Submission by Doug Tanaka
You’ve just bought your first telescope. It came with a complimentary eyepiece, but now you’d like to buy a few more. Orthoscopics, Kellners, Plossls, Erfles, Konigs, Naglers…the choice can be overwhelming. Aside from the telescope itself, eyepieces are an amateur astronomer’s most important pieces of equipment; the cost of a set of premium eyepieces can equal or surpass that of a telescope. This article should make it easier for the novice eyepiece purchaser to select their first set.

Photo by Steve Jurvetson

While it’s possible to choose eyepieces based on the magnifications, they will produce on a given telescope, I base my choice on the size of the exit pupil produced by a particular eyepiece combined with a particular telescope. When eyepiece and telescope are focused, the collected light forms an “exit pupil”—a small circle that hovers just above the eyepiece. To look through the telescope you place the pupil of your eye where this circle comes into focus. If you place an opaque piece of glass or plastic where the exit pupil is focused, you can see the tiny image and measure the circle with calipers. The diameter usually ranges from about 7mm down to .5mm or even less. 

For most people the daytime pupil size of their eye is about 2mm. Dark-adapted eyes are dilated 2-4 times. In children and young adults the dark-adapted pupil can enlarge to 7mm or more. As we get older our pupils are less able to enlarge, with a lower limit of about 5mm for those 60 years of age and older. Since the exit pupil hovers above the eyepiece and we need to place our own pupil at that location to see the image, we can make the most efficient use of the gathered light if the size of the exit pupil is the same as, or smaller than, our own darkadapted pupil size. If we try to look at an exit pupil that is larger than our own pupil, the extra light is blocked by our iris and never reaches our cornea. In other words, if you are 60 years old with pupils that can only dilate to 5mm and you try to look at a 7mm exit pupil, you will be losing 2mm worth of light. Likewise, if you are young with a 7mm pupil, you can’t fully use an 8mm exit pupil. Theoretically, refractor owners are not limited by exit pupil size and can use any size they wish. The problem is that the image will eventually become overly bright and magnification would decrease until they were comparable to binoculars, though they would still be able to see a very wide swath of sky. This is not the case with reflecting telescope because the central obstruction (the secondary mirror) would start to become visible once the exit pupil reached a diameter of about 10mm. To simplify: The first few eyepieces that you buy should have an eyepiece/telescope combination that produces an exit pupil 7mm or less in diameter. If you are middle-aged the exit pupil should be 6mm or less, and by age 60 you should shoot for 5mm. 

Calculate magnification by converting the size of your telescope’s objective into millimeters, multiplying that by your telescope’s focal ratio to get the focal length of your telescope, and dividing that by the focal length of the eyepiece.>To convert inches into millimeters multiply the number of inches by 25.4. Using a 5″, f6 telescope as an example, the 5″ converts to 127mm 5 and multiplying that by the f/ratio we get a focal length of 762mm 127. Then to find out what magnification you would get if you inserted a 14mm eyepiece you would divide the 762mm focal length of the telescope by 14. 762/14 = 54.4 so you would end up with a magnification of about 54x. While this is a very handy way to figure out the exact magnification you will get, you can see that it’s easier to find what eyepiece best suits your purposes by using exit pupil size.

Calculating Exit Pupils

When you bought your telescope you probably noticed that there were two main numbers in its specifications, the diameter of the objective (given in either inches or millimeters) and its focal ratio (f/4.5, f/7, etc). To find out what size exit pupil you’ll get with a given eyepiece you divide the focal length of the eyepiece by the telescope’s focal ratio. For example, an eyepiece with a focal length of 18mm combined with a telescope with a focal ratio of f/6 will produce an exit pupil of 3mm (18/6=3). Now, suppose you’re middle-aged (with a maximum pupil size of 6mm), just bought a telescope with a focal ratio of f/5 and want the largest useable exit pupil. In that case you just multiply your telescope’s f/ratio (f/5) by the desired exit pupil (6mm) and you find you need to buy an eyepiece with a focal length of 30mm. 

You might wonder why anyone would want to buy an eyepiece that produced a smaller exit pupil, and the answer is that magnification increases as the size of the exit pupil decreases. 

All you really need to know is that exit pupils in the 5-7mm range correlate with low magnification and wide fields of view, exit pupils in the 2-4mm range correlate with medium magnification suitable for viewing extended objects like galaxies and nebulae, and exit pupils 1mm or less correlate with high magnifications suitable for planetary viewing or looking at fine detail on the moon. When we put the same eyepiece into telescopes that are drastically different in size but have the same focal ratio, the magnifications produced will be different, but the exit pupils produced will be the same. For example, a 24″, f/5 Dobsonian telescope with a 10mm eyepiece will give a magnification of about 305x, while putting the same eyepiece in an f/5 refractor with an objective size of 3″ will only give a magnification of 38x. Both examples produce exit pupils of 2mm.

The 2mm Exit Pupil

It is relatively easy to calculate the ideal low-powered eyepiece based on your own maximum pupil size and tailored for your specific telescope focal ratio and maximum pupil diameter. But medium-powered eyepieces produce exit pupils that range from 2-4mm in size. Choose one that produces a 2mm exit pupil. This exit pupil most closely matches the resolution of the human eye: about 60 arc-seconds. The resolution of a telescope is 4.55 arc-seconds divided by its aperture in inches. For optimum resolution we need to find the magnification that will produce an image of 60 arc-seconds, which computes to roughly 13x per inch of aperture. This will produce an exit pupil of 1/13 inch, close to 2mm. You’ll find that a 2mm exit pupil will show the most detail in extended objects like galaxies and nebulae.

While it’s true that the largest exit pupils produce the brightest images and, one would think, be the best for deep-sky observing, the background sky will be equally as bright and you’ll find that the overall image will be lacking in contrast, especially in light-polluted areas. With a 2mm exit pupil the overall image (the background sky and the object itself) will be equally darkened but the size of the image will be increased, and one of the properties of the human eye is that it’s easier to see faint things if they are large. At this point you can continue to decrease exit pupil size (increase magnification) to see if more detail can be drawn out. There are many diffuse objects that look better at higher magnifications but in general the 2mm exit pupil will show the most detail.
This will only optimize detail for extended, diffuse objects like galaxies and nebulae. It does not apply to bright objects like stars and planets. Since stars are points of light, they don’t appear to change in brightness as exit pupils get smaller. However, the background sky will get increasingly darker as exit pupils decrease, making it easier to see faint stars. This is valuable to observers who are attempting to split very faint double stars, for example, but not something that most novices will be concerned with. For now, it’s enough to know that a 2mm exit pupil is an excellent all-around size for most observers and will be a favored eyepiece.

Subjectively, I find that a 2mm exit pupil is “cozy”— comfortable to use for a long period, producing the least amount of eye strain. My first telescope had an aperture of 90mm with a focal ratio of 13.9. I soon found that the eyepiece I used the most had a focal length of 24mm. I assumed that this was due to the eyepiece itself. Then I built a Dobsonian telescope with an aperture of 12.5” and a focal ratio of 6. While my “favorite” eyepiece gave nice images in this telescope, it was no longer the one that I used the most.

My new “favorite” was an eyepiece with a focal length of 12mm. 
It wasn’t until I learned about the 2mm exit pupil and its relation to the resolution of the human eye that I began to see the connection. Both combinations gave exit pupils around 2mm. At the time I was involved with various observing groups on the internet. The question “What is your favorite eyepiece?” would often come up. Many replied by specifying which eyepiece they liked the best, citing the brand and focal length, but the most informative replies also specified the type of telescope they used it in. After reading numerous threads (and an almost equal number of arguments!), I began to realize that if a chart were made showing which exit pupil was the “favorite,” the bell curve would be centered very close to 2mm. 
If you are buying just one eyepiece, or a couple of inexpensive eyepieces and one premium eyepiece you should get the best eyepiece you can afford that will produce a 2mm exit pupil. It’s likely to become your workhorse eyepiece.

High-Powered Eyepieces

On the surface your choice of a high-powered eyepiece might seem straightforward. You want an exit pupil around 1mm, so you take your telescope’s focal ratio and buy an eyepiece with the same focal length. But your choice needs to take into consideration the area you live in, the quality of your telescope, and some eyepieces to avoid. 

High-powered eyepieces are good for observing planets, where you want the highest magnification possible without the image becoming blurry. And this is the catch. At the highest magnifications it’s not just the image of the planet that gets magnified but everything else in the observing chain the atmosphere above you, aberrations in your telescope’s mirror or lens, and even the quality of the eyepiece itself. 

Let’s first consider the atmosphere. On some nights the stars twinkle and on some nights they are steady points of light. What causes this is air movement miles above you, usually associated with the jet stream, the narrow band of fast-moving air that moves from west to east. To understand how this affects seeing conditions, imagine you are lying at the bottom of a swimming pool wearing a diving mask, looking up at the sky. If the wind is creating ripples on the surface of the pool you can’t see clearly. If there is no wind, the surface of the pool is smooth and you will be able to see perfectly. So it is with the atmosphere. 
There are two jet streams, the polar, between latitudes 30-70 degrees and the subtropical, between latitudes 20-50 degrees. (These are mirrored in the Southern Hemisphere for a total of four jet streams.) For observers in the US the primary “twinkler” of stars is the polar jet stream. This stream takes a meandering path, like an out-of-control water hose with a high pressure nozzle. The area this stream can influence extends from Northern Canada to most of the US. It does not distribute its time equally across its range but resides mainly along the US/Canadian border (around latitude 50) with occasional forays to the north and south. 

If you live in the north, you should consider purchasing an eyepiece that produces an exit pupil closer to 1mm and if you live to the south, you will be more likely to be able to use an eyepiece that produces a .5mm exit pupil. This is because exit pupils are closely tied to magnification and when we talk about the smallest useable exit pupil we can just as well be talking about the maximum useable magnification. 

Department store claims of 1,000x to the contrary, very few amateur telescopes are capable of achieving decent resolution at even 1/3 this magnification and probably much less. Empirical evidence has shown that a good rule of thumb is to multiply your telescope’s aperture (in inches) by 60x to find its maximum magnification under ideal conditions. Using our 5″, f/6 telescope as an example, the maximum useable magnification under ideal conditions would be 300x (5 x 60 = 300). If you recall, the focal length of this telescope is 762mm, so to find out what size eyepiece would give us this magnification we just divide 762/300 to get an eyepiece with a 2.54mm focal length. This is a very short eyepiece focal length and, in this f/6 telescope would give an exit pupil of 0.42mm. But bear in mind that all conditions must be perfect for this to be useable and realistically the minimum useable exit pupil is closer to 0.5mm. 

The quality of your telescope and eyepiece places a limit on how small an exit pupil you can reasonably use. As another rough rule of thumb, the more expensive your optics, the closer you can go toward a .5mm exit pupil.Another factor to consider when choosing a highpowered eyepiece is the amount of eye relief. This is the distance your eye needs to be from the eyepiece in order to see the image. Plossls are widely used eyepieces because they are relatively easy to make, give a decent field of view, and produce a very flat and accurate image, with very little distortion, but their downside is that eye relief decreases in direct proportion to their focal length. Down to about 17mm they are very nice, but by 10mm they start becoming slightly uncomfortable to use and by 7mm are almost impossible to use. At the shortest focal lengths, you’ll need to hold your eye so close to the eyepiece your eyelashes will brush against the glass leaving oil and/or mascara streaks on the glass. If you want good eye relief with a high-powered eyepiece you will need to spend money on one of the premium designs or use what’s called a Barlow lens. 

This is a negative lens that fits between the focuser and an eyepiece. Technically it lengthens the focal length of your telescope, but for the purposes of eyepiece selection we can also think of it as shortening the focal length of an eyepiece. Barlow lenses can be 2x, 2.5x, 3x, etc. but the most common is a 2x Barlow. When used with an eyepiece a 2x Barlow will effectively cut the focal length of the eyepiece in half. A 14mm eyepiece will give the same magnification (and produce the same size exit pupil) as a 7mm eyepiece. I highly recommend a Barlow lens because it’s like doubling the number of eyepieces you own. Another big advantage is that it will retain the eye relief of whatever eyepiece it is combined with. A 14mm eyepiece acting as a 7mm eyepiece in a 2x Barlow will have the same eye relief as the same 14mm eyepiece used alone. 

If you have purchased a low-powered eyepiece that produces, say, a 6mm exit pupil and another eyepiece that produces a 2mm exit pupil, the addition of a 2x Barlow to your collection will give you the equivalent of a 6mm exit pupil, a 3mm exit pupil, a 2mm exit pupil and a 1mm exit pupil, which should meet nearly all observing needs. 

Your Barlow lens needs to accommodate both 2″ and 1.25″ eyepiece barrels if your low-powered eyepiece has a 2″ barrel. The two common sizes for eyepiece barrels are 1.25″ and 2″. Very inexpensive (read: cheap) telescopes sometimes come with .965″ eyepieces and very high-end research telescopes can accommodate very large barrels of 5″ or larger, but for our purposes we’ll limit the discussion to the two common sizes. The primary difference between eyepieces with 1.25″ and 2″ barrels is the size of their respective field stops, the internal ring which defines how wide the circular image appears to be. This is also known as the Apparent Field of View (AFOV). In 1.25″ eyepieces field stop diameters cannot get larger than 27mm and in 2″ eyepieces the field stop diameter cannot be larger than 46mm. 

The design of the eyepiece is the main factor in calculating its AFOV, with Plossls having AFOV’s around 50-55 degrees, wide-field eyepieces 60-70 degrees, and super wide fields 80 degrees or more. To get a rough idea of how these AFOV’s compare with each other, the view through a Plossl eyepiece would be similar to looking through a cardboard toilet paper tube cut to 1 3/4″ in length, the view through a wide-field eyepiece would be like looking through the same roll cut to 3/4″ and the view through a super wide-field would be like having it cut to 1/4″. 

Plossl Eyepieces

The AFOV is an attribute of the eyepiece by itself, and when combined with a particular telescope will produce what is called the True Field of View (TFOV), the actual area of the sky contained within the image. You can calculate the TFOV you’ll see with a particular eyepiece/telescope combination by dividing the AFOV of the eyepiece by the magnification produced. Where the field stop comes into play is that it sets a physical limit on the TFOV you will be able to see and also limits how long the focal length of an eyepiece can be. For 1.25″ eyepieces that limit is about 32mm and for 2″ eyepieces that limit is about 55mm. 
It would be an easy mistake for the novice eyepiece buyer to purchase a 40mm Plossl eyepiece thinking you’ll see a wider area of the sky than a 32mm Plossl, but closer examination will show that the 32mm Plossl has an advertised AFOV of about 50 degrees while the 40mm Plossl has an AFOV of only 40 degrees. You will see about the same area of the sky but the 32mm eyepiece will have a higher magnification which results in an image with higher contrast. 
While we’re on the subject of higher contrast I should point out that the optimum combination of TFOV and high contrast in 1.25″ eyepieces is found in wide-field eyepieces (about 68 degrees AFOV) with focal lengths of 24mm. This gives an almost identical TFOV as a 32mm Plossl but you will get both higher magnification and contrast. 

If you’re fortunate enough to have a telescope with a 2″ focuser you will be able to use eyepieces that will produce very wide TFOV’s. A 2″ eyepiece is 1.6 times larger than a 1.25″ eyepiece and has 3x the area. A low powered 2″ eyepiece is excellent for viewing the Milky Way and cruising through the sky in general. Combined with a short-tube refractor you can see over 7 degrees worth of sky, the main trade-off being a rather low magnification of 7x. But don’t automatically think you should try to buy all of your eyepieces with 2″ barrels. Below a certain focal length, the area of sky seen with a 1.25″ eyepiece and a 2″ eyepiece with identical focal lengths will be the same, and the same is true for the brightness of the image. The cut-off point will be different for each eyepiece/telescope combination but in general low-powered eyepieces that generate exit pupils in the 4-7mm range are the only ones that benefit from the extra size.

Eyepiece Designs

There are many different types of eyepieces for astronomers to choose from, but to keep things simple I’ll limit the discussion to those that are most likely to be used by the first-time buyer. 

The eyepiece that came with your telescope was most likely a Plossl. This design is over 100 years old and is far and away the most popular eyepiece used in amateur astronomy. That’s because it has a decent AFOV of about 50 degrees, has good color correction, is free of ghost images, and is relatively inexpensive. Modern variations of the original design also correct very well for astigmatism, coma, and field curvature. 

The main drawback with Plossl eyepieces is that the amount of eye relief decreases proportionally as the focal length gets shorter. Earlier I mentioned that eye relief starts to become tight in focal lengths of 10-12mm, but if you need to wear eyeglasses when observing you might be limited to focal lengths over 16mm. The novice should be aware, however, that eyeglasses are only necessary for observing if you have astigmatism. If you are near- or far-sighted you can just tweak the focuser to suit your eyes. I should also add that many people with astigmatism don’t require glasses when using high powered eyepieces because the small exit pupil falls on a much smaller area of the cornea and the effects of astigmatism will be less noticeable. A lesser drawback to a Plossl eyepiece is its AFOV. Up until the early 1980’s this was not a drawback at all since the only eyepiece with a larger AFOV was the Erfle, developed in 1921 for military use. The Erfle has a 60-70 degree AFOV but is pretty much unusable at high powers because of astigmatism and ghost images, although they are very good at low powers showing just a bit of distortion at the edge of the field. The competition changed dramatically, however, in the early 1980’s when Al Nagler of TeleVue Optics introduced the Nagler line of eyepieces with 82 degree AFOV’s. Since then, many companies have jumped in, offering a broad selection of wide-field and super-wide-field eyepieces. Wide-Field and Super-Wide-Field Eyepieces.

The 50 degree AFOV of Plossl eyepieces is about the most an observer can take in at one time with the acute area of the eye. Anything larger than this falls into the realm of peripheral vision and is more sensed than seen, so eyepieces in the “wide field” realm can be considered more luxuries than necessities. But there’s no denying the fact they give luxurious views. 

If you watch a person observing with one of the super-wide-field eyepieces with AFOV’s of 80 degrees or more, you will see them moving their head around as they position their eye left, right, up, down to take in the whole field of view. You would almost think that instead of observing the sky, they were observing the inside walls of the eyepiece, and the experience has often been likened to looking through the porthole of a spaceship. A number of manufacturers now produce eyepieces with AFOV’s over 65 degrees using designs generated by computer, with lens curves so extreme that they were impossible to produce until the advent of modern grinding machines. But as sophisticated as these modern designs are, none of them can reverse optical laws and all have to give up something in order to achieve their expansive views. 

One of these trade-offs, and probably the most common, is called the “pincushion” effect, where straight lines appear to have progressively more curve as they move from the center of the view towards the edge. It is also called the fishbowl effect and is not very noticeable until you pan your telescope across the sky. This effect can even nauseate some observers. But for more stationary viewing, pincushion is not a serious problem and is tolerated by eyepiece designers because it’s the natural outcome of correcting for astigmatism, a problem where stars no longer look like points of light and begin to grow wings the closer they get to the edge of the field. 

Pincushion is a characteristic of the eyepiece itself and will present itself regardless of the telescope used. A similar problem is called field curvature. Field curvature is a characteristic of both the telescope and the eyepiece. Most telescopes have a final focal plane that seems to curve away from you toward the edge of the field (a convex or positive curve) and many eyepieces have a negative, or concave, curve. If the two characteristics happen to match perfectly you will end up with a perfectly flat field, but this is rarely the case in eyepieces that give wide fields of view or, for that matter, in telescopes designed to give a wide field of view. This is one of the major reasons why different eyepieces perform differently in different telescopes and a good reason to try them out before buying. 

Since many of these designs require lenses with extreme curves and extra lenses to correct for various aberrations, they all contain a fair amount of glass which makes them heavy compared to more conventional eyepieces, weighing as much as 2 pounds or more. If you have a relatively small telescope or one with a very narrow window for balance, these heavier eyepieces will throw off your balance. Most telescopes have ways to easily rebalance but this can become a nuisance if you’re frequently changing eyepieces. To find out how heavy an eyepiece your telescope will take without rebalancing, experiment by filling a sock with some sand, adding or removing sand until you find your telescope’s limit. Along with the extra weight, these eyepieces carry extra cost, some with price tags that rival the amount you could spend on a moderately priced telescope. Prices will vary widely but this is definitely a case where you get what you pay for. Most inexpensive wide field eyepieces will exhibit some astigmatism toward the edge of the field and only you know how much you can tolerate when compared to cost. 

Heading the list of premium eyepieces in this class are the Panoptics (68 degree AFOV) and the Naglers (82 degree AFOV) made by TeleVue Optics and the comparable Super- and Ultra-Wides made by Meade. A very good bargain in the low-power category is the 30mm Widescan Type II marketed by Apogee. This eyepiece has a reported AFOV of 85-90 degrees, and costs roughly half the price of the equivalent premium eyepiece. The tradeoff is that the image starts getting soft about 70% of the way from center, but is very sharp on-axis. Another brand of eyepiece that’s an excellent bargain is the Speers- Waler, made in Canada. They also give AFOV’s of 84 degrees or more at very reasonable price. The tradeoff on these is that they are very long and may require an extra amount of in-travel to come to focus.

Eye Relief

Earlier I mentioned eye relief, the distance you need to hold your eye away from the eyepiece in order to see the whole image. With modern eyepiece designs and the use of exotic glass it became possible to make eyepieces specifically designed for very generous eye relief in any focal length, not just the long ones. This is good news for eyeglass wearers who have astigmatism since 20mm, the standard amount of eye relief, allows them to observe without having to remove their glasses. The most noted eyepieces in this class are the Radians, made by TeleVue, with AFOV’s of 60 degrees, the XL line made by Pentax with 65 degree AFOV’s, and the Vixen Lanthanums with AFOV’s which vary from 50-65 degrees depending on the focal length of the eyepiece.

There are several other brands which offer eyepieces with generous eye relief and if this is important to you be sure to check out an eyepiece’s specifications before you buy. If you are buying your first set of eyepieces for your first telescope and you stick with the hobby for any length of time you will probably undergo what is known as “aperture fever,” the desire to upgrade your telescope to something with a wider aperture and greater lightgathering ability. In fact, if you are still in the hobby several years from now the odds are better than even that you will have upgraded to a different telescope. But this is not true of your eyepiece set if you buy quality from the start. Premium eyepieces will perform well in almost any telescope and can remain with you long after that first telescope has been passed down to your grandchildren.

If you have questions about eyepieces, feel free to email the Chief Astronomer at astronomer@bpastro.org