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Coma free zone calculation

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#1 coenie777

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Posted 13 May 2017 - 04:48 PM

I am using the formula: cube of the focal ratio * 0.022, to determine the coma free zone of a telescope.

On one site (think it was Astronomics) it suggest you cube the focal ratio to get a coma free zone in mm.

There are a few other formulas I came across but for the sake of the argument would like to ask that we stick to the one above unless it is grossly misleading.

The answer I will get is how large a diameter I will have in my image circle that has coma less than the size of the airy disk eg. no discernable coma.

I would like to work out the following:

- What would the formula be if I take my seeing into account rather than calculate it based on the airy disk size for the system?

- If I have a coma corrector added which yields a 2x improvement on the calculated results, can I just double the figure I get from the above?

- Is the formula above (using 0.022) calculating the diameter or the radius of the corrected image?

Any views?

#2 Starman1

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Posted 13 May 2017 - 05:31 PM

There are two formulae:

0.022mm times the f/ratio³ (in diameter of field)

and

0.01778mm times the f/ratio³

What these are is a calculation for the size of the field in which the comatic star image is smaller than the Airy disc, so is essentially invisible.

Technically, coma is only zero at the exact center and grows larger from there in a linear fashion, but if you can't see it in the in-focus star image......

So, for example, your f/4 scope has a non-visible "coma-free" zone 1.14 to 1.41mm wide (i.e. diameter)

This is only a tiny portion of the field size in virtually any eyepiece.

Now, add, for one example of many, a TeleVue Paracorr coma corrector to the system, and coma is smaller than the Airy disc over a field several millimeters larger than 40mm.

A 31mm Nagler would see no coma at all (though you wouldn't use a 31mm in an f/4 scope).  For sure, no eyepiece used in the scope would see any coma at all.

Now, we are talking the LINEAR size of the comatic star image, not its APPARENT size.

For any given 20mm eyepiece, the larger the apparent field, the larger the field stop.  The larger the field stop, the larger the linear size of coma at the edge.

So, the wider the apparent field, the more visible coma will be.

Now, compare 10mm eyepieces.  All will have field stop diameters 1/2 the size of the 20mm eyepieces.

So the LINEAR size of coma at the edges of the fields will be exactly 1/2 as large.

Ah, but the magnification is doubled.

And since the comatic star image has a size, doubling the power doubles the APPARENT size of the star images so, lo and behold, the coma at the edge appears the same,

and the wider the apparent field, the more visible coma will be.

When is a coma corrector essential?  I think it's below f/6, though others might say f/5.

It's also essential if you want to use 80-120° eyepieces.  At any magnification.

#3 GlennLeDrew

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Posted 13 May 2017 - 05:37 PM

If you are using lower magnification (larger exit pupils), one does not resolve down to the Airy disk dimension. And so for visual observing the 'coma free zone' at given f/ratio is of fixed apparent angular diameter for all magnifications.

And when imaging, if the Fresnel pattern of diffraction is not sufficiently well sampled, the 'coma free zone' is larger than when the scale of the Airy disk is assumed/applied.

#4 Starman1

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Posted 13 May 2017 - 06:34 PM

If you are using lower magnification (larger exit pupils), one does not resolve down to the Airy disk dimension. And so for visual observing the 'coma free zone' at given f/ratio is of fixed apparent angular diameter for all magnifications.

And when imaging, if the Fresnel pattern of diffraction is not sufficiently well sampled, the 'coma free zone' is larger than when the scale of the Airy disk is assumed/applied.

Yes.

I.e. if the coma free zone is the inner 2° of field at low power, it's the inner 2° at high power.

Glenn,

If an image reveals a fainter outer edge to the star than the eye can see, wouldn't coma be more visible in an image?

#5 Oberon

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Posted 13 May 2017 - 10:47 PM

A 31mm Nagler would see no coma at all (though you wouldn't use a 31mm in an f/4 scope).  For sure, no eyepiece used in the scope would see any coma at all.

?

Why wouldn't you use a 31mm Nagler in an f/4 scope?

#6 Jon Isaacs

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Posted 14 May 2017 - 12:34 AM

A 31mm Nagler would see no coma at all (though you wouldn't use a 31mm in an f/4 scope).  For sure, no eyepiece used in the scope would see any coma at all.

?

Why wouldn't you use a 31mm Nagler in an f/4 scope?

Some wouldn't because the exit pupil is 7.75mm..

I do because I measured my dark adapted pupil at about 7.7-7.8mm.  I decided to try to measure it because I had noticed that some objects were noticeably brighter in the 41mm Panoptic in an F/5 scope than in the 35mm Panoptic and the 31mm Nagler..

And even if one's pupil is less than the exit pupil, the wide field of view can be useful.

Jon

#7 Starman1

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Posted 14 May 2017 - 01:03 AM

Jon's right.

I should have said, "In general, one would not normally use an eyepiece longer than 24-28mm in an f/4 scope."

#8 GlennLeDrew

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Posted 14 May 2017 - 01:06 AM

Don,

Images of sufficient duration reveal subtle things the eye does not perceive due to too-low surface brightness. That includes the fainter outer comatic blur, particularly on dimmer stars. And other stuff, such as the diffraction induced by Newt primary mirror clips and spider diffraction spikes on not-bright stars.

Spot diagrams for optical systems typically show the *maximum* extent of aberrations, even with a comparatively small sample count over the area of the pupil. Coma is a good example, where the extreme perimeter of the blur is typically well enough delineated. But it takes a sample count of many thousands of points distributed throughout the pupil to create a spot diagram that begins to simulate well enough the variation in brightness of the aberration. The outer 'tail' of the comatic blur is of pretty low surface brightness, and so its full extent would be seen only for sufficiently bright stars. For dimmer stars the aberration appears to be of much lesser magnitude/extent.

#9 Nils Olof Carlin

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Posted 14 May 2017 - 05:21 AM

the wavefront error from a paraboloid mirror (assuming: millimeters!! 550 nm green light, aperture defined by the mirror, and RMS error) is ~6.7*d / F3 (F=focal ratio, d= distance in mm from optical axis). The Maréchal criterion (a "generalized" Rayleigh criterion) evaluates to 0.022*F3 in diameter.
This is in the diffraction limited domain where the wavefront error mainly effects the ratio diffraction disk intensity/ring system intensity, thus detail contrast rather than resolution - the contrast of fine planet detail will suffer, but star images won't be bloated.

(At wide fields and low magnifications, you are in the ray optics domain where the maximum comatic blur is 3d/16F^2 IIRC).

"The answer I will get is how large a diameter I will have in my image circle that has coma less than the size of the airy disk eg. no discernable coma."

Optical images don't form that way, and this is a physically almost meaningless criterion (even though not seldom used!).

See simulated images at successively increasing coma: the third image at the Maréchal criterion, the second and 4th at 0.5 and 2.5 times that respectively. The central ("Airy") diffraction disk is lowered but not widened at small amounts of coma, while the diffraction rings are successively more asymmetric and strengthened.

Vladimir Sacek expresses this clearly at
http://www.telescope...aberrations.htm

'As an initial indicator of optical quality, optical designers often consider a system close to "diffraction-limited" if its ray spot radius doesn't exceed the Airy disc radius. Called the Golden rule of optical design, it is still a very loose indicator of optical quality which, depending on the type of aberration, can be associated with aberration levels of anywhere from ~0.5 to 0.999 Strehl.'

#10 Jon Isaacs

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Posted 14 May 2017 - 07:25 AM

Don,

Images of sufficient duration reveal subtle things the eye does not perceive due to too-low surface brightness. That includes the fainter outer comatic blur, particularly on dimmer stars. And other stuff, such as the diffraction induced by Newt primary mirror clips and spider diffraction spikes on not-bright stars.

Spot diagrams for optical systems typically show the *maximum* extent of aberrations, even with a comparatively small sample count over the area of the pupil. Coma is a good example, where the extreme perimeter of the blur is typically well enough delineated. But it takes a sample count of many thousands of points distributed throughout the pupil to create a spot diagram that begins to simulate well enough the variation in brightness of the aberration. The outer 'tail' of the comatic blur is of pretty low surface brightness, and so its full extent would be seen only for sufficiently bright stars. For dimmer stars the aberration appears to be of much lesser magnitude/extent.

Another factor in the equation is the resolution of the eye at large exit pupils, no one is resolving the Airy Disk with a large exit pupil.  To see images like those in Nils' post requires very small exit pupils, no greater than 1mm, probably smaller.  This means that at large exit pupils, it actually takes quite a bit of coma for it to be visible.  The field stop of the 31mm Nagler is 42 mm, at F/5, the diffraction limited field is 2.75 mm.  With the excellent correction of the 31mm Nagler, coma is not visible over a much larger field simply because the eye's resolution.

Jon

#11 Starman1

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Posted 14 May 2017 - 09:33 AM

the wavefront error from a paraboloid mirror (assuming: millimeters!! 550 nm green light, aperture defined by the mirror, and RMS error) is ~6.7*d / F3 (F=focal ratio, d= distance in mm from optical axis). The Maréchal criterion (a "generalized" Rayleigh criterion) evaluates to 0.022*F3 in diameter.
This is in the diffraction limited domain where the wavefront error mainly effects the ratio diffraction disk intensity/ring system intensity, thus detail contrast rather than resolution - the contrast of fine planet detail will suffer, but star images won't be bloated.

(At wide fields and low magnifications, you are in the ray optics domain where the maximum comatic blur is 3d/16F^2 IIRC).

"The answer I will get is how large a diameter I will have in my image circle that has coma less than the size of the airy disk eg. no discernable coma."

Optical images don't form that way, and this is a physically almost meaningless criterion (even though not seldom used!).

See simulated images at successively increasing coma: the third image at the Maréchal criterion, the second and 4th at 0.5 and 2.5 times that respectively. The central ("Airy") diffraction disk is lowered but not widened at small amounts of coma, while the diffraction rings are successively more asymmetric and strengthened.

comacomp.jpg

Vladimir Sacek expresses this clearly at
http://www.telescope...aberrations.htm

'As an initial indicator of optical quality, optical designers often consider a system close to "diffraction-limited" if its ray spot radius doesn't exceed the Airy disc radius. Called the Golden rule of optical design, it is still a very loose indicator of optical quality which, depending on the type of aberration, can be associated with aberration levels of anywhere from ~0.5 to 0.999 Strehl.'

an article in S&T on coma back in the '90s quoted coma as being less than the size of the Airy disc at 0.0007" x f/r³, or 0.01778mm x f/r³

the same article quote Sidgwick as saying 0.0036mm  f/r³ and Sinnott as 0.0088mm x f/r³

I don't recall how they calculated their figures, but all of these are more stringent than the 0.022mm x f/r³

Any ideas why?

Edited by Starman1, 14 May 2017 - 09:34 AM.

#12 Nils Olof Carlin

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Posted 14 May 2017 - 11:06 AM

Don,

an article in S&T on coma back in the '90s quoted coma as being less than the size of the Airy disc at 0.0007" x f/r³, or 0.01778mm x f/r³

the same article quote Sidgwick as saying 0.0036mm  f/r³ and Sinnott as 0.0088mm x f/r³

I don't recall how they calculated their figures, but all of these are more stringent than the 0.022mm x f/r³

Any ideas why?

I vaguely recall seeing that article too (by Sinnott IIRC) but I don't know by what criteria these numbers were derived. Maybe subjective - where the authors would find coma noticeable or objectionable (though I think 0.0036 mm is on the unreasonably stringent side).

Finally, after doing my best with my limited maths, I figured out that expression for wavefront error (factor 0.022 mm), and knew just what assumptions were behind it.

Much like the quarter-wave Rayleigh criterion, it is rather lenient and in practice, you would set a more stringent goal for collimation (as you would for spherical aberration!) Maybe half?

#13 coenie777

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Posted 14 May 2017 - 11:25 AM

Thanks for the responses. Busy digesting it (read, try to make sense of it).

Nils regarding this:

(At wide fields and low magnifications, you are in the ray optics domain where the maximum comatic blur is 3d/16F^2 IIRC).

Would you say that this should be the better criterion to use if your primary usage of the scope is astrophotography?

From Don's response I see that the other formulas provide the size of the coma where it is less than the size of the airy disk. If my airy disk size is calculated to be 1.44" but my seeing is 3", does that mean that I will not see coma out further from the centre (up to the point where the coma size is <=3")?

Lastly please also comment on the effect a corrector would have on the situation. In my MN190 I am told the meniscus corrects coma 2x better than without it. Can I take the above arrived at answers from the calculations and just double them for my system (roughly) or not? For example the diameters Don calcuted were 1.14 to 1.41mm from centre, would these be 2.28 to 2.82mm in a MakNewt?

#14 Oberon

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Posted 14 May 2017 - 11:34 AM

A 31mm Nagler would see no coma at all (though you wouldn't use a 31mm in an f/4 scope).  For sure, no eyepiece used in the scope would see any coma at all.

?

Why wouldn't you use a 31mm Nagler in an f/4 scope?

Some wouldn't because the exit pupil is 7.75mm..

I do because I measured my dark adapted pupil at about 7.7-7.8mm.  I decided to try to measure it because I had noticed that some objects were noticeably brighter in the 41mm Panoptic in an F/5 scope than in the 35mm Panoptic and the 31mm Nagler..

And even if one's pupil is less than the exit pupil, the wide field of view can be useful.

Jon

Gotcha.

Of course, at f/4 one would use a Paracorr...thats f/4.6, and a pupil of 6.7mm.

But I digress.

#15 Starman1

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Posted 14 May 2017 - 01:17 PM

Thanks for the responses. Busy digesting it (read, try to make sense of it).

Nils regarding this:

(At wide fields and low magnifications, you are in the ray optics domain where the maximum comatic blur is 3d/16F^2 IIRC).

Would you say that this should be the better criterion to use if your primary usage of the scope is astrophotography?

From Don's response I see that the other formulas provide the size of the coma where it is less than the size of the airy disk. If my airy disk size is calculated to be 1.44" but my seeing is 3", does that mean that I will not see coma out further from the centre (up to the point where the coma size is <=3")?

Lastly please also comment on the effect a corrector would have on the situation. In my MN190 I am told the meniscus corrects coma 2x better than without it. Can I take the above arrived at answers from the calculations and just double them for my system (roughly) or not? For example the diameters Don calcuted were 1.14 to 1.41mm from centre, would these be 2.28 to 2.82mm in a MakNewt?

Ah, thinking like an astrophotographer, not a visual observer.

To an APer, the size of "seeing" is the worst-case scenario--whatever occurs in photos of some length.

To the visual observer, seeing fluctuates all over the place.  For instance, on a night of what an APer would call 3" seeing,

the visual observer might see seeing fluctuate from 0.5" to 3", which is why waiting for moments of calm seeing rewards the visual observer

with momentary "lifting of the veil" experiences.

The Dawes limit for my scope is 0.36", and the Sparrow limit even lower.  To not interfere with visual observing of close doubles, coma

would have to be well under the size of the spurious disc, let alone the Airy disc, which is larger than the spurious disc.

I have occasionally taken my coma corrector out of the system to see what the stars look like without it.

I think I could split a close double only dead center in the field without it.  Anywhere else, the star images look terrible.

And that's at f/5 (5.75, coma-corrected).  Given what I see in star images, coma has to be pretty small to not be visible--at any power (assuming not masked by astigmatism).

The figures I quoted were the less stringent calculations based on a newtonian.  If coma is 50% corrected in the Mak-Newt, it would be reasonable to double those diameters.

But that assumes that "2X better corrected" means "coma is half sized in a linear sense".

#16 coenie777

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Posted 14 May 2017 - 03:13 PM

Ah, thinking like an astrophotographer, not a visual observer.

You got me Don

Thanks for the reply around the corrected impact. I did mean "coma is half sized in a linear sense".

All this talk has made me realize how critical a coma corrector's placement has to be to get the best results. I think that is also why I am still struggling with the MN190. The coma correction introduced by the meniscus (or a coma corrector) has a sweet spot for which is was designed. Place it anywhere outside of that "sweet spot" and you will see degraded results, although still better than without it.

Appreciate all the advice

#17 Nils Olof Carlin

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Posted 15 May 2017 - 04:11 AM

Coenie,

at http://www.telescope...cs.net/coma.htm (about halfway down the page), Vladimir S discusses the coma as affected by the aperture stop - not always the edge of the primary, in many cases it is instead the edge of the corrector.
For a paraboloid mirror, no difference - for a spherical mirror (k=0), coma is cancelled when the stop is at the radius of curvature. If midway (where the corrector is usually placed in SCT, MN and SN types), coma is halved (compared to a paraboloid of the same dimensions). For a Schmidt camera, the corrector is at the ROC thus cancelling coma fully. Thus, as I understand things, the task of the corrector is not to lower coma but to cancel the spherical aberration of the (spherical) primary. The downside of full coma correction in a Schmidt camera is a twice as tall optical tube (and a larger primary than the aperture-defining corrector).

A coma corrector used with paraboloid mirrors is something quite different.

#18 Redbetter

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Posted 15 May 2017 - 04:23 AM

A 31mm Nagler would see no coma at all (though you wouldn't use a 31mm in an f/4 scope).  For sure, no eyepiece used in the scope would see any coma at all.

?

Why wouldn't you use a 31mm Nagler in an f/4 scope?

Some wouldn't because the exit pupil is 7.75mm..

I do because I measured my dark adapted pupil at about 7.7-7.8mm.  I decided to try to measure it because I had noticed that some objects were noticeably brighter in the 41mm Panoptic in an F/5 scope than in the 35mm Panoptic and the 31mm Nagler..

And even if one's pupil is less than the exit pupil, the wide field of view can be useful.

Jon

I don't have an f/4, but if I did I am certain I would be using a Paracorr making it an f/4.6.  Exit pupil of the 31 would be 6.7mm, close to perfect for dark sky.

#19 Jon Isaacs

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Posted 15 May 2017 - 06:10 AM

Gotcha.

Of course, at f/4 one would use a Paracorr...thats f/4.6, and a pupil of 6.7mm.

But I digress.

One might use a Baader MPCC.  Or one just might not use a Paracorr.  I don't always use a Paracorr at F/4, this thread is, after all, about not using a coma corrector and understanding just how much coma there is to be seen.

Jon

#20 coenie777

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Posted 15 May 2017 - 02:56 PM

Coenie,

at http://www.telescope...cs.net/coma.htm (about halfway down the page), Vladimir S discusses the coma as affected by the aperture stop - not always the edge of the primary, in many cases it is instead the edge of the corrector.
For a paraboloid mirror, no difference - for a spherical mirror (k=0), coma is cancelled when the stop is at the radius of curvature. If midway (where the corrector is usually placed in SCT, MN and SN types), coma is halved (compared to a paraboloid of the same dimensions). For a Schmidt camera, the corrector is at the ROC thus cancelling coma fully. Thus, as I understand things, the task of the corrector is not to lower coma but to cancel the spherical aberration of the (spherical) primary.

Nils, refering to your last statement, if the corrector is only correcting spherical aberration, where did the coma go to? I understand spherical aberration to be similar to coma but producing different results. Are we saying that a spherical mirror does not have coma? Since a MN only has the meniscus to correct the image and it manage to produce less coma, is this, from the argument above, meaning to say that the spherical aberration correction being corrected results in less pronounced coma?

The referance article is a bit advanced for my quick reading and understanding so please bear with me. I need to upskill on a lot of the technical terms used first to even begin to make sense of the arguments made.

#21 Vic Menard

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Posted 15 May 2017 - 07:50 PM

Read here: http://www.telescope.../Mak-Newton.htm , specifically, "...coma is reduced to ~30% of that in a comparable paraboloid."

#22 Moon Rock

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Posted 15 May 2017 - 11:46 PM

There are two formulae:

0.022mm times the f/ratio³ (in diameter of field)

and

0.01778mm times the f/ratio³

What these are is a calculation for the size of the field in which the comatic star image is smaller than the Airy disc, so is essentially invisible.

Technically, coma is only zero at the exact center and grows larger from there in a linear fashion, but if you can't see it in the in-focus star image......

So, for example, your f/4 scope has a non-visible "coma-free" zone 1.14 to 1.41mm wide (i.e. diameter)

This is only a tiny portion of the field size in virtually any eyepiece.

Now, add, for one example of many, a TeleVue Paracorr coma corrector to the system, and coma is smaller than the Airy disc over a field several millimeters larger than 40mm.

A 31mm Nagler would see no coma at all (though you wouldn't use a 31mm in an f/4 scope).  For sure, no eyepiece used in the scope would see any coma at all.

Now, we are talking the LINEAR size of the comatic star image, not its APPARENT size.

For any given 20mm eyepiece, the larger the apparent field, the larger the field stop.  The larger the field stop, the larger the linear size of coma at the edge.

So, the wider the apparent field, the more visible coma will be.

Now, compare 10mm eyepieces.  All will have field stop diameters 1/2 the size of the 20mm eyepieces.

So the LINEAR size of coma at the edges of the fields will be exactly 1/2 as large.

Ah, but the magnification is doubled.

And since the comatic star image has a size, doubling the power doubles the APPARENT size of the star images so, lo and behold, the coma at the edge appears the same,

and the wider the apparent field, the more visible coma will be.

When is a coma corrector essential?  I think it's below f/6, though others might say f/5.

It's also essential if you want to use 80-120° eyepieces.  At any magnification.

New guy here. I would like to start by saying Thank You to all for the great info here on CN.

Last month I bought a Meade LX70 8" F5 while it was on sale at Astronomics. I'm not an entire newb at stargazing, but my previous scopes were all slower refractors. This is my first fast scope. So, before it even arrived I've been researching here for some good eyepieces. I had about decided to get the Meade UWA 20, 14 and 8.8 but now I'm not so sure.

How bad do you think the coma would be in my scope with the Meade UWA's? Can the coma corrector wait for more funds or will it be better to get it at the same time and postpone one of the EP's?

Will different EP's like the AT Paradigm ED's or Meade HD60's be a better option?

Any suggestions would be appreciated.

Thanks.

David

#23 Starman1

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Posted 16 May 2017 - 01:44 AM

You can postpone the coma corrector.

Jut remember that you can get better star images at the edges of the field than you see.

The coma may not bother you at f/5.  In that case, you saved some \$.

#24 Moon Rock

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Posted 16 May 2017 - 11:39 AM

That's good news. I appreciate your feedback.

I picked up the first one this morning already - the UWA 8.8mm price was lowered today on Amazon to \$80 bucks. Had to get it.

David

#25 starcanoe

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Posted 16 May 2017 - 12:07 PM

Okay, we have the equation(s) for "diffraction limited" FOV relating to coma and f ratio.

What is the one for the eyeball can't resolve it? Such equation would be nice where you could plug in various eye resolutions so as to reflect how picky or not you want to be.

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