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<table width=75% cellpadding=3><tr><td>
<p><i>"There is hardly anything in the world that
some man can't make a little worse and sell a little cheaper, and the
people who consider price only are this man's lawful prey." - John Ruskin
</i></td></tr></table>

<p>
<font size=4 color=ff0033><b>WARNING!!!</b><br> Never use a
telescope to look directly at the Sun.<br> Doing so will lead to permanent
blindness!<br>Very special equipment is required to do solar observing
safely.</font>
</p>
</center>

<p>
Purchasing a telescope places many people at the mercy of the
manufacturer, especially those who have little or no previous experience
with these optical instruments. The purpose of this information sheet is
to explain the important issues relating to telescope design and to offer
guidance on the selection of an instrument that will best meet your
particular needs.</p>

<p>
Regardless of specific design, there are several optical
characteristics that relate to the successful purchase of an instrument
which will provide years of future enjoyment in astronomical observation.
Likewise, there are misconceptions that some manufacturers exploit in
order to sell substandard equipment to the public.  Let's first explore
some of these issues.</p>

<h2>Power-- A Major Misconception</h2>
<p>
Most inexperienced telescope buyers suffer from the misconception that
"power" or "magnification" is the most important criterion in judging a
telescope.  The uninitiated person almost always assumes that the higher
the magnification of an instrument, the better.  Realizing this, some
manufacturers emblazon their telescope advertising and packaging with such
claims as "475 power" or "475x", and the like.  This sort of claim is most
often found with small "department store" refractors.</p>

<p>
In reality, most experienced observers gravitate toward lower
magnifications, rather than higher ones.  The reason is simple: the lower
the magnification, the sharper and brighter the image. In addition, lower
magnification displays a wider area of the sky, and this in turn, slows the
tendency of an astronomical object (star, planet, etc.) to drift out of the
field of view-- an apparent motion caused by the Earth's rotation.  Also,
any instability-- or jiggle-- in the telescope and its mounting is
amplified with higher and higher power views.  This makes higher powers
more difficult to use, as even the slightest touch of a finger to the
instrument-- particularly one on a flimsy mount-- can cause the image to
bounce around annoyingly.  Furthermore, atmospheric turbulence plays havoc
with higher power viewing, while this "boiling" effect is much less
prominent under lower magnifications.</p>


<h2>Light-- Gathering and Focusing</h2>

<p>
Rather than magnification, a much more important telescope
specification is its <b>aperture</b>.  Simply put, aperture is the
diameter of the main optical element, or <b>objective</b>, of the
instrument (the main lens in a refractor telescope, or main mirror in
reflector). In even simpler terms, the fatter the telescope, the larger
the aperture. A major purpose of a telescope is to gather more light than
the eye alone can see, and the bigger the scope's objective, the more
light-gathering ability it has. The larger the aperture, the fainter the
sky object that can be seen.  This is particularly important when
considering that the light-gathering of a telescope objective is
proportional to the area of the lens or mirror (and to the pupil of the
human eye).  Therefore, a two-inch objective will gather four-times the
light of a one-inch objective, and a three-incher will gather nine-times
the light of the one-inch model.  This effect takes on added significance
when you factor-in that a one-inch lens-- having a diameter three-times
that of the pupil in a dark-adapted human eye (about 1/3-inch) gathers
nine-times the light of the eye alone.  Using this relationship, it soon
becomes apparent that a three-inch objective will gather about 90 times
the light of the eye alone, and a ten-incher can gather 900 times the
light of the naked eye. <i>Of course, telescope size also has a practical
impact upon convenience. A big scope is great for viewing, but is of
little real use if-- given your particular circumstances-- its large size
makes you unable or unwilling to transport and set it up.</i></p>

<p>Aperture is also a major factor in determining the maximum
magnification of a given scope.  Although the selected pairing of a
telescope and an eyepiece can <i>theoretically</i> gain you extremely high
magnification, there is a practical limitation to power.  For most
telescopes, the rule of thumb is that you can only expect to get up to
about 50 power (or 50x) per inch of scope aperture (or about 2x per
millimeter of aperture) of <i>usable magnification</i>.  And this rule is
only for ideal viewing conditions, which is seldom the case.  In fact,
turbulence in the atmosphere generally lowers this to an average limit of
about 25x per inch of aperture (1x per millimeter).  Going back to the
example of the typical department store scope-- which usually has an
aperture of 2.4 inches (60 mm)-- the maximum usable magnification of such
an instrument is really only about 120x under ideal viewing conditions, or
about 60x under more average viewing conditions.  This is a far cry from
the 400-500x claims of these scopes' manufacturers!</p>

<p>Along with aperture, the most critical specification for a
telescope's
optical performance relates to its <b>resolution</b>, or how accurately the
lenses or mirrors are manufactured.  This is usually referred-to as the
lens' or mirror's <b>wave-number</b>.  For a telescope to work, its
lens(es) or mirror(s)  must be able to bend light in a precisely-controlled
fashion.  A good lens or mirror should be able to bend the light
intersecting its edges as well as at its center-- and all points in
between-- in such a way that all that light is accurately focused to almost
precisely the same point from the lens or mirror.  However, no lens or
mirror is perfect, and the measure of this imperfection is expressed in
<i>fractions of a wavelength</i> of light. The smaller the fraction, the
better the lens or mirror.  For instance, a mirror rated at 1/16-wave
accuracy is considered much better than one measured at 1/2-wave. A good
telescope objective lens or mirror should always be rated at 1/8-wave or
better.  In fact, since wave-error is cumulative within a telescope, any
smaller secondary optical surfaces-- such as the flat diagonal mirror in a
Newtonian reflector-- should be rated at 1/16-wave or better to maintain
good optical performance.</p>


<h2>Long or Short, Fat or Skinny-- Focal Length and Focal
Ratio</h2>

<p>
There are other telescope characteristics to watch for, as
well. These are
<b>focal length</b> and <b>focal ratio</b>.  Unlike wave-number, however,
these specifications have less to do with absolute optical quality than
with the types of observing for which the instrument is best suited.  Focal
length refers to the distance from the objective lens or mirror where the
light converges to a focus within the scope.

<a class=small href="flength.gif">see diagram</a>

Together with a suitable eyepiece, a longer focal-length telescope
objective can deliver a higher-power view than a scope with a shorter
focal length and a similar eyepiece.  (Note that the final image
magnification is also dependent upon the eyepiece's focal-length.)</p>

<p>Focal ratio, or f-ratio refers to the relationship between
a telescope's
focal length and its aperture.  A telescope with a focal length many times
longer than its aperture-- a comparatively long, skinny scope-- will have a
high f-ratio.  On the other hand, an instrument with a comparatively short,
fat tube will have a low f-ratio. 

<a class=small href="fratio.gif">see diagram</a>

(Rough assessment of a scope's f-ratio
by external visual appearance becomes more complicated, though, in the case
of instruments such as a Schmitt-Cassegrain.  In this case, the folded
light-path within the telescope means that the instrument can have a higher
f-ratio but a short, fat tube.) F-ratio is calculated by dividing the
scope's focal length by its aperture.  For example, a telescope with a
1000mm focal length and a 125mm aperture has an focal ratio of <i>f/8</i>. 
On the other hand, an instrument with a 560mm focal length and a 125mm
aperture has a focal ratio of about <i>f/4.5</i>.  Telescopes which are
around <i>f/10</i> or higher are considered optimal for higher-power lunar
and planetary viewing and for splitting double stars, while instruments
that are <i>f/6</i> or less-- particularly those with larger apertures--
are optimized for lower-power, wide-field (rich-field) views of nebulae,
star clusters, and other deep-sky objects.  Falling right in between,
<i>f/8</i> scopes are considered a decent compromise between the other two
types, and make good instruments for all-around viewing.</p>

<h2>Telescopes-- The Major Types</h2>
<p>
Telescopes available for amateur astronomers these days can
be divided into three major categories: the <b>refractor</b>, the
<b>reflector</b>, and the
<b>catadioptric</b>. Each design has its advantages and disadvantages,
including issues relating to observing application, maintenance,
convenience, and cost.</p>

<p>The <a href="refractr.gif">refractor</a>
uses a large lens for its objective, placed at the front of
the telescope tube.  This lens focuses the light down into a small image
near the rear-end of the scope, where the eyepiece enlarges that image.
Refractors-- especially those with higher f-ratios-- are optimized for
higher-power views of the Moon and planets, and are good for splitting
double stars, because they have no internal obstructions like secondary
mirrors which can diffract light.  Good-quality refractors are probably the
best telescopes that money can buy.  On the down side, a high-quality
refractor tends to be quite expensive, due to the larger number of optical
surfaces present in its achromatic lens which must be precisely
manufactured.  In fact, good refractors carry with them the highest
cost-per-unit-of-measure of aperture of all telescope types.  Although
there are inexpensive, small-diameter refractors which can be found as
"department store" telescopes, these are often of substandard quality, and
should be avoided, if possible.</p>

<p>The <a href="reflectr.gif">reflector</a>
uses a large parabolic mirror at the rear-end of the
telescope to focus light back up toward the front of the tube.  In the case
of the popular <b>Newtonian</b> reflector (named for Sir Isaac Newton, who
invented it), that light is intercepted by a smaller, flat, secondary
mirror (positioned diagonally), and reflected out through an opening in the
side of the tube to the eyepiece. Newtonian reflectors are the best
telescopes for those wanting high-quality on a budget. It's not uncommon
to find quality Newtonian scopes with six- to ten-inch diameter apertures
for just a few hundred dollars. No other telescope can touch the
quality/cost ratio of a Newtonian reflector. As far as disadvantages,
Newtonian reflectors do require occasional <b>collimation</b>, or optical
alignment of their optical elements, in order to maintain peak performance.
Reflectors can also suffer from <b>coma</b>, a characteristic which makes
stars near the outer edges of an eyepiece field look like slightly
elongated blobs rather than pinpoints of light. However, coma is generally
not objectionable in f-ratios of <i>f/8</i> or higher, and in lower f-ratio
instruments a higher-quality eyepiece can help minimize coma as well.</p>

<p>
Finally, the catadioptric telescope has a lens-- called the
corrector plate-- up front, and large mirror at the rear. Additionally,
this design has a smaller, convex secondary mirror just behind the
corrector plate which folds the light-path and reflects the light back
down to the rear of the scope-- through a small hole in the large mirror--
and into the eyepiece behind.  Catadioptric telescopes-- 

<a href="schmcass.gif">Schmitt-Cassegrains</a>

and

<a href="makscass.gif">Maksutov-Cassegrains</a>

-- offer convenience, in that their folded internal light paths make
for very compact instruments. This leads to scopes which are very
good for high-power viewing, with high f-ratios, but without the
long, cumbersome tubes found in comparable refractors and Newtonians.
Though the larger number of optical surfaces in a catadioptric scope tends
to lower image-resolution, tight manufacturing tolerances can minimize this
problem. Schmitt-Cassegrains are among the most popular of all telescope
designs for serious amateurs, and are most-often purchased in eight- to
ten-inch aperture models from manufacturers like Celestron and Meade.
However, the convenience of this design comes at a price: 
Schmitt-Cassegrains are generally around three-times the cost of a good
Newtonian of comparable diameter, and Maksutov-Cassegrains are even more
expensive.</p>

<h2>Finders</h2>
<p>
Finders are important for aiding in sighting-in objects through the
telescope. Lack of a good finder can make observing through even the best
telescope a frustrating experience. Finders can range from small simple
tubes to larger finderscopes. A finderscope is actually a small telescope
mounted and aligned with the main scope. A finderscope provides a
low-power, wide-field view of the sky, making it much easier to aim at
objects than with the relatively higher magnification (and narrower view)
of the main scope.  Finderscopes have crosshairs within the eyepiece to
facilitate precision aiming.</p>

<p>
The finderscope is often yet another pitfall associated with department
store telescopes. Many times, these finderscopes have very small,
low-quality objectives. In fact, some manufacturers of these cheap scopes
even try to reduce optical aberrations in their finderscopes by placing a
"stop-ring" behind the objective lens.  While this practice does cut down
on aberrations, it also has the side-effect of making images very dim.
Either way, such finderscopes are virtually unusable for most astronomical
applications. A good finderscope should always have an "achromatic"
objective lens with a diameter of at least 30mm. (For example, a 6x30
finderscope is a six power unit with a 30mm-diameter objective.)</p>

<h2>Eyepieces and Accessories</h2>
<p>
Few beginners give much thought to telescope accessories. But often, the
proper accessories can make the difference between enjoying a good
telescope and becoming frustrated by it to the point that the instrument
merely collects dust.  One perceived advantage of the department store
telescope is that it usually comes with what appears to be a complete set
of accessories.  Unfortunately, the inclusion of three or four eyepieces,
an image-erector, a finderscope, and other accessories along with a
telescope for less than $300, certainly means that quality is sacrificed.
In fact, lots of accessories at low cost is a sure sign of trouble.  You
should generally avoid these instruments.</p>

<p>
The first accessories needed to make a telescope work are 

<a href="eyepiece.gif">eyepieces</a>.

Usually, quality instruments come without, or with only a single eyepiece
(but rather than feeling that you've gotten cheated when buying such a
scope, you can probably assume that the scope [and eyepiece] are of much
better quality). Eventually, most telescope users will want to add to
their eyepiece collections, since eyepieces of different focal lengths will
provide different magnifications.  Again, remember that you should always
start out viewing an object under lower power.  This will give you the
sharpest, brightest image, and the accompanyingly wider-field view will
also make it easier to find objects.  As with telescopes, eyepieces come in
different designs.  They vary widely in price, and some are better than
others for certain applications.  And there are some eyepieces that are so
poor, you'll want to avoid them for virtually all uses.</p>

<p>
Keep in mind that magnification is dependent upon both the telescope's
focal length and the eyepiece's focal length. Simply divide the telescope
focal length by the eyepiece focal length to calculate the magnification.
For example, a 1000mm focal-length scope paired with a 20mm eyepiece will
provide a magnification of 50x.  On the other hand, a 10mm eyepiece on the
same scope will yield a magnification of 100x.</p>

<p>
There are three other things to consider when buying eyepieces: <b>optical
quality</b>, <b>field size</b>, and <b>eye relief</b>. Of course, optical
quality is pretty self-explanatory, though there are some specific things
to keep in mind, such as image <b>brightness</b>, <b>sharpness</b>,
<b>freedom from aberrations</b> (such as <b>chromatic aberration</b>, in
which images suffer from rainbow hues around the edges), and <b>flatness
of field</b>, in which stars at the edges of the eyepiece field are focused
at the same point of focus-mechanism movement as stars at
the center of the field.  Eyepiece field size refers to how large a visual
"window" the eyepiece provides, but is independant of magnification.
Instead, field size is a lot like seeing the world with good peripheral
vision as opposed to the view that you'd get looking through toilet-paper
tubes.  Cheaper eyepiece designs provide narrow field sizes, and give the
observer a restrictive "tunnel vision" effect.  Eye relief is the distance
you must place your eye from the eyepiece to see the entire field.  Better
eyepieces of a given focal length will provide a longer eye relief, which
is particularly useful for eyeglass wearers.  But shorter focal-length
(higher-power) eyepieces nearly always provide shorter eye relief than
longer focal-length models within the same class of optical design. 

In addition, always look for eyepieces which are "fully coated" or
multi-coated".  These refer to special coatings applied to the glass
elements of the eyepiece to enhance light transmission (which will make
objects look brighter) and minimize objectionable "ghost" images when
observing.</p>


<p>
Also, pay attention to an eyepiece's <b>barrel size</b>.
Most good telescopes use eyepieces with 1-1/4-inch barrels, while cheaper
scopes tend to have smaller .965-inch barrels. The two sizes are not
directly interchangeable.</p>

<p>
The cheapest and simplest eyepieces are <b>Huygenians</b> and
<b>Ramsdens</b>. These have only two lens elements each, and are rated poor
at best in optical quality, field size, and eye relief. Both designs date
back to the 1700s, but amazingly, are the eyepiece types that are nearly
always supplied with small refractor telescopes. (Most experienced
observers see these eyepieces as good only as small paperweights, and
therefore, should be avoided for use in all but the most non-critical
observing!)  The shorter focal-length units are simply unusable, as their
images are too dim and fuzzy.  Eye relief is extremely short with
Huygenians and Ramsdens, and field sizes of both are extremely narrow.</p>

<p>
The <b>Kellner</b> eyepiece is a three-element design good for f/10 or
higher telescopes, but doesn't perform as well on rich-field scopes (f/6 or
lower). While Kellners' field sizes tend to be a bit narrow, they are a
big improvement over Huygenians and Ramsdens. Also, short-focal-length
Kellners have uncomfortably short eye relief, making them less desirable
for high-power applications. Kellners are fairly low-cost, compared with
many other eyepiece designs.</p>

<p>
The three-element <b>RKE</b> is an Edmund Scientific proprietary design,
and is an improvement over the Kellner eyepiece.  Eye relief is good, and
the field size is moderately so.  This design represents a good balance
between performance and economy.</p>

<p>
<b>Orthoscopics</b>, <b>Erfles</b>, and <b>Plossls</b> all have four or
more elements each, and are considered excellent eyepieces in most
respects.  Of the three, the four-element Orthoscopic has a narrower field,
but gives some of the sharpest images available.  The five- or six-element
Erfle provides very wide, picture-window views of the universe, but suffers
from lack of edge-sharpness in the shorter focal lengths.  Erfles are
generally harder to find these days, as they tend to be rather expensive
and are surpassed in performance by some newer wide-field designs.
Four-element Plossls are among the most highly-regarded eyepieces around
today, and while more expensive than Kellners and Orthoscopics, are quite
reasonable when compared to the wide-field "connoisseur" eyepieces.
Optical aberrations in the Plossl are minimal, and eye-relief and field
size are very good.  The <b>Nagler</b> is the "Rolls Royce" of telescope
eyepieces. It is a super performer, providing some of the best views of
the night sky that can be experienced. Of course, this performance comes
at a steep price-- one that few observers can justify.</p>

<p>
Avoid the temptation to buy zoom eyepieces. Although it's always
interesting to enlarge or reduce the size of an object with the turn of a
knurled ring, that convenience is more than offset by degraded sharpness
and brightness, making the zoom eyepiece anything but a bargain.  Always
stay with fixed focal-length eyepieces.</p>

<p>
Good eyepieces cost money. Be prepared to spend at least $50 each for
quality ones. The good thing is that you can accumulate eyepieces one by
one, instead of having to buy an entire set at one time. Don't get cheap
after buying a good scope by purchasing substandard eyepieces. There are
few things that can make a good telescope perform more poorly than a cheap
eyepiece.</p>

<p>
A quality <b>Barlow</b> lens is one of the most valuable telescope
accessories you can buy. A Barlow is an image amplifier that fits between
the telescope and an eyepiece-- effectively turning low-power eyepieces
into higher-power ones. In fact, buying a quality Barlow is like doubling
your selection of eyepieces, for roughly the cost of a single eyepiece.
They usually come in 2x and 3x models. Another advantage of the Barlow
benefits eyeglass wearers. Instead of using a higher-power eyepiece which
has short eye relief-- a problem for viewing with eyeglasses-- the
combination of a low-power eyepiece and a Barlow provides the best of both
worlds, in that the observer can have the comfort of long eye relief for
wearing glasses and high-power views at the same time.  The third advantage
of a Barlow benefits rich-field scopes.  While these instruments normally
aren't optimized for higher-power viewing, the use of a Barlow/eyepiece
combination effectively raises the focal-ratio, thereby improving the
rich-field scope's high-power performance.</p>

<p>
Note that telescopes normally invert their images.  While <b>image-erector
prisms</b>-- devices that turn a telescope image right-side up again-- are
desirable for terrestrial viewing, they are not for astronomical
observation. Image erectors tend to dim the scope's image, and often make
it less sharp, too. However, since there's no real "up" or "down" in
space, astronomers don't care whether the image is inverted. They do,
however look for maximum image brightness and sharpness, as should you.
Therefore, avoid image erector prisms for astronomical use. Some telescope
designs, however, require the use of a star diagonal to place the eyepiece
in a comfortable position. While these devices do upright the image, they
also produce one that's inverted left-to-right.  Good star diagonals don't
appreciably degrade their images, though the cheaper ones can.</p>

<h2>Mounts</h2>

<p>
Like eyepieces, telescope mounts are often overlooked as an important issue
when purchasing.  Even if a telescope possesses good optical properties,
its performance will be discouraging if its mechanical parts are flimsy.
Once again, cheap scopes usually fall far short in this category.  While
most telescope mounts will work okay under very low magnification, any
shakiness or instability becomes apparent as soon as magnification
increases.  Always look for a really beefy mount when scope hunting.
Spindly-legged tripods and small, light-weight mount-swivels should be
avoided.  If you can, try checking the rigidity of the mount by putting-in
a higher-power eyepiece.  If the slightest touch causes the image to jiggle
infuriatingly, look for another model.</p>

<p>
Telescope mounts come in two basic designs-- 

<a href="altaz.gif">altazimuth</a>

and

<a href="equatorl.gif">equatorial</a>.

The altazimuth mount uses vertical and horizontal pivot points.  With
this mount, the telescope can be turned 360 degrees with respect to
the horizon and 90 degrees up and down.  The altazimuth mount is
good for terrestrial viewing, but can also be used for astronomical
observations of shorter duration and at lower powers.  Equatorial mounts
have a polar axis and a declination axis.  When properly aligned with the
celestial pole, rotation around the polar axis can directly follow the
apparent motion of sky objects caused by Earth's rotation.</p>

<p>
Altazimuth mounts are best for beginners and those whose astronomical
observing is best described as "casual".  Scopes with altazimuth mounts are
easy to set up and use, and require no special expertise to use properly.
Dobsonian mounts form a subcategory of altazimuths, and are used on medium-
or large-diameter instruments.  These mounts are inexpensively constructed
of materials such as plywood and heavy-duty plastics, and are very sturdy
and stable.</p>

<p>
Equatorial mounts are best for more-experienced observers, as they require
a bit more attention to detail set up.  However, these mounts can make
tracking sky objects easier-- especially good for extended high-power
viewing.  Such a mount can even be fitted with a "clock drive" motor, which
can automatically track sky objects.  The equatorial mount is a must for
astrophotography.</p>

<p>
It's important to become a knowledgeable consumer before buying a
telescope. Following these tips should help you to avoid frustration in
your first scope purchase.</p>

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