Author Topic: Eyepieces for the Beginner  (Read 4855 times)


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Eyepieces for the Beginner
« on: September 30, 2014, 10:02:05 AM »
Eyepieces for the Beginner

   No telescope is complete without eyepieces, and no astronomical accessory is so seemingly complicated, either. A million different ones, with a welter of different specs, are 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 to us is set by the magnification. In turn, the magnification 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 five things:

      a. Telescope focal length
      b. Eyepiece diameter
      c. The unsteadiness of the atmosphere, or ‘seeing’
      d. Telescope aperture
      e.  The size of the pupil of your eye

   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. Eyepieces with one of three diameters are sold. The smallest are 0.965” in diameter; they are the least common and generally associated with small, less-expensive scopes (exceptions exist). Most popular are 1.25” diameter eyepieces, and for most scopes these are perfectly adequate. Also commonly found are 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 the subject of 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 the maximum true field 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.

        1. Suppose my 1220mm focal length scope came with a 1.25” diameter, 26mm   
    focal length, 50 degree Afov eyepiece. The Tfov of this eyepiece is 1.22 degrees,
    which is less than the Tmax of 1.46. That’s OK, although I haven’t achieved the
    maximum Tfov.
        2. Looking for a wider view, I consider a 40mm, 44 degree Afov, 1.25” diameter   
   eyepiece. In this case, the Tfov computes to 1.44 degrees, which is just barely under
   maximum, and the difference so small it isn’t worth worrying about. The optical
   designers knew what they were doing.
        3. To see how much better we get by going to 2” eyepieces, we investigate
   a 55mm, 50 degree Afov unit. The Tfov is 2.25 degrees, very close to the 2.35 degree   
   Tmax upper limit. The larger barrel allows us 60% wider field of view.

   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(mm)        0.965”  1.25”      2”
    400                    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 in note 2)

   1000                1.4      1.8     2.9        
   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 fields of view you want to have.

   We have another issue at the low end of magnification.  The cone of light coming out of the eyepiece has a minimum diameter, called the exit pupil, set by the telescope’s aperture and the magnification.  If the exit pupil exceeds the diameter of the pupil of your eye, then the light falling on the iris surrounding the pupil is effectively wasted; your telescope’s aperture has effectively been reduced.  The maximum pupil diameter of the human eye is about 8mm in childhood, and declines thereafter: roughly 7mm as a young adult, 6mm in middle age, 5mm for old adults, and 4mm in the very aged.  Compute the focal length of the eyepiece that corresponds to your eye’s pupil diameter by this formula:

            fmax   =    PF/D        where:  P is the eye’s pupil diameter in mm
                                                      F is the focal length of your telescope in mm
                                                      D is the aperture of your telescope in mm

Using an eyepiece with a focal length greater than fmax results in light loss.  The minimum full-light magnification is then:

             Mmin =  F/fmax


   Now let’s get a handle on the upper magnification limit. This one is set by either the unsteadiness of the atmosphere or the aperture of the telescope. Both of these cause irreducible ‘fuzz’ in the image. Going too high in magnification makes little sense because you get to a 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 aperture telescopes 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, making the next task 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 going from one to the next results in no more than a 2 to 1difference 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 near a city whose rising heat plume degrades seeing. Wanting the maximum field of view, we use 2” eyepieces for the low magnifications. 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 a 10mm or  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 those “other factors” are still lurking about. While the basic scheme above will not change, these considerations 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. Eyepieces are often 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. A number of long eye relief designs are available nowadays (though they tend to be a bit more pricey) so you should be able to find something useable. 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.  We already discussed above how exit pupil can limit the low end of magnification before light is wasted.  But 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 5 classes of Afov: older designs from 40 to 45 degrees, many designs in the 50-55 degree range, 60-70 degree wide-fields, 82-85 degree very wide fields (Nagler types), and most recently, 100-110 degree ultra-wide 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 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, big Afov eyepieces have some drawbacks. 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. They show the almost identical chunk of sky (the 20mm makes a bigger image of it), leaving 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. Many Barlows offered for sale, of which by far the most common is the 2X (that is, doubles the magnification by halving 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 magnifications. 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, fussing with two optical elements is a little more inconvenient when switching magnifications. Using a good quality Barlow will result in 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 observers. Planets are at best low-contrast objects, and demand eyepieces that do not degrade the contrast of the image coming though them. The tendency is to favor simpler designs with fewer lens elements, thus reducing both the number of internal reflections and light scattering off any tiny surface imperfections left by the lens polishing process. It’s best to discuss this matter with the dedicated planetary observers, who are the real experts here. Expect a lot of arguments :-)

     h. Shadow of the Secondary. Essentially all telescopes except refractors 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. Good designs can be well made, good designs can be cheaply made, and poor designs exist as well. 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 astronomers, or with salespeople, you run into a welter of oddball names. The naming of eyepieces seems to follow no consistent pattern. Some are known by the name of 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, XW, LE, ultima, ultrascopic, 3000, 4000. So if you’re confused about the names, it’s not your fault. They don’t make a lot of sense, nor do they matter much. An eyepiece by any name still has its:

     Focal Length
     Apparent Field of View
     Eye Relief
     Parfocal (or not) with others
     Optical Quality (sharpness, lack of aberrations, coatings, 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!

   Note 1. It really isn't the diameter that is the actual limit, but an internal opening called the field stop. This is usually somewhat less than the diameter in order to remove aberrations from the lens edges. Let that go for now; you'll get a decent approximation using the inside diameter. If you want to do very exact calculations, you'll have to get the actual field stop sizes from the makers of the eyepieces of interest.
   Note 2. The formula given for Afov is an approximation. For those who demand the ‘real thing’, it is tan{Afov/2} = F/f * tan{Tfov/2}.
   Note 3. Again, this is an approximation. The exact formula is tan{Tmax/2} = D/2F.
« Last Edit: July 17, 2015, 11:39:10 AM by buynoski »

John Pierce

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Re: Eyepieces for the Beginner
« Reply #1 on: February 21, 2015, 11:49:15 AM »
shorter version  8)    the following is based entirely on my casual experiences over the past umpteen years

I wear glasses for mild-to-moderate astigmatism, so eye relief of 15-20mm is ideal, and I like wide fields of view.   at higher magnifications, however, the exit pupil is smaller, so wearing glasses is less important.

for most beginner to intermediate scopes, a range of 3-4 1.25" eyepieces evenly spaced between about 25mm to about 7mm are most useful, say, 25, 15, 10, and 7mm, which in a 1200mm FL scope such as the typical 8" dobson, will give you about 50X, 80X, 120X, and 170X. 

if you're on a tight budget, Plossl's are a great choice, especially for the 25-12mm range, a 7mm plossl is a bit of a pinhole.     Plossls usually have a 52 degree apparent field of view.  the lower power (higher focal length) plossls have decent eye relief, but as they get shorter focal length, the aperture and eye relief gets smaller and smaller, hence my pinhole comment.   Televue plossls are the gold standard, but the better import ones aren't bad, like the Orion premium plossls (the cheaper generic orions aren't so hot anymore).

for somewhat more money, the Explore Scientific 82 degree line are awesome up to 14mm (above 14mm, the 82 deg wides are 2" and more $$$).   their 24mm 68 wide is also very very good.   I'm currently using the ES 24/68, 14/82, 8.8/82, and 6.8/82 as my main eyepieces.  I also have the 4.7mm but rarely use it due to the high power.   These have excellent eye relief, and very good contrast, they list for $139 each but I managed to scrounge my set for $100 each by working sales.  Also, all the ES eyepieces are very closely parfocal, I don't even have to TOUCH my focuser when I switch between the 14 and the 8.8 for instance.

for big dough, its hard to beat Televue Panoptic and Naglers, but now you're talking 2" eyepieces that each cost nearly as much as a beginners telescope.