Paul C. Buff, Inc. Technical Forum

No photo reflector is a truly parabolic curve. This is a term that is thrown around loosely. If one really studies and plots true parabolas one will quickly find an effective reflector must deviate from true parabola to provide even, usable light patterns. This particularly applies to umbrellas and PLM which are segmented approximations by nature of their construction.

I did at least 50 vector plots and samples in order to arrive at the optimal PLM arc.

There is also the issue that with umbrella construction techniques it is physically impossible to make the rods exactly follow a given arc plot, so it's a lengthy process of trial and error to arrive at the optimal design.