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# Coma and magnification--a mystery

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### #1 Starman1

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Posted 04 February 2013 - 03:54 PM

So here is the optical explanation for the visibility of coma in a short f/ratio newtonian reflector as revealed by the eyepiece:

Coma grows larger in a linear fashion from the center. A very short distance out from the center, the amount of coma still lies within the Airy disc and is not visible. Outside of that, coma steadily increases until the size of the comatic star image crosses a visible threashold.

Ergo, if we take 4 20mm eyepieces, of 50 degree, 68 degree, 82 degree, and 100 degree, the wider the apparent field, the more visible coma should be. The wider apparent field extends further out into the focal plane of the scope, and reveals star images of more coma. If I multiply correctly, the size of a comatic star image at the edge of a 100 degree eyepiece should be twice as long, radially, as a comatic star image at the edge of a 50 degree eyepiece.

Let's hypothetically double the magnification, so the true fields seen (i.e. the width of the image seen on the focal plane of the scope) are 1/2 as wide.
The comatic stars at the edge of the field in every eyepiece would be 1/2 as wide.

Yet, the magnification has doubled, making the comatic star images twice as big. When you double the magnification on an object 1/2 as wide, the result is 1, so the comatic star images at double the power should appear identical, as long as the apparent field doesn't change, at all powers. The linear size of the star image decreases, but the apparent size does not.

So if you use a coma corrector at low power, so long as all your eyepieces have the same apparent field of view, you should need the coma corrector all the way to the highest power your scope can produce.

Therein lies the mystery. Many, if not most, people report that the visibility of coma goes down as they raise the magnifications. That doesn't make sense from the standpoint of optics. So is there a reason or group of reasons why that might pertain?

I've thought about it and came up with this:
1) since the comatic star image behaves a little like an extended object, as the magnification is raised it grows fainter. Since the outer parts of the star image in a comatic star are fainter than the inner parts of the star image, perhaps they fade to invisibility. This might especially be true if the scope is being used in a light-polluted environment.
2) Many people have narrower apparent field eyepieces for high power than they do for low power. The objects being viewed are typically smaller, and many people do not feel pressed to pay the big bucks to maintain the ultrawide fields as the powers go up and the objects they're viewing get smaller. Narrower apparent fields, remember, show smaller comatic star images at the edge.
3) People look at the edge in a low power eyepiece because they're looking at big objects--star clusters, nebulae--and so they see the coma at low power. At high power, they're looking at smaller objects and not paying attention to the edge at all.
4) The eye requires a larger apparent size to see faint details as the object gets fainter. As the apparent size of the comatic star image stays the same at all powers (given equal apparent fields in the eyepieces), perhaps the fall off in apparent brightness of the outer edges of the comatic star image actually requires MORE magnification to make it visible (or, in another sense, an even larger apparent field) as the magnification goes up.
5) perhaps the higher-power eyepieces display less field curvature than the lower power eyepieces because of their smaller field stops. Field curvature could cause stars at the edge of the field to grow in size because they would be ever-so-slightly out of focus compared to the stars in the center. That would make the apparent size of the stars at the edge smaller at higher powers.

Perhaps we've all stumbled onto a psycho-physiological phenomenon that is related to the way a brain sees an image. I'm not sure of the answer as to why coma is found to be less visible at higher powers. Even some older texts say the same thing.

I did a recent test of my 12.5" f/5 scope without a coma corrector, and since it's been so many years since I viewed without coma correction, I wasn't surprised to see coma at all magnifications. And, I thought, it was pretty noticeable at all magnifications. I can't say it seemed the same at all magnifications, but i did find it objectionable at all magnifications all the way to a 1mm exit pupil, so count me as one who WILL use a coma corrector for all eyepieces.

Does anyone else have a different reason for why many observers don't see as much coma at higher powers? Or, perhaps, the EXACT reason why so many observers don't? I don't exactly feel like Sherlock Holmes, but it is a mystery.

### #2 GlennLeDrew

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Posted 04 February 2013 - 05:37 PM

A very cogent analysis, Don. I'm sure all your listed contributions to the seeming reduced visibility of coma at higher magnifications come into play at one time or another. You might add another:

6) As field size decreases, statistically there will be fewer bright stars contained within.

### #3 Tim L

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Posted 04 February 2013 - 05:44 PM

Don,

Thanks for posting this. I picked up a GSO coma corrector a while ago, but haven't yet got much use out of it. I tried testing it with a low-power EP (as per the conventional wisdom), but my eye's astigmatism is so bad at that exit pupil, I couldn't recognize any improvement.

After reading this and other posts, I'm going to try again with a 10mm 82-deg EP and slightly defocus to see if I can see the oval coma shape off axis. I'd like to be able to figure out the spacing for visual use on my coma corrector.

### #4 Starman1

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Posted 04 February 2013 - 05:55 PM

Don,

Thanks for posting this. I picked up a GSO coma corrector a while ago, but haven't yet got much use out of it. I tried testing it with a low-power EP (as per the conventional wisdom), but my eye's astigmatism is so bad at that exit pupil, I couldn't recognize any improvement.

After reading this and other posts, I'm going to try again with a 10mm 82-deg EP and slightly defocus to see if I can see the oval coma shape off axis. I'd like to be able to figure out the spacing for visual use on my coma corrector.

One of the primary reasons, I believe, why some people find coma unnoticeable or unobjectionable in low power eyepieces in scopes like f/4.3 or f/4.5 is what you point out--astigmatism so dominates the stars at the edge that coma is insignificant as an aberration.

If you use the ovality test at the edge of the field, make sure it's a relatively bright star you test, and ignore the fact the secondary shadow will appear off-center in the star image. By the way, in many or most eyepieces the star will not appear completely round when defocused at the edge because the eyepieces themselves are not perfectly corrected in either astigmatism or distortion. When you do this, you'll probably settle for the "least oval" solution, You may not be able to find a completely round edge-of-field star image at any setting of the eyepiece-coma corrector distance. That won't matter much when in focus.

### #5 Vic Menard

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Posted 04 February 2013 - 05:56 PM

Well, I use a coma corrector in my f/4 Dobsonian at all magnifications. Coma and field curvature are first on my hit list, but the underlying reason is the synergistic gain when paired with eyepieces that are designed for use with the coma corrector.

Perhaps at higher magnifications the brighter background stars are less numerous. I've read a few articles describing the best "richest field" telescope and, given a fixed AFOV, depending on the threshold magnitude of the dimmest background stars (easily seen, seen with scrutiny, or seen with averted vision...) the size difference varies considerably. In this respect, the observer preference defines the optimal aperture. I suspect coma detection could fit in a similar category.

And then there are observers who feel coma correction isn't necessary until the focal ratio falls below f/4.5. I think those same observers might call me "picky".

### #6 johnnyha

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Posted 04 February 2013 - 09:27 PM

Could it have anything to do with the diminishing size of the field stop?

### #7 FirstSight

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Posted 04 February 2013 - 09:50 PM

Well, I use a coma corrector in my f/4 Dobsonian at all magnifications. Coma and field curvature are first on my hit list, but the underlying reason is the synergistic gain when paired with eyepieces that are designed for use with the coma corrector.

Well, Vic if my assumption is correct that you're at Winter Star Party at this very moment, perhaps you'll have some opportunity to field-test some of Don's theories (or your own) about the relationship of coma vs focal-ratio. Surely a half-hour sometime experimenting without a coma corrector in your scope might be a worthwhile sacrifice in the interest of science. I'd try some experimenting myself, but unfortunately I'm stuck at home in N.C. this year instead of WSP, and we're socked in solid under clouds tonight. But next suitable clear night out, I plan to experimentally dabble a bit with this issue, though I don't have quite the technical sophistication of you or Don to grasp the nuances of what I might be seeing...

### #8 Starman1

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Posted 05 February 2013 - 01:23 AM

Could it have anything to do with the diminishing size of the field stop?

Yes, the field stop diminishes in size as you raise magnification, keeping apparent fields the same.
But the increase in magnification merely expands the apparent size of the comatic star back up to the same size to the eye as the more comatic star at lower magnifications.
If a star at the edge of a 50 degree field at 100X is 0.2mm wide to the eye, the star at the edge of the field at 200X is 0.1mm wide (half the linear width) times 2 (double the magnification) = 0.2mm wide to the eye.
Yet people say coma is less objectionable at high power. That's the mystery.

### #9 Astrojensen

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Posted 05 February 2013 - 03:48 AM

When the true field decreases in size with the increase in magnification, at one point you'll hit a size where all stars across the field are resolved airy disks and coma is small enough to be hidden inside them. The maximum true field diameter at which point this happens depend on the f/ratio and the magnification where it happens depends on the diameter of the field stop of the eyepiece and the apparent field of said eyepiece and the according focal length.

Clear skies!
Thomas, Denmark

### #10 Nils Olof Carlin

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Posted 05 February 2013 - 04:21 AM

hi Don,

One possible explanation of the paradox: it may be a matter of transition from the pure domain of wave optics in the center of the field where aberrations are small in terms of RMS wave aberrations, to the edges of a low-power field where the wavefront deviation is many wavelengths and the image is well represented by ray optics, and the comatic image will form the classic "ice-cream cone" image of coma in ray-traced images.
In your example of f/5, coma wavefront error is within 1/14 wave RMS in a circle of 2.8 mm diameter - here the airy disk will have more or less accentuated and skewed rings, brighter to one side, but not an elongated "coma" image, as farther out.

This image gives some idea of what to expect - the images, for f/5, are at 0, 0.7, 1.4 and 3.5 mm from the center of the field. Only the last image begins to look like coma. Assuming a 1 mm exit pupil, this is for 0, 8, 16, 40 deg off center. Only in the last image is coma obvious as such.

Within the 2.8 mm dia circle, the wavefront error will of course affect planetary contrast just as a similar wavefront error from any other mirror aberration, but star images would not immediately suggest coma unless you look for the asymmetric ring.

You write: " the amount of coma still lies within the Airy disc and is not visible." This is a classic mixing of metaphors - the Airy disk is purely wave optics, the rays that are projected from the mirror to within or outside the disk is something entirely else. This is not uncommon shorthand, and things scale nicely, but it should not be taken literally. For "diffraction limited" optics, in any reasonable sense, wave optics are mandatory, as is wavefront error.

Nils Olof

### #11 Sasa

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Posted 05 February 2013 - 04:50 AM

Don, I was wondering about it some time ago as well. I think, there are two main contributions. As was already mentioned, there are much less bright stars in the field when using higher magnifications.

The other reason is seeing. You compare coma to airy disc size, but with large dobsonians (I mean 200mm and more) your resolution is more limited by the atmosphere. At high magnification your scale is the blured star while at low magnifications the effects of atmosphere are negligible. So the visual "coma-free" regions is not anymore linear function of magnification.

BTW, at those times I derived a coma equivalent of the "2D[mm] rule" for maximum useful magnification. The coma in Newton should become visible if you are f*f/2 degrees out of axis. So for example, coma in my former f/5 Newton should become visible when you are 13 degree of the axis, and in my former f/6.4 Newton when you are 20 degrees away (Nagler).

My favourite object of checking coma was Trapez. For example in N150/750, coma was clearly visible from about half of the FOV of Panoptic 19mm.

### #12 Jon Isaacs

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Posted 05 February 2013 - 05:46 AM

Within the 2.8 mm dia circle, the wavefront error will of course affect planetary contrast just as a similar wavefront error from any other mirror aberration, but star images would not immediately suggest coma unless you look for the asymmetric ring.

This is something I have noticed at the eyepiece. At higher magnifications, the effect of coma is visible as reduced off-axis planetary sharpness/contrast/detail, i.e. a smaller sweet spot.

I also agree with the Glenn's comment about the reduced probability of there being bright stars at the edge. When I want to observe aberrations like coma, astigmatism and/or field curvature, I start with a reasonably bright star and then move it off-axis to inspect it.

Jon

### #13 Starman1

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Posted 05 February 2013 - 10:23 AM

When the true field decreases in size with the increase in magnification, at one point you'll hit a size where all stars across the field are resolved airy disks and coma is small enough to be hidden inside them. The maximum true field diameter at which point this happens depend on the f/ratio and the magnification where it happens depends on the diameter of the field stop of the eyepiece and the apparent field of said eyepiece and the according focal length.

Clear skies!
Thomas, Denmark

Yes, but the zone where coma is contained within the Airy disc is only 2.22-2.75mm at f/5 and smaller for eavery f/ratio shorter. Since even minimal fields of view in eyepieces are substantially wider, this is not the issue.
Of course, 43 degree field Orthos do have very small field stops in shorter focal lengths.
But people who use only orthos in a dob may never notice coma, either.

### #14 Starman1

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Posted 05 February 2013 - 10:42 AM

Nils Olof,

Thanks for correcting how I stated the initial problem. I should have said that coma is unlikely to be visible at all when the smear of the star image doesn't result in any eccentricity of the diffraction pattern, but you understood what I meant.

The issue, here, isn't where in the field coma becomes visible, but why higher power eyepieces of identical apparent field don't display coma to most people when lower power eyepieces do.

I like the dearth of stars in the field idea, because it is so obvious.

But I'm beginning to think that doubling the size of a comatic star image 10mm off axis does not result in exactly the same appearance of that star that the comatic star image 20mm off axis has at half the power. Your illustration seems to show that and I think I need to spend a little time with some math of the comatic images to see if the apparent width of the star image is identical in both cases. It should be.

### #15 Starman1

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Posted 05 February 2013 - 10:48 AM

As an aside, Nils Olof Carlin's illustration shows well why coma is a more commanding problem the wider the apparent field of the eyepiece gets.
And the difference in eyepieces used was one of the reasons I thought many people don't see coma at higher powers.

Enter TeleVue, where the higher-power Ethos actually have WIDER apparent fields than the lower power Ethos. Not a good prescription for reducing the presence of coma at higher powers.

### #16 GlennLeDrew

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Posted 05 February 2013 - 11:05 AM

Don,
Did you mean higher power Ethos vs lower power Nagler (or other design)?

### #17 Darren Drake

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Posted 05 February 2013 - 11:28 AM

Glenn,
I think Don may have been refering to the 3.7mm and 4.7mm Ethoi since they have 110 degree fov instead of the 100 degree fov.

### #18 GlennLeDrew

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Posted 05 February 2013 - 11:36 AM

Darren,
Of course! He did specify *apparent* FOV, while I'm sure I must have been stuck on true FoV.

### #19 Jon Isaacs

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Posted 05 February 2013 - 12:16 PM

Yes, but the zone where coma is contained within the Airy disc is only 2.22-2.75mm at f/5 and smaller for eavery f/ratio shorter. Since even minimal fields of view in eyepieces are substantially wider, this is not the issue.
Of course, 43 degree field Orthos do have very small field stops in shorter focal lengths.
But people who use only orthos in a dob may never notice coma, either.

I think Nils's point was that even within that "coma free"/ diffraction limited circle, the coma does affect planetary views. I believe the coma free region is defined as the region where the Strehl has dropped from 1.00 to 0.80..

I think of my fast Newtonians as Catadioptic telescopes..

Jon

### #20 dscarpa

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Posted 05 February 2013 - 01:37 PM

Thanks for all the info! I talked to Rob last night and will be getting SIPS with my 11" F/5 STS. It should be a plus for lunar viewing too. David

### #21 Astrojensen

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Posted 05 February 2013 - 02:42 PM

I think of my fast Newtonians as Catadioptic telescopes.

And I think I should get a coma corrector and do the same. Niels' post has been a bit of an eye opener for me, as it showed just how much coma affects resolution and contrast, even in an f/5 newton, where it is normally considered not too big of an issue.

It is pretty dang hard to keep planets in the sweet spot at +180x all the time, unless you have a tracking scope. Hmm. Equatorial platform or coma corrector? I do have a coma corrector for my binoviewer, but not for my single eyepieces.

Clear skies!
Thomas, Denmark

### #22 Astrojensen

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Posted 05 February 2013 - 02:47 PM

The other reason is seeing. You compare coma to airy disc size, but with large dobsonians (I mean 200mm and more) your resolution is more limited by the atmosphere. At high magnification your scale is the blured star while at low magnifications the effects of atmosphere are negligible. So the visual "coma-free" regions is not anymore linear function of magnification.

I think this is true. Seeing will almost always limit the resolution at high magnification.

Clear skies!
Thomas, Denmark

### #23 Jon Isaacs

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Posted 05 February 2013 - 03:20 PM

I think this is true. Seeing will almost always limit the resolution at high magnification.

It is probably true that most often it does. But probably more often, thermal equilibrium is the problem...

But when the seeing is excellent, the scope cooled down and rock solid thermally....

In any event, Standard Operating Procedure for me is to put a Paracorr in the focuser of any scope faster than F/6. I don't ask myself whether I need it at 400x, I ask myself what might I gain if I were to remove it. About the only thing that makes sense if I want a wider field of view with my lowest power eyepiece.

Jon

### #24 Starman1

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Posted 05 February 2013 - 03:21 PM

Yes, but the zone where coma is contained within the Airy disc is only 2.22-2.75mm at f/5 and smaller for every f/ratio shorter. Since even minimal fields of view in eyepieces are substantially wider, this is not the issue.
Of course, 43 degree field Orthos do have very small field stops in shorter focal lengths.
But people who use only orthos in a dob may never notice coma, either.

I think Nils's point was that even within that "coma free"/ diffraction limited circle, the coma does affect planetary views. I believe the coma free region is defined as the region where the Strehl has dropped from 1.00 to 0.80..

I think of my fast Newtonians as Catadioptic telescopes..

Jon

That zone is, IIRC, 0.0007 inches x the f/ratio cubed (x 25.4 to convert to millimeters).
or, 0.01778mm x F/R^3.
For f/6, the zone is 3.84mm wide
For f/5, the zone is 2.22mm wide
For f/4.5, the zone is 1.62mm wide
For f/4, the zone is 1.14mm wide
For f/3, the zone is 0.48mm wide

In my 12.5" f/5 dob, the image scale on the focal plane is 2.166'/mm
The image of Jupiter will always be smaller than 0.5mm, well within the coma-free zone. But only if held in the center of the field.
In my 31 Nagler, with a 42mm field stop, yielding a 91' field, only the center 4.8' of that field is not compromised by coma. That's less than 0.3% of the total field of view!!!

I, too, regard my newtonian as a catadioptric scope. My highest-power eyepiece has a field stop 10.4mm wide. With a Paracorr, the entire field is essentially coma-free. Without it, only the center 3.8% of the field is free from coma. Since f/5 is about as slow a dob as I'm likely to own, a Paracorr is an essential, IMO.

So let's look at the field stop of a distortion-free orthoscopic in 5mm (1mm exit pupil). That field stop in a distortion-free 43 degree field is 3.94mm wide.
A 2.22mm coma-free zone dominates the AFOV, and coma is not likely to be bad anywhere in the field, even though it is there.

So, once again, it seems that AFOV helps determine the impact of coma.
You and I like wide eyepieces.....and coma correctors.

### #25 Starman1

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Posted 05 February 2013 - 03:37 PM

I think of my fast Newtonians as Catadioptic telescopes.

And I think I should get a coma corrector and do the same. Niels' post has been a bit of an eye opener for me, as it showed just how much coma affects resolution and contrast, even in an f/5 newton, where it is normally considered not too big of an issue.

It is pretty dang hard to keep planets in the sweet spot at +180x all the time, unless you have a tracking scope. Hmm. Equatorial platform or coma corrector? I do have a coma corrector for my binoviewer, but not for my single eyepieces.

Clear skies!
Thomas, Denmark

Thomas,
Though it's a segue from the original post, I think you would find a coma corrector like the Paracorr beneficial in several ways:
--expanding the coma-free zone
--making fainter stars more visible everywhere in the field of view
--improving star images by reduction in coma and field flattening
--allowing the drift of an object across the field to not seriously damage the image quality
--improving the resolution of star clusters--especially globulars
--allowing the use of even wider field eyepieces
--providing an accessory to which filters attach so you can change eyepieces without changing filters from eyepiece to eyepiece
--improving the image quality from nearly every eyepiece
--revealing whether astigmatism or coma dominates the outer field in an eyepiece
--improving the visibility of small details within a nebula by concentration of the point sources that make up the detail. [I did a test on M27's outer "ropy" tendrils that arch around the perimeter of the fainter sections, and the coma corrector made them more clearly visible and more tightly focused.]
--you can get large refractor images without paying large refractor prices.
--slightly reducing the impact of seeing on star images.

It might be difficult to justify a \$500 accessory for a \$500 scope, but I guess what you'd have afterwards would be a truly magnificent \$1000 scope. Ever price a 10" refractor and mount? Takahashi has one for \$277,000.

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