Sorry for reviving this old thread, but I became intersted in the subject, and was baffled by (1) the idea that shims can fix front/back focus issues, and (2) why this seems to help some, but not others.
First, I found a good detailed explanation of how phase-detection AF works (unfortunately, in Russian):
http://www.slrmaster.com.ua/wp/service/camera_repair/sistemy-avtofokusa-2/ .
Thanks for that link, it shows some nice diagrams. Have you seen Doug Kerr's
Principle of the Split Image Focusing Aid ? His website seems to be down at the moment, but you can usually get it from
http://doug.kerr.home.att.net/pumpkin/Split_Prism.pdf
This helped me to figure out what are the two main equations for the system. The detailed explanations (and my nice plot) can be found here:
http://photography-on-the.net/forum/showthread.php?t=967488&page=2 (post #20).
Interesting, but I see some problems with your analysis. You say, by modifying the lens to sensor distance you can solve both equations, and that's true - that's exactly how focussing is done (at least with a simple model of a lens). So adding or removing shims will shift the focus... until you trigger autofocus again, then the quality of focus depends on the AF sensor's ability to determine it, and that's all about measuring d.
In your original post on POTN you wondered if the body told the lens something like "focus at the object's distance of 3m". This myth has been comprehensively debunked (e.g.
http://forums.dpreview.com/forums/readflat.asp?forum=1031&message=35911287 - ignore Erik's posts, they won't help you).
Doug Kerr recently expressed the essential idea that you need to understand what's going on -
"The way in which SA [spherical aberration] gets into the picture is that the AF system works wholly with marginal rays: rays that come only from portions of the exit pupil near its edge. In the actual image on the film or sensor, these rays, because of SA, do not converge at the same point along the axis as, for example, the rays passing through the center of the exit pupil.
"Therefore, the point of 'best focus' when all rays are used (as for the actual taken image) will not be the same as the 'best focus' when only marginal rays are in play (as on the AF detector). ('Best focus' on the actual taken image is perhaps the focus situation in which the circle of confusion from SA was smallest)."
Here's the ProPhoto thread where he said it -
http://www.prophotohome.com/forum/canon-1-series-digital-slr-eos-5d/91885-canon-eos-af-scheme-chuck.html (the quote is from post 59).
If you don't want to read the whole thing, here are the main conclusions:
Focus is confirmed when the AF sensor says so, via an iterative closed-loop process. Quality of focus depends on the AF sensor's ability to make that judgement, and that depends on the best focus correction value that the body receives from the lens.
If you don't want to read the whole thing, here is the main conclusion:
- Adding/removing shims should help you to fix front/back focusing only if the camera is properly calibrated.
So presumbaly people for whom shim manupulation didn't do much had not well calibrated cameras.
That's a very interesting idea, and it certainly fits with Joe Miller's experience with a calibrated body.
You might also be interested in my experience of getting my gear calibrated -
http://forums.dpreview.com/forums/readflat.asp?forum=1031&message=31555078 
