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Coma free zone calculation

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Tsar Daniels:
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?

Tim Jauregui:
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.

Kapil Majmudar:
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.

hiswacoka:

--- Quote ---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.


--- End quote ---
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?

Grant Buchanan:

--- Quote ---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.


--- End quote ---

?

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

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