Peak Value Method
Peak value method is probably the most well known and may be the most widely used method. It is based on the simple concept that as you come closer to focus, the light from a star will be concentrated in an ever smaller region and therefore the intensity values recorded by the CCD will increase. The point on the focus scale where the intensity is at its peak should be the point of best focus. Nearly all camera control programs display peak value in their focus modes. I will evaluate the effectiveness of this method later in this paper.
3D Wire Frame Plot
The 3D wire frame plot shows a star profile in 3 dimensions. The idea here is that focus will occur where the plot shows the narrowest and highest plot. Right now, the only program I am aware of that uses this is Cyanogen's MaxImCCD. I have found that although this method is nice-looking, it is mostly good for getting close to focus. In my experience the plots tend to look the same when dealing with very fine focus adjustments.
Full Width at Half Maximum (FWHM) X and Y
Full width at half maximum is the width of the star profile (in pixels or arc seconds) at the point at which the intensity value is half of its maximum. In this case, it is plotted both in the horizontal (X), and the vertical (Y) axes. MaxImCCD also displays this information. The focus screen shot from MaxImCCD (below) shows the display of peak value as well as the wireframe plot and FWHM (X-Y).
Full Width at Half Maximum (FWHM) Radial Profile
Full width at half maximum radial profile displays at the FWHM as a single number derived mathematically from the same star data. It can be thought of as an average representation of star size. One program that displays this information in its focus mode is Axiom Research's Mira (ACCI) shown below. It also displays a 2D graph of the data. Note that like MaxImCCD, it also displays peak value.
Hartmann Mask (Visual)
Another popular technique is the Hartmann mask. The illustration below shows a two hole Hartmann mask in place on a C8 on the left (the tape is not a peace sign, it just covers some extra test holes). On the right is the pattern you will see when aimed at a bright star and well out of focus. As you approach focus, the star images will merge and become one at focus. I will do a comparative analysis of this technique later in the paper.
Plotted Hartmann Mask
The plotted Hartmann mask is a variation on the Hartmann mask technique. In this case, the same mask as above is used on the telescope and the resulting out-of-focus image is analyzed with the imaging software. The exact separation between the center of each star image is determined and the position of the focuser is noted. The camera is then taken to the other side of focus and another image taken and is is likewise measured. The results are plotted as below. You can see that this is basically a simple ray trace and should allow a very accurate positioning of the focuser at focus. One caveat here is that this method will not work if you are moving a magnifying mirror to focus as in that case you are actually changing the focal length as you focus and that will skew the results.
Diffraction technique was recently brought to amateur attention by Warren Offut in his Winter 1995 article in "CCD Astronomy" magazine. This article can be found on Sky and Telescope's website and gives a nice description of his use of this technique. As seen below in the out-of-focus image on the right and the in-focus image on the left, the idea is to maximize the length, minimize the width, and eliminate or at least equalize the doubling of the diffraction spikes. The diffraction spikes are the spikes that are oriented at a 45 degree angle in these images of a bright star (the vertical spikes are blooming spikes). They can be formed by the spider already in a scope or by a diffraction device as described in Warren's article, or by a device like I constructed for my C8 (used for the image below). It is worth noting that in an ideal case, the spikes will be double "all at once" and come together all at once at focus. Various optical issues can cause this to not be the case (as in this example), the most common being slight mismounting of the camera so as not to be perfectly orthogonal to the optical axis or imperfect alignment of the spider vanes. I have not found this to be a problem for the in-focus images. I have seen it to some degree on nearly every system I have tested this on - including some high quality refractors. In many cases it actually helps to tell you when you have passed focus as the split spike "flips" to the opposite side. You may have guessed that this is my preferred technique. In the next section I will attempt to show you why.
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