1. Determine the pupil size
To best match your telescope/eyepiece combination for your
use, you have to know how wide the pupil of your eye can open in the dark.
On average, this maximum decreases as we age; while the average teenager's
pupil can dilate to 7.5 mm., the average 78 year old's eye can only reach
about 5 mm. Enter the age below, and this program will show an average
value for your age group. If you actually know what your maximum pupil
dilation is, you can correct the data (the actual measurement might vary
as much as a millimeter from the estimated value).
Remember your maximum pupil diameter when studying eyepiece/telescope
combinations with the top table. Again, if the Exit Pupil a given combination
delivers is larger than the maximum diameter of your eye's pupil, not all
of the light the telescope gathers and focuses will make it in to your
eye to be seen.
2. Theoretical Magnitude limits your telescope
Based on the telescope information entered in above, the
tables below gives some figures for what its performance capabilities might
be. The actual performance you will get, as noted above, will be dependent
on not only these theoretical limits (which you may actually surpass under
the right conditions), but also on variables in the atmospheric conditions,
your eyesight and observing skill, and the quality of your optics. Magnitude
is the measurement of the brightness of an astronomical object; the lower
the number, the brighter the object is (the faintest stars you can see
in from in town may be 3.rd magnitude, while out in the country you might
see 6.th magnitude ones; the brightest stars actually have negative magnitudes:
Sirius is -1.4).
This value is complicated by the fact that magnification
also dims the brightness of the sky background, increasing the contrast
of stellar objects to the background. When stars are magnified (within
the "optimum" magnification range of a telescope, as described
in Section 4, below), they remain as "points", so changing magnification
within that range does not strongly effect the apparent brightness of stars
and other stellar objects. Therefore, the actual limiting magnitude for
stellar objects you can achieve with your telescope may be dependent on
the magnification used, given your local sky conditions.
Other types of objects are rated with the same magnitude
scale, based on the total amount of their light that reaches us; if the
object is large, though, that light is spread out over an area. In other
words, an 8.th magnitude star and an 8.th magnitude galaxy put equal amounts
of light into your eyepiece, but the light from the star is concentrated
into a bright "point", while that of the galaxy is spread over
a larger area, and will be harder to see.
For such extended objects, the object's surface brighness
decreases at the same rate the sky's does as magnification is increased,
so there is no improvement in contrast from magnification (as opposed to
stellar objects, as noted above). Instead of listing a limiting magnitude
for extended objects (since that would actually have to be based on an
object's brightness per unit surface area, not its total magnitude), we'll
give a "Brightness Factor" for the achieved surface brightness
of an object viewed through your telescope, comparing to its surface brightness
through the telescope to what you'd see with your your unaided eye. Surprisingly,
our telescopes are not providing (once the image is magnified) a higher
surface brightness than the unaided eye does; all that light gathering
power is going into providing a bigger image.
If the above factor is 1, when you look at the Moon (for
example) through the telescope, the image there will have the same average
surface brightness per square arc second as the Moon does to your unaided
eye (although the image will be much larger in angular size, of course,
through the telescope). If the value is less than 1, the surface of the
Moon (or whatever object) will be dimmer by that factor per unit of surface
area than it appears to your unaided eye. If the value is over 1.0, then
the exit pupil for your selected telescope/eyepiece combination is larger
than your eye's pupil, and this would cause light loss, bringing the achieved
Brightness Factor back down to 1 (or potentially less, especially in reflecting
telescopes with central obstructions).
As you change the eyepiece values, note that the brightness
factor will go down at higher powers, and up at lower ones. As noted, even
though higher magnifications will make extended objects look fainter, they
can still be useful in observing some fainter objects because: 1) the eye
can spot moderately large faint objects with more ease than it can tiny
ones and; 2) it may be easier to spot a faint object against a blacker
sky (even if the actual sky/object contrast is no greater). Overall, the
Brightness Factor can give some guideline as to how relatively bright a
particular object will look in different telescopes and at different magnifications
(all other observing conditions being the same).
3. Theoretical Resolution limits for your telescope
The Resolving Power for a telescope tells what the size
of the smallest details which can be seen through it, atmospheric conditions
allowing. Beyond a certain point (usually accepted to be 0.5 arc seconds
for locations at our altitude), the atmosphere always prohibits seeing
any smaller details, even if the telescope's optics could deliver them.
Indeed, our seeing often creates a resolution limit well above this level.
As an example of resolving power, if you can look at two
stars (of similar brightness) which are just 1 arc second apart in the
sky, and see the two separated (not blurred together into one point of
light), your telescope is resolving 1 arc second detail. Again, the figure
shown is based on the telescope information entered above, and actual performance
will vary with other factors as noted earlier.
Applying that theoretical resolving power we've computed
to an astronomical object, our Moon. What is the smallest feature you can
theoretically resolve on the lunar surface, near the center of the Moon's
face, if your observing conditions, telescope optics, and eyes are all
top-notch?
4. Other eyepiece considerations
Experienced observers have found that using eyepieces which
deliver Exit Pupils in the range of 2-4 mm. usually give the best images,
especially when observing faint objects. Indeed, diffuse, low brightness
objects may sometimes be seen within this range, and invisible outside
of it. For brighter objects, such as the planets, higher magnifications
may be desirable, but the sharpest appearing views will still probably
be found within this range.
For larger objects, which need a larger True Field for you
to see their full extent, lower magnifications can certainly be used (watch
out for oversized Exit Pupils, though); but for the best picture, you might
want to consider using an eyepiece within this range which has a larger
Apparent Field to reach your desired True Field.
5. Airy disk and image scale
Note that some telescope manufacturers
will often advertise the magnification of the scope, and give really big,
impressive numbers. The problem is that the number is essentially meaningless.
The magnification of a telescope is a combined function of the scope and
the eyepiece that is used, so the user can set the magnification to almost
any arbitrary value by selecting a suitable eyepiece.
Whether the resulting image is clear, or barely visible,
depends on other properties of the telescope. Therefore the magnification
is not the most important measure of a telescope. What actually is the
most important measure is the diameter of the objective, or more simply
the scope diameter, because that determines both the resolving power and
the light-gathering power.