Since diffraction technique is my prefferred method, I elected to use it to compare to the other methods. If it turned out at any point in my tests that another method was better, I planned to retest with that method as the standard. The first test was a comparison of diffraction to peak value and FWHM (X-Y). The procedure was as follows:
1) Achieve precise focus using diffraction.
2) Step gradually away from focus.
3) Take 10 sequential FWHM (X-Y) readings and 10 peak value readings at each step point.
4) Retake the diffraction image when finished to confirm out-of-focus.
5) Perform series as quickly as possible to minimize thermal effects
As you can see from the rather extreme scatter of the peak value readings, it is impossible to determine from peak value which focus series represents the actual point of best focus. As you can see from the summary of the procedure, it was the first series that was actually at optimal focus.
This data looks somewhat better, with the first series showing an slightly lower overall FWHM. There is still quite a lot of overlap, however - enough so that I would not want to use it as a reliable focus method. Even if one were to use this method to focus, it is clear that multiple passes would be required which is somewhat time consuming. As we shall see later, this presents its own set of problems.
The data for FWHM(Y) looks just as random as the peak value data (even though it would seem that it should be more like the "X" data). It is obvious what is being seen in these plots is the effect of seeing. The exposures used were 2 second exposures on a typical medium brightness star that was present in the same field but well away from the bright star used for the diffraction focus at the start and the end of the run. The night was quite average in terms of stability. I have also tried longer exposures (5 and 7 seconds) in an attempt to average the scintillation, with results that were not significantly different.
For those that are unconvinced that the focus was really changing by a significant amount during the previous set of tests, shown below are the starting (in-focus) and ending (out-of-focus) diffraction images. It is clear from not only the diffraction spikes but also the blooming spikes and the dimmer stars that the end image was not precisely focussed. The amount that the focuser was moved from beginning to end was .006 inches - which is about what one would expect from the depth of focus numbers at this F ratio (appx. F7 on the RC Cass). Remember that the maximum depth of focus at this F ratio is appx. .007 inches and that is the entire (end-to-end) range.