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Wild Card 001.1 “More Than You Ever Wanted to Know about Eyepieces, Coma, and Astigmatism”

Posted by Rick Shaffer   05/31/2004 12:00AM

Wild Card 001.1  “More Than You Ever Wanted to Know about Eyepieces, Coma, and Astigmatism”
This is a "follow up" on Wild Card 001. It reminds me of the celebrated "Chicken-Heart That Ate New Jersey", but, it is what it is.

FIRST: A Note about “Spherical Aberration of the Exit Pupil”:

If you look at the figure I included in WC 001, you’ll notice that our perfect telescope jams all the parallel bundles of light through a perfectly flat, perfectly circular disk we call the exit pupil. So, if you just put the pupil of your eye exactly at the eye point, the exit pupil of the telescope will exactly coincide with the entrance pupil of your eye. The result will be that all the light being gathered by the telescope will find its way into your eye.

Enter the real world of wide angle eyepieces. Sometimes the designer of an eyepiece must make a compromise in the design. In order to get the wide field that most buyers seem to want, one of the compromises made is to allow the bundles of light coming from the periphery of the field to cross the optical axis farther back than they would with a perfect eyepiece. And the bundles a little farther in toward the center of the field cross a little closer to the ones at the center, and so on. The result of this is that the ideally flat exit pupil is really spherical in this kind of an eyepiece.

This is called “spherical aberration of the exit pupil”. It’s an obscure aberration which can be present in any eyepiece, but is only really acute in some wide angle eyepieces.

The first premium wide angle eyepiece, the 13-mm Nagler, suffered from this aberration. Did “Uncle Al” Nagler put his name on a defective eyepiece? NO! And the fact that I’m using mine to this day, more than 21-years after I bought it, attests to that.

So, if the original Nagler-13 “suffers” from this nasty aberration, why isn’t it important? It’s because the original Nagler was only made in focal lengths of 13-mm and shorter. With any telescope slower than f/4, the exit pupil would be 3.3-mm or smaller. Now, the eye of almost any user who’s dark adapted will open up to at least 5-mm, and usually, much more than that. What happens is that the observer’s eye can be placed a little closer to the eye lens than it might if it weren’t open wider than that diameter. This allows it to both catch the bundles of light from the periphery of the field and not miss those toward the center of the field.

What happens if a Nagler-13 or a similar eyepiece is used during the day, when no one could become dark adapted. The eye isn’t opened up enough to take in the entire spherical exit pupil, and it can be moved around to see the entire field, but not at the same time. When it’s looking at the center of the field, there appears to be a kidney-bean of “darkth” near the edge. It’s maddening for us, because, we’re used to being able to easily find the exit pupil, and we can’t. I guess it’s really fortunate that Uncle Al never sold many Nagler-13s to folks who wanted a wide angle eyepiece with their shooting scopes.

THEN: "Coma, Astigmatism & Wide Angle Eyepieces":

If W. C. Fields were alive today, he’d probably observe that there was a “veritable plethora” of posts on the subject of coma in the “Dobsonian” forums this week. There seems to be a lot of confusion about what coma is, whether or not we see it in our eyepieces, and how it can be suppressed. And lurking in the background is “Uncle Al” Nagler, who gave us the Paracor. (Of course, Al’s not giving anything away. He’s much too good a businessman for that! The Paracor will cost you about about $300.)

First, coma is an off-axis aberration of the objective of a telescope. Refractors, Newtonians, Maks, SCTs, all of them can show coma off axis. But only the fast Newtonian reflector really suffers from enough coma for us to worry about, so that’s what kind of telescope we’ll consider in this discussion.

Coma is dependant on the f/ratio of a telescope. So, if we look a half inch off axis of a 6” f/4 telescope, we’ll see the same amount of coma as we’d see a half inch off the axis of a 30” f/4. (Remember this is the linear distance off-axis, not the angular.)

As the f/ratio of a telescope goes up, coma goes down. And, it’s not a linear relationship. The following table will illustrate this:

Amount of COMA present in the field of a Newtonian Reflector


Let’s look it over and see what conclusions we can reach:

1. For those of you who are actually modern citizens of the World, and use the Metric System of measurement routinely, the above table should be no problem. For those of us “Colonials” here in the USA, there shouldn’t be a problem, either, because there are no linear measurements at all! Please “RTFB”, and remember that! However, if you want to know how big the comatic image of a star is in the focal plane of your telescope, use the following formula:

Diameter of Comatic Image = EFL*TAN(Value in Table/3600)

2. Note that the table is set up in the “1-2-5” pattern that engineers like. That’s just so I could cram as much useful info into one table as I could. Just don’t try to read it as if the jumps between tables were regular. For that, we’d need more roughage. (Fiber, for you younger folk!)

3. If you look at the left part of the table, it becomes readily apparent that the field within which your telescope can resolve as well as diffraction will allow is rather small in fast Newtonians. Say, for example, we were discussing a perfect 12.5”, which resolves to about 0.36” (on a the night of our dreams!). We find by looking at the table that an f/4 will have a field of perfect definition that’s less than the value in the first column! If it were an f/6, the field is certainly bigger, but it’s still pretty small. So, from inspecting the left-hand part of the table, we can reach a couple of conclusions:

a. Coma is one reason why serious planetary observers have generally stuck to longer Newtonians on clock-driven Equatorial mounts. The longer f/ratio gets them a bigger field of perfect definition, and the equatorial mount allows them to keep the planet they wish to observe within that field.

b. But more and more amateurs are using big, fast Dobsonians. They neither wish to have an f/7 or f/8 mirror. Nor do they wish to lug an equatorial mount to their observing site or set it up and align it when they get there. THIS is one of the big reasons to own a Paracor. As Al Nagler's sketches show (see image left), the Paracor increases the “sweet spot” to a “sweet lawn”.

4. If you look at the large field angles, you can see that the coma is truly large. In fact, you can see that the coma at the edge of the 4-degree field of an f/4 telescope is almost twice the apparent diameter of Jupiter! Trying to photograph the sky with such a fast telescope won’t be very pleasing. In fact, near the edge of the field, many fainter stars really won’t be imaged at all because their light will be spread out over the frame so much that the light will be lower than the sensitivity of the recording medium.

5. Now take another look at the table, but, this time, look at the column on the right. It shows the percentage of coma you get with respect to the coma an f/4 mirror provides.. One thing that jumps out is that an f/6 mirror has only 44% as much comas as an f/4. This would seem to verify the conventional wisdom that, to avoid seeing much coma in your eyepiece, choose an f/6 telescope. As we’ll see a bit later, that’s only part of the story.

There are a lot of folks who have bought various wide-angle eyepieces for use with fast Newtonians expecting great views. Instead, they’ve found that the star images in the outer half of the field of these eyepieces resemble balloons rather than tight, little points of light. A lot of these same folks assume that the problem is the coma of their fast Newtonians.

Coma certainly isn’t desirable, but, except for critical viewing of planets, it’s not the horrible aberration its reputation would suggest. The reason is that the shape of the aberration isn’t symmetrical. Rather, it turns a star into a “fan”, or comet-shape, which explains the Latin name, coma. To see that fan-shape, take a look at the following URL:

The fan shapes you saw in James Mulherin’s excellent presentation look pretty ugly. And photographically, they are. But we really don’t see about 60% of those “fans” with any but the brightest stars in the field. Instead, we find big blobs. What’s going on?


Ever since the “war surplus” Erfle eyepieces became available after WWII, amateur astronomers in the USA have had a love affair with wide angle views. And, when the typical “big” Newtonian was an f/6 to f/8, the Erfle eyepieces worked reasonably well. After all, they were designed to work with something like f/8 objectives. But Erfle eyepieces have an Achilles heel. They really don’t work well below f/6, and they don’t work particularly well at that focal ratio.

When the supplies of surplus eyepieces ran out, similar wide angle eyepieces, again, made in Asia, began appearing. Then, of course, Al Nagler raised the bar with his 13-mm eyepiece. That first view through a Nagler-13 made it obvious that an eyepiece could have the following features:

- It could be very sharp,
- It could handle f/4 or faster Newtonians,
- It could have an absurdly large field,
- It could provide a long eye relief, and,
- in a pinch, it could make a really effective cudgel!

Al followed the Nagler-13 with a 9, 11, 7, and 4.8. All of them are Smyth-type eyepieces, those that use a negative group of lenses just inside the focus of a telescope to both lengthen the effective focal length of the objective and pre-correct for aberrations that the positive group of lenses will introduce. It’s this layout that allowed Al to make his Nagler eyepieces so well corrected. In fact, the Naglers were the first eyepieces that were corrected to essentially eliminate their own astigmatism. Despite the other wonderful attributes listed above, this is the crucial point of this whole discussion!

Newer glasses became available. Also, the Nagler-series of eyepieces demonstrated that the market was ready for an individual eyepiece that cost as much as good telephoto lens for a 35-mm SLR. This allowed Al Nagler to design a whole new series of Naglers, the improved Type 2, and actually sell them. That series stopped at 20-mm, but other, later Naglers have topped out at 31-mm, with an eyepiece so big that it looks like it’s capable of running for governor of whatever Western state it chooses!

Due to the advent of the Naglers and other TeleVue eyepieces, other purveyors of eyepieces have been forced to reassess what they were either making or importing. The result is that there are a lot of variations out there. Some are excellent, and some just have a wide field. But almost all of them have one thing in common. They don’t introduce coma into the view. The paraboloidal mirror does that. And , as I’ve already mentioned, coma isn’t particularly easy to see, anyway. Why do we see blobs of starlight over half the field in some of these eyepieces and get a good view with others?

The reason is the astigmatism the eyepiece introduces. The reason that some of these wide angle eyepieces introduce so much astigmatism is that they weren’t designed to work with fast Newtonians. They work just fine with an f/10 SCT, but they’re completely out-manned at something like f/6 or faster.

I can’t tell you how much astigmatism a particular eyepiece introduces when used with a fast Newtonian. The reason is that I don’t have the eyepiece design parameters. And it’s extremely, highly, absurdly unlikely that Uncle Al or any other top flight eyepiece designer will give them to me! So, I can only suggest a test you can do to try to weed out the eyepieces that could go by the brand name “balloonmaker”:

1. First, you really need to know that the telescope you’re using has a well figured mirror. I don’t have space to tell you how to do this. Just know that you need a really good, really fast Newtonian. If you’re deciding how to equip a telescope you plan to either buy or build, find a good one that’s as close to your desired scope as possible.

2. Make sure that the telescope is cooled down and that tube currents are minimized. Also, the telescope must be well-collimated.

3. Point the telescope at the brightest star you can see that’s above, say, 60-degrees altitude. The higher the better.

4. Focus the telescope on the star at the center of the field of the eyepiece you’re testing.

5. Slowly move the star to the edge of the field, and notice where it begins to “balloon”. A well-corrected eyepiece won’t do that until the star has reached at least the 75% of the radius. A “baloonmaker” will do it at 50% of the field or less.

6. I contend that one really important criterion for rating wide angle eyepiece performance is how wide a “non-balloon” field it has. If you’re comparing two eyepieces, the one that has the wider sharp field will likely be the better eyepiece.

If you still don’t believe that eyepiece astigmatism is the cause of most “ballooning” in the field of wide angle eyepieces, do this simple test. When you have the bright star near the edge of the field, run it through focus. What you’re likely to see is a star image that’s a long ellipse on one side of the best focus, and outside of focus is another long ellipse at right angles to the one inside. If you see that, you’re seeing mostly eyepiece astigmatism. What’s keeping the images from being perfect lines is the mirror’s coma.

If you see a lot of “coma” in the outer edges of the field of a high-power, wide angle eyepiece, you’re seeing another symptom of an eyepiece that can’t handle the steep light cone of your fast mirror. Since the eyepiece is only covering a small real field, there shouldn’t be much coma visible. Of course, what you’re really seeing is the astigmatism caused by the eyepiece.

If you place a Paracor in the light path, you’ll notice two things:

1. The image scale will be about 15% bigger, because the Paracor is a mild Barlow lens.

2. The off-axis balloons will be smaller, because the coma is mostly gone, but the astigmatism will only be slightly smaller due to the longer effective focal length of the combined system.

3. So, even though the Paracor does exactly what it’s claimed to do, it can’t make an eyepiece that’s not designed for a fast system work well with that fast system.

A Paracor costs a lot of money, but, if you have a well-figured fast mirror, it can remove most of that last bit of off-axis aberration your mirror provides. But, if you have eyepieces that aren’t working well with your mirror, a Paracor won’t help much. Only better eyepieces will do that for you. (Sorry to keep hammering on this, but a lot of amateurs simply don’t think about this!)

Here’s an alternate approach to solving the problem I’ve outlined above.

Let’s say you have an excellent fast Newtonian, but you’re stuck with eyepieces that don’t work well with it. You can’t afford a Paracor and all-new premium wide-angle eyepieces. What to do? I’d suggest getting a high quality Barlow lens that multiplies about 1.5-1.8X. This will both increase the power your present eyepieces deliver, but it’ll also radically reduce the astigmatism you see near the edge of their fields, because your eyepieces will be working with a shallower light cone. And, now that you’re effectively using a longer-EFL telescope, you can ad something like a 35- to 40-mm wide angle eyepiece to get back the lowest power you lost when you added the Barlow.

OK, to summarize:

1. The only way to minimize coma with a fast mirror is to buy a Paracor.

2. A Paracor won’t help an eyepiece that’s not designed to work well with a fast mirror. The improvement will be marginal, at best.

3. In some cases, the use of a high quality Barlow lens will do a lot to improve the view through a set of eyepieces that aren’t working well with a fast mirror.

Finally, there is an alternative to the Paracor. It’s called the Pretoria eyepiece. It was designed in the early 1980s by H. W. Klee and M. W. McDowell of the National Physics Research Lab in Pretoria, South Africa. They designed this eyepiece in response to a suggestion by the late Robert E. Cox, the long-time conductor of the "Gleanings for ATMs" column in S&T, and the associate editor of Telescope Making magazine.

It is a 28-mm eyepiece with a 50-degree field. Nothing remarkable there. What is remarkable is that it was designed to eliminate the coma of a paraboloidal mirror! It also suffers from no astigmatism and has a flat field. It also has a fairly long eye relief and suffers from no visible reflections.

Bob Cox had one made up, and several of us got to use it at either the 1984, 1985, or 1986 RTMC. Can't remember which. It was certainly a special eyepiece. You could put a planet or double star near the edge of the field and it looked as good as it did in the center!

Bob was able to persuade the folks at University Optics to have Pretoria eyepieces made in Asia for import into the US. They imported and sold the eyepiece in a 28-mm and 16.8-mm version. I've never seen the 16.8-mm version, but do have a 20-mm version that Don Yeier of Vernonscope was selling in the mid-90s. I use my 28-mm and the 20-mm as the two main eyepieces with my 20" f/4 Newtonian, along with my venerable 13-mm and 9-mm Naglers. They're among the finest eyepieces I've ever used.

The 50-degree field is a limitation, but literally every square degree of the field is useable, which makes up for it. Also, the throughput of these eyepieces is amazing. I've done tests of the Pretoria against other eyepieces. The test is, how dim a star near the Full Moon can you see? The Pretoria always wins.

I love the wider field of view through other premium eyepieces, but, for critical viewing, I always go back to my Pretorias.

For reasons I don't understand, the Pretoria wasn't a popular eyepiece until UO stopped importing them. Now you can't find them. The folks who have them won't sell them, because they know what they have.

Quick technical note. As with the Naglers and others, the Pretoria is a "Smyth-Type eyepiece configured as I outlined above. You can read a long article written by Klee and McDowell about the Pretoria eyepiece in "TM29".

OK. Enough eyepieces for now. Through a quirk of numbering, this column bears the label “Wild Card 001.1”. That’s so I could technically keep my promise to write about “SETI, a ‘Big Ear’, and Practical Jokes” in “Wild Card 002”. That’s next week….