Matthew Buynoski's Eyepiece Expose
Eyepieces for the Beginner

No telescope is complete without eyepieces, and no astronomical accessory is so seemingly complicated, either. There are a million different ones, with a welter of different specs, available from a horde of manufacturers and distributors. No wonder the person starting out into astronomy gets a headache when they try to figure out what they need.

The purpose of any telescope is to show us celestial objects and the size that these objects appear is set by the magnification. In turn, the magni- fication is set by the focal length of your telescope and the focal length of the eyepiece in use with it. That is: 

    Magnification =  F/f           where: F is the telescope focal length
                                          f is the eyepiece focal length
Any given telescope will only support a certain range of magnifications, limited in one way or another by four things: 
          a. Telescope focal length
          b. Eyepiece diameter
          c. The unsteadiness of the atmosphere, or 'seeing'
          d. Telescope aperture
The lower end of the magnification range is controlled by the eyepiece diameter. Light coming out of the telescope must fit into the eyepiece, and smaller diameter eyepieces just can't fit in as much of it as their larger diameter cousins. This is similar to looking through a pipe; you can see a wider area through one a bigger one. For high magnifications this diameter limit isn't a problem because you're only looking at a small area of the sky, but it becomes important when you want wider fields of view.

There are three diameters of eyepieces usually sold. The smallest are 0.965" in diameter; they are the least common and is generally associated with small, less-expensive scopes (there are exceptions). Most popular are the 1.25" diameter eyepieces, and for most scopes these are perfectly adequate. Also commonly found are the 2" diameter eyepieces, especially among owners of longer focal length telescopes. The inside diameter is what actually limits the light (a slight fib, see Note 1), and it is a bit less that the outside diameter. We'll use 24mm, 31mm, and 50mm for the inside diameters of 0.965", 1.25", and 2" diameter eyepieces, respectively.

For the moment let's put off the question of which size to choose and explore a little on fields of view. The actual area of the sky you see when looking into the telescope/eyepiece combination is called the True field of view, or Tfov. However, optical designers can make this area appear wider or narrower, and the width as you look at it is called the apparent field of view, or Afov. This is a lot like watching television on a 10" or a 27" set. Both present exactly the same television show (same Tfov), but it appears larger on the 27" set (bigger Afov). We can relate both fields of view and the magnification in one simple relationship: 

  Afov = (F/f) * Tfov   where:  Afov is the apparent field of view, in degrees
                                Tfov is the true field of view, in degrees
                                F/f is the magnification
                               (Small fib here, too. See Note 2)

Optics also tells us that the maximum Tfov, or Tmax, for any given telescope is set by the eyepiece's diameter and the telescope's focal length: 

      Tmax = 57.32 * D/F   where: D is the eyepiece's diameter in millimeters
                                  F is the scope's focal length in millimeters
                                  57.32 is a conversion factor that makes Tmax
                                     read in degrees.
                                 (Another fib. See Note 3)

So, if we know our scope's focal length, we can rapidly figure out what the maximum true field is for any eyepiece diameter. For this example, let's use a telescope with a focal length of 1220mm. This means that 1.25" (31mm) diameter eyepieces can never show more than 1.46 degrees of sky (57.32 times 31 divided by 1220 is 1.46), and 2" (50mm) eyepieces are limited to no more than 2.35 degrees. We use this to see whether any given eyepiece makes sense by comparing its Tfov to Tmax. If the computed Tfov is larger than Tmax, the light from the outer part of the field of view doesn't reach your eye and is wasted. Let's run some examples.

After finding an eyepiece with the maximum Tfov that is useful in your telescope, you know the bottom of your magnification range. Simply divide your scope's focal length by that eyepiece's focal length, since magnification = F/f = Afov/Tfov.

Let's go back to that question of which size of eyepiece to choose. Your telescope may limit the choice; it may be designed to work with or have a narrow exit tube that only allows some of the sizes to fit. If you are going to go up in size, then you should check to make sure the wider diameter eyepieces are neither mechanically incompatible nor vignetted by the telescope tube (if so, you won't get any increase in field of view). Otherwise, the choice boils down to the maximum field of view we want to have through the scope. If you don't care about wide views or have a short focal length scope, then smaller diameter eyepieces will be just fine. If you love big wide views and/or your scope has a very long focal length, then you'll need the bigger diameter ones. Here's a little table that shows the Tmax in degrees for all three common eyepiece diameters and a number of telescope focal lengths. If your scope's exact focal length isn't in the table, its Tmax won't be very far from the Tmax of the focal length just above or below yours: 

        Telescope  Max True Field (Tmax) in Degrees
          Focal       for Eyepiece Diameters of:
         Length          0.965"   1.25"            2"
     -------------------------------------------------
           400mm          3.4     4.4     7.2
           500            2.8     3.6     5.7
           600            2.3     3.0     4.8
           700            2.0     2.5     4.1
           800                            1.7     2.2     3.6  (the table was computed
           900                            1.5     2.0     3.2   using the formula
          1000                            1.4     1.8     2.9   found in Note 2)
          1200                            1.1     1.5     2.4
          1400                            1.0     1.3     2.0
          1600                            0.9     1.1     1.8  For comparison, the full
          1800                            0.8     1.0     1.6  moon spreads across just
          2000            0.7     0.9     1.4                  about 0.5 degrees of sky.
          2200            0.6     0.8     1.3
          2400            0.6     0.7     1.2
          2600            0.5     0.7     1.1
          2800            0.5     0.6     1.0


    Choose the eyepiece diameter that gives you the field of view you want to
have.


    Now let's get a handle on the upper magnification limit. This one is
set by either the atmosphere or the aperture of the telescope. Both of
these cause irreducible 'fuzz' in the image. There is no sense going too
high in magni- fication because you get to the point where all you do is
make the 'fuzz' bigger but gain no additional detail. The atmospheric
unsteadiness, called 'seeing', varies from night to night and place to
place, but usually limits us to using magnifications below something like
220-250X. You will sometimes be able to go up to 300X, but only rarely
beyond that. Smaller telescopes also tend to run into their diffraction
limit. This is set by the size of the aperture, and the Rule of Thumb is to
disallow magnifying beyond 2.0 to 2.4 times the aperture expressed in
millimeters (50-60 times the aperture in inches). That is,  a 102mm (4
inch) aperture scope is going to have around 204X-245X maximum
magnification. I should mention that this Rule of Thumb is subject to
argument and is dependent on the viewer's personal feeling of what is sharp
and what isn't; people also differ in visual acuity.


   OK, so now we have a lower limit and an upper limit. It remains to fill in
the middle. When you are taking out one eyepiece and putting in another,
you can more easily lose track of the object you're looking at if you make
too big a jump in magnification. Try to set up your eyepieces so that from
one to the next there is no more than a 2 to 1 difference in magnification
at the lower end of the range, and no more than about 1.5 to 1 at the upper
end (control is touchier at high mag.). This is a practical limit. If you
are very skilled in centering things and have a rock-solid mount that
doesn't jiggle or shake at all when you switch eyepieces, then you can
spread these ratios out.


   A word of caution: this method assumes that the Afov of all the eyepieces
are similar. If they're not, you have to use Tfov as the factor to ratio at
2:1 or 1.5:1 from eyepiece to eyepiece, rather than magnification. This
takes a little more computation but the idea is otherwise the same.


   Observing habits do differ, but you will probably end up doing most of your
observing in the 50X to 200X magnification range.  Guide  your selection
somewhat to have at least a couple of magnifications in that range.


    Let's do an example using a 203mm aperture scope with a 2032mm focal
length. Maximum magnification will rarely be over 300X because of the fact
that the scope will be used in a city whose rising heat plume degrades
seeing. Wanting the maximum field of view, we use 2" eyepieces for the low
magni- fications. Looking in the table for 2" diameter and 2000mm, Tmax for
this scope is about 1.4 degrees. Looking at the available 2" eyepieces for
lower magnification, we find a 55mm, 50 degree Afov unit with a  Tfov of
1.4 degrees, just at the Tmax limit. Thus the lowest magnification is set
at 2032/55 or 37X. The upper limit is set by the atmosphere; 2032mm/300X is
roughly 7, so the highest magnification eyepiece will be a 7mm unit that
gives 290X (just under the nominal 300X limit). To fill in the middle, we
expect to go down by a factor of 1.5 from the 7mm, which means an 11mm
eyepiece, and up by a factor of 2 from the 55mm, to about a 27mm eyepiece.
There's a more than 2:1 magnification gap between the 27mm (75X) and 11mm
(185X), so maybe we will put in a fifth eyepiece and narrow all the ratios
down, or maybe leave it at 4 eyepieces and try to select focal lengths to
even the gaps [say 22mm (92X) and 12mm (169X) instead of 27mm and 11mm].
The exact focal lengths you compute are often not sold, and there will be
other factors to consider, so you will have to have some flexibility.


    Wow, sounds like you're done, but...there are those "other factors" still
lurking about. While the basic scheme above will not change, these
consider- ations can affect your choice of eyepieces: parfocality, weight,
eye relief, exit pupil, Afov, Barlow lenses, contrast, and the shadow cast
by a secondary mirror.



    

  • 
        a. Parfocality. You will notice that eyepieces seem to be designed
in 'series'. Several different focal lengths will be offered that share
other
design features. When the optical designs are coordinated this way, the
eyepieces can be made parfocal with each other (But they may not be,
either. Check before buying).  For eyepieces to be parfocal means that if
you take one out of the telescope and put another in, there is little or no
need to refocus. A parfocal eyepiece set is not a necessity, but it is a
definite convenience (especially at high magnifications). For some reason,
though, the fact that an eyepiece series is parfocal tends to receives
little attention in most promotional literature.

  • 
        b. Weight. Some eyepieces are very small and weigh only a couple of
ounces; others weigh over two pounds. This can be annoying if it requires
rebalancing your scope as you switch eyepieces in and out. Much of this factor
depends on what type of mount your telescope is on; if you have a mounting
system that demands close balance, then it makes some sense to get eyepieces
of similar weight.

  • 
       c. Eye relief. This is the distance from your eyeball to the eyepiece
when you are looking through it. Enough eye relief is a requirement for people
who must observe with glasses on. If this is the case for you, then before
buying any eyepiece, put it in a telescope and look through it to ascertain if
will work comfortably with your glasses on.  There are a lot of long eye
relief designs nowadays (though they tend to be a bit more pricey) so you
should be able to find something usable.  Eye relief is also an issue if
you have long eyelashes and/or use mascara; eyelashes rubbing on the
eyepiece will entail much more frequent cleaning of the outer lens element.
Eyepieces with short eye relief can also increase the spread of
conjunctivitis, a consideration if you do a lot of public star parties.

  • 
        d. Exit pupil. This is the diameter of the light beam coming out of
the eyepiece, and is equal to the telescope aperture divided by the
magnification. For example, an 11mm eyepiece on a 900 mm focal length, 102mm
aperture scope (magnification of 900/11 = 82X) has an exit pupil of 102mm/82
= 1.2mm. Exit pupil can be another limit on the lowest magnification. People
differ in how much the pupil of the eye dilates in the dark. For older
observers, this can be as low as only 5mm or so, and it is possible at low
magnifications to have the exit pupil exceed 5mm. If so, then some of the
light coming out of the eyepiece will fall on the iris of your eye and is
effectively wasted. This makes your view dimmer than it otherwise could be.
Exit pupil can put a practical limit on the highest useable magnification
as well; if the light beam is very narrow, it can accentuate 'floaters' in
your eye as essentially all of the light can be going through--and
distorted by--one floater. On the other hand, a narrow exit pupil may help
those with astigmatism as the distortion of the eyeball that causes it is
less dramatic over a smaller area. Some astigmatic observers report that
they can take off their glasses at high magnification due to this effect.

  • 
       e. Afov. You will notice the eyepieces seem to come in 4 classes of
Afov. There are older designs that run anywhere from 25 to 40 degrees, the
large majority in the 45-55 degree range, 65-70 degree wide-fields, and 82-85
degree extreme-fields. Looking into an eyepiece has some similarity to looking
out of a porthole; you see a round image with a blank area around it. Now
imagine walking toward the porthole; you see less blank wall and more of
what's outside the porthole. Get close enough and you barely notice the
surrounding wall; it's almost as if you were outside. Afov behaves the same
way; a large Afov's makes it seem almost as if you are no longer looking
into a telescope but "right out there" in the sky. How large an Afov you
need to achieve this sensation of unconfined spaciousness, if you achieve
it at all, is entirely subjective. You'll have to look for yourself; it's a
very personal perception. For instance, I see little difference between the
60-70 Afov designs and the 82-85 degree designs, but others find only the
latter give them the effect. Caveat! This spatial effect can be
captivating, and viewing through large Afov eyepieces can lead to
dissatisfaction with 'lesser' units forever afterward. Besides their
considerably higher cost, there are a couple of other disadvantages with
big Afov eyepieces. They contain a lot of glass, and the resulting
heaviness can definitely affect scope balance. They are also fairly bulky
and require a much larger eyepiece case.
    If you do elect to get eyepieces with differing Afov's, then you should go
over your selection to make sure you have a series that ratios the Tfov's
(rather than the magnification) by about the same 1.5 to 2 numbers we used
before. For example, it makes little sense to buy a 20mm, 82 degree Afov
eyepiece and a 32mm, 50 degree Afov eyepiece. On, say, a 1220mm focal
length scope, we compute a substantial difference in magnification (61X for
the
20mm, 38X for the 32mm). But because of its huge Afov, the 20mm has a Tfov
of 1.34 degrees, actually slightly larger than the  32mm's Tfov of 1.31
degrees. As they show the almost identical chunk of sky (the 20mm makes a
bigger image of it), there is no reason to have both even though they
differ in magnification by a factor of 1.6.


  • 
        f. Barlow lenses.  A Barlow is a diverging lens mounted at the
bottom of a tube the eyepiece fits down into, and effectively cuts the focal
length of any eyepiece. There are many Barlows offered for sale, of which
by far the most common is the 2X (that is, doubles the magnification or
halves the effective focal length). The advantage of a Barlow is that you
don't need to buy as many eyepieces. If you buy a 20mm eyepiece and a 2X
Barlow, it's like having a 20mm and a 10mm. If you're on a tight budget, a
decent Barlow (cost roughly equal to one eyepiece) can get you a wider
variety of magni- fications. For example, say you have a 1220mm scope with
152mm aperture. Figure an upper magnification limit of 300X (atmospheric
and diffraction limits are both about this number) which translates to an
eyepiece focal length of 4mm. The lowest useful magnification with 1.25"
eyepieces on the example scope is about 38X, which you get from a 32mm
focal length eyepiece with 50 degrees Afov. The budget is tight, so
expensive 2" eyepieces are out of the question. Since a Barlow in part of
the  plan, we get the equivalent of a 4mm by using an 8mm eyepiece with the
Barlow. The 32mm also gives us a 16mm equivalent when used with the Barlow.
So far we have effectively 4mm, 8mm, 16mm, and 32mm. Adding a 12mm eyepiece
will "fill out" the higher magnifications, so that the final list looks
like this:





  Magnification     How Achieved            Equiv. Focal Length

 ---------------------------------------------------------------
      305X        8mm eyepiece, 2X Barlow          4mm
      203X       12mm eyepiece, 2X Barlow          6mm
      153X        8mm eyepiece                     8mm
      102X       12mm eyepiece                    12mm
       76X       32mm eyepiece, 2X Barlow         16mm
       38X       32mm eyepiece                    32mm





    
    Not bad, we covered our entire range with six well-spaced
magnifications for roughly the price of 4 eyepieces. On the down side, it
is a little more inconvenient to have to fuss with two optical elements
instead of one when switching magnifications. If you get a good quality
Barlow, there is little
to no noticeable degradation of the image, but do evaluate cheaper ones
carefully. Lastly, not all Barlows work with all eyepieces; some
combinations cause vignetting or optical distortions, so you will want to
check out your candidate combinations before buying.

  • 
        g. Contrast. This is mostly an issue with critical planetary obser-
vers. Planets are at best low-contrast objects, and demand eyepieces that
do not degrade the contrast of the image coming though them. There is a
tendency to favor simpler designs with fewer lens elements, thus reducing
the number of internal reflections and light scattering off any tiny
imperfections left by the lens polishing process. It's best to discuss this
matter with the dedi-
cated planetary observers, who are the real experts here.

  • 
        h. Shadow of the Secondary. Essentially all telescopes except
refrac- tors have a secondary mirror which is in the middle of the main
aperture. If your telescope has a secondary, its shadow at low
magnification can be large with respect to the pupil of your eye and become
objectionable. The effect is at its worst in daylight when the eye's pupil
is smallest and the dark shadow more obvious against the daylit view. So,
if you plan to use the scope during the day, check to make sure the lowest
magnification eyepieces give you a satisfactory image. This is much less of
a problem at night, when the pupil of the eye is fully dilated, plenty of
light gets in around the shadow, and the shadow tends to get lost against
the dark sky anyway.




    What about faults like internal reflections, coma, aberrations, and so
forth? Eyepieces can have any or all of these, just like any other optical
device. There are good designs that are well made, good designs cheaply
made, and poor designs.  The only way you can really tell if any particular
unit is good enough to your eye is to use it and see for yourself. That's
why comparing eyepieces is one of the general amusements among amateur
astronomers at star parties. Eyepieces are quite a competitive business,
and generally quality scales with price. Most if not all name-brand
eyepieces have pretty good performance at the center of the image. As you
go up in price, this "sweet spot" increases as a percentage of the total
area in view. In addition, more money tends to buy more features: better
baffling/blackening, more and better lens coatings, larger Afov, more eye
relief, and parfocality.


    When you go off to discuss eyepieces, either with other amateur astro-
nomers, or with salespeople, you run into a welter of oddball names. The
naming of eyepieces seems to follow no consistent pattern. Some are known the
person who invented their optical design: Erfle, Plossl, Ramsden, Huygens,
Nagler. Some are described after a feature of their design: orthoscopic
(i.e. to have a flat field), panoptic (alluding to the wide field of view),
super-wide (again, wide field), ultra-wide (yet again, wide field). Some
have a series name hung on them by the maker or seller: LV, XL, LE, ultima,
ultrascopic, 3000, 4000. So if you're confused about the names, it's not
your fault. They really don't make a lot of sense, nor do they really
matter much. An eyepiece by any name still has its:



       Focal Length
       Apparent Field of View
       Eye Relief
       Weight
       Diameter
       Parfocal (or not) with others
       Price
       Optical Quality (sharpness, lack of aberrations, etc)




    These are what you need to keep in mind when working out what eyepieces
are best for you. Note that a lot of them require a use test. Will the weight
unbalance your scope?  Did you check to see if they were really parfocal? Is
the optical quality high enough for you? These questions (and others) can only
be answered by using the candidate eyepieces on your scope. Here's where
other amateur astronomers can be a great help; many kinds and sizes of
eyepieces are usually found at observing sessions and normally the owners
don't mind helping you evaluate some.


    That's the end of the lecture. Good luck choosing your eyepieces!