Here are some of my thoughts and bits and pieces collected from around the web on auto-guiding.
Like many people I've pondered on what the 'correct' value of the focal length of a guide-scope should be. That is given the main camera is imaging at focal length X, what focal length should I use for the auto-guider?
Searching around the web and asking people came up with the first 'rule'...
Use a guide scope at least 1/3 the focal length of the imaging scope, or longer.
Whilst it may work, I was never really satisfied with this rule, what basis did people use to come to this conclusion? So the quest continued.
Next I found someone (sorry I forgot who it was:( ) who gave me what he called a G-ratio figure of merit. This ratio is based on the ratios of the main and guider sensor resolutions in arcseconds, this means it uses both the focal lengths and the imaging sensor pixel sizes. This is more like it, as means an auto-guider with small pixels does not need as long a focal length guide scope as one with big pixels.
The G-ratio is defined as...
G-Ratio = (guider arcsec/pixel) / (imager arcsec/pixel)
or (easier to work out)...
G-Ratio = (imager focal length) / (guider focal length) * (guider pixel size) / (imager pixel size)
The conventional wisdom again was to get this ratio to a figure of about 1/3.
But then I thought about modern auto-guiders and auto-guiding software (I use AstroArt & Maxim). These can laughably easily achieve centroid calculations on the guide star image of 0.1 pixels, and a more realistic best working value may be 0.066 pixels or 1/15th of a pixel*. So perhaps a better G-Ratio to aim for would be somewhere between 1/15 and 1/5**.
I am working on the basis that the 'best' guide scope is the one that provides the auto-guider with the widest, fastest field of view. That way you have more chance of getting an nice bright guide star to work with.
Also there is no point in making the auto-guider work at a resolution that is much higher than your seeing allows. So having a nice long guide scope that allows the auto-guider to work at 2 arcseconds a pixel is useless if your seeing is 2 arcseconds. Why? Because remember the auto-guider actually calculates to 1/15 of a pixel - in this case 0.13 arcseconds resolution (worst case 0.4 arcsecs).
Also consider the mount; how accurately can it be guided?
For me seeing is probably the limiting factor at say 2 arcseconds on most nights. Working this backward means I am wasting my time with a guider resolution greater than 30 arcseconds a pixel. Working this out for the STV which has 7.4 micron pixels gives...
arcseconds/pixel = (pixel size in um) / (focal length in mm) * 206
fl = (pixel size in um) / (arcsec /pixel) * 206
fl = 7.4 / 30 * 206
fl = 50mm
Wow! Can you believe that number? Well yes actually. If you think about it SBIG supply an eFinder lens for the STV which they claim you can use to auto-guide to better than 1 arcsecond. That is half my assumed figure, and the focal length of the eFinder lens? It is 100mm twice the figure I calculated above.
Forget all about ratios and figures of merit. Work out what accuracy your mount/seeing/image scale allows, plug it in to the formula above and see what focal length you actually require. If you like add a bit for leeway, but I bet it still comes out way lower than 'conventional' wisdom dictates. Personally I use a cheap (£5-£10 second hand) 200mm f/4 Pentax thread camera lens with my auto-guider when imaging with my refractor, it is more than enough. With the SCT I am starting to use an off-axis guider (guiding at the same focal length as the imager) to eliminate mirror shift problems.
For an excellent article on what exposures and corrections to make when auto-guiding please read Jim McMillans article that you can find on this web page. I recommend you browse the hosting site, but here is a direct link to the PDF file.
* - This is a big assumption!
The calculation of the centroid is dependent on numerous factors including: uniformity of CCD pixel sensitivity (though this can be mitigated to some extent by assuring that the guide star creates largish ADU counts, and performing automatic dark subtraction - or even full calibration of the guide images!); the software algorithm used; the size of the star image on the chip, assuming 16bit ADC etc. For shorter focal lengths, the guide star may form an image only a few pixels across, this will severely limit the software's ability to calculate an accurate centroid - in this case a 'slight' defocus may be beneficial in giving the software more pixels with which to work.
** - For an imperfect camera with only 8bit digitisation, centroid calculation accuracy will come right down. I do not have empirical data, but a little less than 1/10 pixel accuracy 'feels' about right.
For you to give it a try! Sorry there is no error checking in this code, make sure you enter values carefully.