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RMS and resolution, how to use those values?

Guiding Mathematics
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Paolo avatar
Paolo avatar
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). This equals to 0.5895 <= 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). This equals to 0.345 <= 0.426. All good also in this case.


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

I have difficulties to deduce something meaningful from the guiding/imaging ratio. Consider it the following way:
A star should be considered as a perfect point. Due to diffraction at the aperture (giving an intensity distribution, following an Airy function) and the seeing (following a Gaussian distribution), a star isn't usually projected into a single pixel (for typical pixel sizes) but spread out over several pixels.

This fact tells you something about the right image scale of your camera-OTA combination: try to have an angular resolution of around 2/3 of seeing. Rule of thumb, depending on who you ask: 1"/pixel. And that's the "static" consideration. No Earth rotation, tracking, guiding or whatsoever.

Now, the RMS you mention: it gives you the average guiding error. Also this would be modeled through a gaussian. The effect on the above "smeared" out star is that the star will move around it's "static" position with this RMS. Hence, if your stars swirls around with 1" and your RMS is 0,5", the total standard deviation is 1,12" (the square-root of the sum of the squares). Given your camera's pixel scale, you can estimate how "large" the star will be (given it's not blown out through saturation). Finally, it'll be your decision if this value is too fluffy for you or not.

For your specific values: I recommend getting a focal reducer for your SCT (with the FL your giving, I bet you have an 8" f/10). Your image scale is too aggressive. Also the guiding camera would probably like to be binned while guiding on an OAG. I'm using a 8" f/10 SCT, reduced to f/7.5 with a guide scope at f=240mm. The imaging train has a resolution of 0,320"/pixel and the guiding 2,4"/pixel. That's a ratio of 7,5 and with my mount, I achieve (1) an RMS of 0,4" to 0,5" and round stars in the subs.

Cheers,
Björn
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Paolo avatar
Paolo avatar
I don't have such a big scope ATM, but what I'm planning to buy in the future is an RC10 smile

Thanks a lot for the explanation!