The Math of Autoguiding

When pairing up two cameras for astrophotography, I’ve run into issues where the cameras and scopes are mismatched in such a way that autoguiding software, even with an automatic calibration tool can’t quite configure it so that you get good guiding. Instead you get all sorts of streaking introduced by the autoguider compensating in ways it doesn’t need to.

Almost all of it comes down to really just trying to make sure the light coming into the imaging camera doesn’t move a whole lot. The first step is to figure out the image scale for each camera. The formula for calculating that is:

Arcseconds/Pixel = (206.265 / (focal length in mm) ) * (pixel size in microns)

In the case of a Canon Rebel XSi that I use, the pixels are 5.2 microns in size (µm). The guide camera I am using has pixels that are 4.65 microns. I use a 10″ LX200 and an Orion 80ED. Say I am running the LX200 at f/8 and the Orion 80ED at its native focal length as a guide scope.

In this case, the XSi is running at 0.53 arcseconds/pixel, and the guide camera is running at 1.59 arcseconds/pixel. This isn’t too bad, as we aren’t capturing beyond the resolution limit of the LX200, nor the Orion 80ED, but we are really close in both cases. We do have one problem though. One pixel of movement in the guide star is equivalent to 3 pixels of movement in the imaging camera (as a ratio of one to the other).

It gets worse too, seeing will affect the size of our guide stars, and will make the centroid of the star appear to move a little bit. For us to image at this focal length well, we pretty much have to be guiding at 1/3rd of a pixel. That isn’t possible, but attempting to use settings that would adjust at these subpixel ranges will likely cause us to overcorrect too much (as a result of seeing, 1/3rd of a pixel is still within the realm of a good subpixel guide program, in perfect seeing conditions). 

So right off the bat, we know that we will likely be unable to guide at subpixel levels with this pairing very often, and will need to lower the sensitivity of the autoguiding software to get better results on average nights. And in fact this is exactly what I encountered the first time I tried to guide with this setup. The guide software kept trying to overcorrect and lead to exposures I couldn’t use. After I turned down the sensitivity, I was getting much better guiding, but still subject to some flexture (likely from the wedge and the 80 lbs of weight bolted to it). Although I will need some more nights before I can nail down exactly how much flexture I actually have.

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