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RMS, binning, resolution: how to use those values?

3 replies to this topic

#1 polslinux

polslinux

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Posted 13 April 2021 - 06:58 AM

Hello all,

I have some doubts on how to use those numbers to help me better understand how everything works together.

For the sake of simplicity, let's ignore seeing

Let's consider the following gear:

• guide camera 2.9um pixel, guide scope 205mm FL. Resolution is (2.9/205)*206.3 = 2.918 arcsec/pixel
• imaging camera 4.2um, imaging scope 350mm FL. Imaging resolution is (4.2/350)*206.3 = 2.476 arcsec/pixel
• guide camera 2.9um pixel, imaging scope 2032mm FL. Resolution is (2.9/2032)*206.3 = 0.294 arcsec/pixel
• imaging camera 4.2um, imaging scope 2032mm FL. Resolution is (4.2/2032)*206.3 = 0.426 arcsec/pixel

The guiding/imaging ratio when using the short FL scope with the guide system is (2.9*350)/(4.2*205) = 1.179

The guiding/imaging ratio when using an OAG with a long FL scope is (2.9*2032)/(4.2*2032) = 0.69

Let's say that my mount total RMS is stable at 0.5" every night. Am I correct in saying that:

1. when using the short FL system, in order to have round stars (0.5*1.179) <= (imaging resolution [2.476]). All good in such a case.
2. when using the long FL system + OAG, in order to have round stars (0.5*0.69) <= (imaging resolution [0.426]). All good also in this case but, due to the seeing, I should bin 2x2 in order to be less oversampled.

Now the question is: is my thinking correct? If not, what's the correct way to obtain the numbers I'm looking for?

TL;DR: how can I calculate what value of "Tot RMS" gives round stars (binning 2x2 allowed) with the setups I wrote at above?

Edited by polslinux, 13 April 2021 - 07:05 AM.

#2 SilverLitz

SilverLitz

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Posted 13 April 2021 - 09:22 AM

I do not think over/under sampling has anything to do with roundness of stars.  It is only the dividing line where extra resolution is achievable.  Until you reach critical sampling, finer image scale (either more FL or smaller pixels) will show up as more resolution in your photos.  As you get finer in image scale, your S/N will deteriorate (requiring more integration time).  So it is inadvisable to go past critical sampling.  The rule of thumb of this critical sampling is ~seeing/3.  Your mount's guiding performance will also impact your achievable resolution limit, e.g. worse mount performance or alignment/adjustment increases critical sampling level.

I think where the ratio of guiding/imaging scale come into play is the limit of autoguiding performance.  A rule of thumb of this that I have heard, is good guiding performance is limited by guiding imaging scale/3.  So using your guide scope, do not expect your Total RMS guiding error to be much better than 1.0", while using an OAG this limit would be much lower at ~0.1" (though this low would be unachievable as other factors, such as seeing, PE, and PA errors, would swamp it).

#3 polslinux

polslinux

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Posted 13 April 2021 - 09:41 AM

Hmmm, about the guiding/imaging scale and autoguiding performance I know the following:

RMS_TOT = sqrt(RA_Error^2 + DEC_Error^2)

Wanting RMS_TOT = 0.5" and putting RA_Error = DEC_Error = x, we then have:

0.5" = sqrt(x^2 + x^2) = sqrt(2*x^2) = x*sqrt(2)
x = 0.5" / sqrt(2) = 0.35"

This means that if we want to achieve a guide with total RMS of 0.5", each axes can have an error of max 0.35".
If we then do (x / guding_image_scale), we want the value to be close to 0.100 pixel (guiding software cannot go lower than that AFAIK). For the ASI290MM-Mini with guide scope 50mm f/4.1 the value is: 0.35 / 2.918 = 0.120 px , which is very close to the software limit.

Therefore, the best total RMS I can get with this setup is:

sqrt(guiding_image_scale * 0.1px + guiding_image_scale * 0.1px) = sqrt(0.2918^2 + 0.2918^2) = 0.413"

This doesn't take into account multi stars guiding and other advanced stuff I'm not aware of

Edited by polslinux, 13 April 2021 - 09:43 AM.

#4 polslinux

polslinux

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Posted 14 April 2021 - 06:24 AM

I've found something here on CN that might be the solution to what I'm looking for.

The formula to understand whether seeing/guiding/image scale is good is:

sqrt(seeing^2 + sampling^2 + guiding tot rms^2)

If we consider 3" for seeing (I live in a Bortle 7 zone, so I do not expect anything better than 2.5 I guess), the formula would result in:

imaging camera with short FL scope: sqrt(3^2 + 2.476^2 + 0.5^2) = 3.922"

imaging camera with long FL scope: sqrt(3^2 + 2.476^2 + 0.5^2) = 3.071"

That's very interesting, because this means that:

1. theoretically, I will get better stars with an RC10 rather than with my current 70mm quadruplet
2. guiding at 0.5 tot RMS would be enough to have round stars with an RC10
3. super low RMS guiding doesn't really matter much. In fact, guiding with a tot RMS of 0.25" would lower the amount to 3.040 (in the second case). Dunno how evident that would be in the final image. I guess not that much.

Now the question is: when I'll have the possibility to image small and far away planetary nebulae, does it mean that I would probably be better off cropping rather than binning?

Because binning 2x2 would indeed double the SNR, but it would also halve the image resolution. While cropping would double the object size, which is not bad for my final goal of printing my images.

What do you think?

Edited by polslinux, 15 April 2021 - 01:18 AM.

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