Chris,
we discussed this topic already. It is NOT important whether the whole curve is hyperbolic or parabolic. I gave a lot of experimental data and showed that a quadratic fit (parabola) excellently works for fitting the data in the narrow region that is used by a auto focus run (see Proposal of a "Quadratic Fit" Auto Focus evaluation method - Auto Focus - Main Sequence Software ). One important point is: the coefficient of determination, R², would serve as a very good quality judgement of the AF run.
Bernd