f stop associated with AF point
First of all F5.6 and F2.8 are arbitrary numbers picked up by Canon and in my opinion at least F5.6 limitation doesn't make any sense to me. Focus depends on contrast and amount of light reaching the sensor, so even F1.4 lens won't focus in very low light or low contrast (try to point into blue sky and see for yourself), on the other hand some people cover the F-stop pin on TC to fool the camera the lens is more or less F5.6 and get perfectly good focus even with combined aperture of F8 or higher as long as camera's computer doesn't know it. Higher precision of center point focus with F2.8 lenses make little more sense, since DOF is much narrower with lens wide open and higher precision is a good thing here, but again I would bet good money, that in good light and contrast that sensor would work fine with F5.6 lens as well if it was allowed. So I suspect it's all one, big BS and main reason for limitations is Marketing. Buy faster, more expensive lenses. Maybe there was specific technical reason to choose F5.6 and F2.8 to meet the specs etc. way back when, but I don't believe auto focus sensors sensitivity didn't improve over the years to allow higher F-stop number lenses to work.
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