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# Formula for Coma free zone

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### #1 RGM

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Posted 09 December 2014 - 07:38 AM

I have seen the formula used to calculate the diameter of the coma free portion of the FOV a few times here on CN.  I have tried to search for it, with no luck.

It is one that gives an answer in mm, and compared to the field stop diameter of your eyepieces.

Thanks

### #2 Jeff Morgan

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Posted 09 December 2014 - 08:21 AM

Your answer has two parts.

Firstly, I believe you can find the formula you are looking for here:

http://www.telescope...aberrations.htm

Secondly, how big does the cometic blur have to be to see it?

That is a harder one. The generally accepted number is around 3 arc minutes due to lowered resolution of low-light vision. But what if you are doing lunar or planetary? Also, there is variation in visual acuity from person to person. One persons "sharp focus" may be "soft image" to another person.

### #3 RGM

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Posted 09 December 2014 - 08:35 AM

Jeff, I found that one during my search, but it is not the one I am looking for.   There is a simpler one based on focal ratio and uses cube ( power of 3).  It gives an answer in milimeters.

### #4 Starman1

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Posted 09 December 2014 - 12:00 PM

The "coma-free" zone is that zone where the distortion of the star image does not yet exceed the size of the Airy disc.

The formula I use, and have seen often quoted is:

0.0007" x f/ratioÂ³

or, in millimeters

0.01778mm x f/ratioÂ³

A less-stringent application uses a different figure:

0.022mm x f/ratioÂ³

In neither case is coma likely to be visible to even the pickiest observer.

The difference between them is small.

In my f/5 newtonian, it's 2.22mm versus 2.75mm

If I'm using an eyepiece with a 36mm field stop, whichever figure is used, only the very center of the field is without coma.

Remember that linear size of a comatic image and apparent size of a comatic image are two different things.

The linear size is important to know, but it is the apparent size (which also takes magnification into account) that determines

what we see.  For example, the linear size of coma at the edge of the field in a 10mm 100Â° eyepiece is 1/2 the size of the comatic star

at the edge of the field in a 20mm 100Â° eyepiece.  But since the magnification is doubled, the apparent size of the comatic stars

at the edge are the same in both eyepieces.

Edited by Starman1, 09 December 2014 - 03:33 PM.

### #5 RGM

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Posted 09 December 2014 - 01:00 PM

Don, that is the formula I was looking for.  Thanks

### #6 GlennLeDrew

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Posted 09 December 2014 - 02:05 PM

As magnification is increased, the 'coma-free' zone shrinks due to the enlargement of the aberration. Because of this, for visual work a fixed linear field does not apply. Rather, it is fixed in apparent angle. If this zone were to subtend, say, 30 degrees apparent at low power, it will subtend the same 30 degrees apparent at moderate and high power.

### #7 Starman1

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Posted 09 December 2014 - 03:34 PM

As magnification is increased, the 'coma-free' zone shrinks due to the enlargement of the aberration. Because of this, for visual work a fixed linear field does not apply. Rather, it is fixed in apparent angle. If this zone were to subtend, say, 30 degrees apparent at low power, it will subtend the same 30 degrees apparent at moderate and high power.

Exactly.

### #8 Jeff B1

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Posted 09 December 2014 - 03:44 PM

The coma free field (CFF) in inches by:   CFF = 0.000433(F/R) 3, where F/R is the focal ratio.

The angular field (I) in degrees:   I = tan -1 (CFF / FL) , where ID is the field stop or field lens I.D. and FL is the focal length of your primary mirror.

Most likely the same as posted before in millimeters

Edited by Jeff B1, 09 December 2014 - 03:45 PM.

### #9 Jon Isaacs

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Posted 09 December 2014 - 04:01 PM

The coma free field (CFF) in inches by:   CFF = 0.000433(F/R) 3, where F/R is the focal ratio.

The angular field (I) in degrees:   I = tan -1 (CFF / FL) , where ID is the field stop or field lens I.D. and FL is the focal length of your primary mirror.

Most likely the same as posted before in millimeters

A couple of thoughts:

-  I believe that CFF = 0.000433(F/R)3 inches provides the radius of the Coma Free Field and is the equivalent of 0.011 FR3.

-  In practice, one can replace  I = tan -1 (CFF / FL)  with I = CFF/FL.. since this angle will always be small..

- Good job with the exponents. I had forgotten that CN version 3 allows for that..

Jon

### #10 Starman1

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Posted 09 December 2014 - 04:04 PM

A CFF of 0.000433" x f/rÂ³ is a field radius figure.  Double that for the Everhart standard for diameter.

It is looser than Sinnott's diameter formula (0.0007" x f/rÂ³)

and is a re-statement of the Everhart diameter formula (0.000866" x f/rÂ³)

However you express it, it is a small field.

Note that when you use a coma-corrector, you can reduce the aberration to a size smaller than the Airy disc much farther from center.

The TeleVue Paracorr II, as one example, will put an entire 40mm wide field's coma inside the Airy disc down to f/3.5.

To all intents and purposes, coma is eliminated.

### #11 Jon Isaacs

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Posted 10 December 2014 - 06:11 AM

A CFF of 0.000433" x f/rÂ³ is a field radius figure.  Double that for the Everhart standard for diameter.

It is looser than Sinnott's diameter formula (0.0007" x f/rÂ³)

and is a re-statement of the Everhart diameter formula (0.000866" x f/rÂ³)

However you express it, it is a small field.

Note that when you use a coma-corrector, you can reduce the aberration to a size smaller than the Airy disc much farther from center.

The TeleVue Paracorr II, as one example, will put an entire 40mm wide field's coma inside the Airy disc down to f/3.5.

To all intents and purposes, coma is eliminated.

It is my understanding that the definition of the coma-free region is the area in which the Strehl of a perfect mirror is 0.80 or better.

Jon

### #12 starcanoe

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Posted 10 December 2014 - 09:13 AM

Would be interesting to see how small the coma free field is when you require the amount of coma to degrade the Strehl no worse than a good APO refractor...something like 0.95 give or take a bit.

### #13 sawsatch

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Posted 10 December 2014 - 04:06 PM

Is coma a viewable factor in an 8" f/5.7 Dob with a Zambuto mirror? (I'm getting that one from Teeter's next year.)

Edited by sawsatch, 10 December 2014 - 04:07 PM.

### #14 Starman1

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Posted 10 December 2014 - 04:27 PM

Is coma a viewable factor in an 8" f/5.7 Dob with a Zambuto mirror? (I'm getting that one from Teeter's next year.)

There is coma, even at that f/ratio, but few observers use a coma corrector with a scope that long.

If you use 100Â° eyepieces and want refractor-like pinpoint star images to the edge, you might use one,

but few people would ever be that picky.  And if you use 40-70Â° eyepieces and seldom look at the edge of the field,

and don't care if they're a little distorted at that point (whether from coma, field curvature, distortion, or astigmatism), then you won't even think about a coma corrector.

If you LOOK for coma, you'll probably see it (well, if all other edge issues are absent, that is), but it's highly unlikely to bother you.

Edited by Starman1, 10 December 2014 - 04:28 PM.

### #15 sawsatch

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Posted 10 December 2014 - 05:18 PM

Great discussion; both technical and practical.

### #16 GlennLeDrew

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Posted 10 December 2014 - 05:51 PM

Is coma a viewable factor in an 8" f/5.7 Dob with a Zambuto mirror? (I'm getting that one from Teeter's next year.)

A fundamental aberration like coma is quite egalitarian, respecting all brands equally. That is, the most perfect Zambuto of given size and f/ratio will exhibit the identical comatic blur as found for a low-cost, machine-made mirror from across the Pacific. (For other aberrations it will be a different story.)

### #17 Jon Isaacs

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Posted 10 December 2014 - 06:41 PM

Is coma a viewable factor in an 8" f/5.7 Dob with a Zambuto mirror? (I'm getting that one from Teeter's next year.)

There is coma, even at that f/ratio, but few observers use a coma corrector with a scope that long.

If you use 100Â° eyepieces and want refractor-like pinpoint star images to the edge, you might use one,

but few people would ever be that picky.  And if you use 40-70Â° eyepieces and seldom look at the edge of the field,

and don't care if they're a little distorted at that point (whether from coma, field curvature, distortion, or astigmatism), then you won't even think about a coma corrector.

If you LOOK for coma, you'll probably see it (well, if all other edge issues are absent, that is), but it's highly unlikely to bother you.

I don't consider myself particularly picky but I do appreciate a clean round stars across the field of view.. A little more than a year ago, I purchased a used Starsplitter 13.1 inch F/5.5 and I was hopeful that I would be happy with the views without a Paracorr to correct the coma.. But it was not more than 15 minutes into the first night that it was clear to me that my Paracorr was going to be a fixture in the focuser of this scope..  I guess it's just that when those essentially perfect images are possible, why not?

Analyzing the visual impact of coma and the coma free zone is not so easy.. The linear size of the coma free zone is proportional to the cube of the focal ratio but the angular diameter is proportional to the square of the focal ratio for a given aperture.. To further complicate the issue is the fact that coma is two dimensional, generally it is thought of in terms of it's linear size but it does have an area and the area would seem to be proportional to the square of length so visually, it's visual impact is probably more closely approximated by the fourth power of the focal ratio..

And then one can look at coma as a function of aperture.. The linear size of the coma free region is independent of aperture but the angular size is inversely proportional to aperture..  This means that at equal magnifications, the smaller scope will have a greater coma free region.. At 200x, the coma free region of a 5 inch F/5 is right at 50 degrees, the coma free region of a 10 inch F/5 is 25 degrees (AFoV)..  Lots of ways to make comparisons.. the brightness of the stars, the range of magnifications..

When all is said and done, the visual impact of coma is best gauged by simply putting an eyepiece in your telescope and taking a look..

At F/4, most everyone finds a coma correct an essential, at F/8, most everyone finds a coma corrector unnecessary..   Somewhere between the two.. there's a lot of room for personal preference.

Jon

### #18 Peter Besenbruch

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Posted 11 December 2014 - 12:06 AM

At F/4, most everyone finds a coma correct an essential, at F/8, most everyone finds a coma corrector unnecessary..   Somewhere between the two.. there's a lot of room for personal preference.

I'd say f6 is a kind of tipping point. Most people don't need to use a corrector there, and certainly not at f7. At f5.5 I would use a corrector if I had 2" eyepieces, or possibly ultra wide angle ones.

Ever consider a 13.1", f8?

### #19 Ernest_SPB

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Posted 11 December 2014 - 03:08 AM

In visual applications coma free field of view should be estimated in terms of AFOV - angular field of view free from coma (AFOV-CF). It looks easy to estimate the filed like AFOV-CF = N*F-ratio^2, where N - some numerical factor evaluating coma tolerance for observer (N = 1/2 - for coma blur less 3 angual minutes), F-ratio^2 - square of F-number.

e.g. for Newtow with F-number 5, AFOV-CF = 5*5/2 = 12.5 degree, if eye of observer tolerates coma blur with 3 angular minutes

In most cases own field aberrations of most eyepieces (astigmatism, field cirvature, later color) exceed these 3 angular minutes, and it is more realistic to set N with 1 getting easier formula AFOV-CF = F-ratio^2 - AFOV free from coma is just square of F-number for Newton telescope in visul mode.

So we can represent the table F-number/AFOV-CF:

F4 - 16

F5 - 25

F6 - 36 (classic ortho will have whole thir FOV free from coma)

F7 - 49 (super plossl are coma free in F7 Newton)

F8 - 64 (WA eyepieces are coma-free in F8 Newton)

F9 - 81 (even Naglers are coma free in F9 Newton!)

Edited by Ernest_SPB, 11 December 2014 - 03:18 AM.

### #20 Jeff Morgan

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Posted 11 December 2014 - 11:58 AM

In visual applications coma free field of view should be estimated in terms of AFOV - angular field of view free from coma (AFOV-CF). It looks easy to estimate the filed like AFOV-CF = N*F-ratio^2, where N - some numerical factor evaluating coma tolerance for observer (N = 1/2 - for coma blur less 3 angual minutes), F-ratio^2 - square of F-number.

e.g. for Newtow with F-number 5, AFOV-CF = 5*5/2 = 12.5 degree, if eye of observer tolerates coma blur with 3 angular minutes

In most cases own field aberrations of most eyepieces (astigmatism, field cirvature, later color) exceed these 3 angular minutes, and it is more realistic to set N with 1 getting easier formula AFOV-CF = F-ratio^2 - AFOV free from coma is just square of F-number for Newton telescope in visul mode.

So we can represent the table F-number/AFOV-CF:

F4 - 16

F5 - 25

F6 - 36 (classic ortho will have whole thir FOV free from coma)

F7 - 49 (super plossl are coma free in F7 Newton)

F8 - 64 (WA eyepieces are coma-free in F8 Newton)

F9 - 81 (even Naglers are coma free in F9 Newton!)

Interesting. Final image quality in a Newtonian is of course the product of many factors. At f/5 the need for a coma corrector is obvious. At f/6 I find it tolerable without one. At f/7 it fades to the background, I really have to be hunting for coma to see it (my current large Newtonian is f/7).

But of all of the Newtonians I have looked through; commercial or homebuilt, coma corrected or non, fast or slow; the only one that approached the ideal of "refractor like" was f/9. While guys like Thomas Cave and Clyde Tombaugh managed it, for me it would just be a bit much with for a 16" mirror.

### #21 Jon Isaacs

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Posted 11 December 2014 - 02:15 PM

Jeff:

How were you able to produce the field curvature necessary to achieve that refractor like view?

Jon

### #22 Ernest_SPB

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Posted 11 December 2014 - 03:38 PM

With the same F-ratio Newton has much lesser field curvature and astigmatism then refractor (without field corrector).

### #23 Jeff Morgan

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Posted 11 December 2014 - 11:49 PM

Jeff:

How were you able to produce the field curvature necessary to achieve that refractor like view?

Jon

Field curvature? What field curvature?

### #24 Jon Isaacs

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Posted 12 December 2014 - 09:54 AM

Jeff:

How were you able to produce the field curvature necessary to achieve that refractor like view?

Jon

Field curvature? What field curvature?

Jeff:

Nice bird watching scope you have there..   The birds can nest right there in the objective.

Jon

### #25 Jeff B1

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Posted 12 December 2014 - 11:16 AM

In visual applications coma free field of view should be estimated in terms of AFOV - angular field of view free from coma (AFOV-CF). It looks easy to estimate the filed like AFOV-CF = N*F-ratio^2, where N - some numerical factor evaluating coma tolerance for observer (N = 1/2 - for coma blur less 3 angual minutes), F-ratio^2 - square of F-number.

e.g. for Newtow with F-number 5, AFOV-CF = 5*5/2 = 12.5 degree, if eye of observer tolerates coma blur with 3 angular minutes

In most cases own field aberrations of most eyepieces (astigmatism, field cirvature, later color) exceed these 3 angular minutes, and it is more realistic to set N with 1 getting easier formula AFOV-CF = F-ratio^2 - AFOV free from coma is just square of F-number for Newton telescope in visul mode.

So we can represent the table F-number/AFOV-CF:

F4 - 16

F5 - 25

F6 - 36 (classic ortho will have whole thir FOV free from coma)

F7 - 49 (super plossl are coma free in F7 Newton)

F8 - 64 (WA eyepieces are coma-free in F8 Newton)

F9 - 81 (even Naglers are coma free in F9 Newton!)

Interesting. Final image quality in a Newtonian is of course the product of many factors. At f/5 the need for a coma corrector is obvious. At f/6 I find it tolerable without one. At f/7 it fades to the background, I really have to be hunting for coma to see it (my current large Newtonian is f/7).

But of all of the Newtonians I have looked through; commercial or homebuilt, coma corrected or non, fast or slow; the only one that approached the ideal of "refractor like" was f/9. While guys like Thomas Cave and Clyde Tombaugh managed it, for me it would just be a bit much with for a 16" mirror.

Sometimes I ask my wife to give me a swift kick for building the 16" f/6.9.  The primary already had a small center hole for a Cass but in a weak moment Joyce and Parker talked me into it!  Oh well, the image are spectacular even on an 8-foot ladder    Clyde advised me to go ahead with plans for a 16" f/50 Cass glass made. Old Clyde was right.  Sitting under a scope is easier at times.

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