Question: I have a prime Sigma f1.4 50mm lens on my Nikon D90 in `P` mode and focus mode on a set point of the field and notice that when I am using a tripod and change the f-stop that the camera changes the autofocus. Is it just resampling and presumably getting the same focus or does the focus change from one f-stop to the next?

Answer: 
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> does the focus change from one f-stop to the next
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Depth of field changes when you change the aperture, so the camera is probably adjusting to ensure that the object at the selected AF point remains in focus. This is particularly important when you increase the aperture (i.e. move to a lower f-number), giving you a narrower depth of field. AF systems aren't perfect, and what the system judged to be acceptably in focus at small aperture may not be acceptable a larger aperture. So yes, the camera is probably "resampling," but it's probably doing so because a small adjustment may be necessary.
If you think about a bigger change in depth of field, like f1.4 to f11, it is a bit more obvious: the autofocus has more 'probably sharp' points to pin down, therefore he needs to recalculate. If you have a smaller change in f-stop, the same happens, but on a much smaller basis and is barely noticeable.