Can somebody help me to understand how to get the ray fan plot from the OPD plot?

In the case where i only have defocus and some piston as wave front errors, the first derivative of the OPD curve (polynomial of 2nd degree) should lead me to a linear function, describing the slope of the OPD at any pupil coordinate (independent of the piston, since it doesn`t change the slope of the OPD curve).

However, whenever i try to calculate the ray fan value at a certain pupil coordinate, it always deviates from the value thatis shown in the ray fan plot at that point. Why is that? Maybe i am making a thinking error.

My recipe would be as follows:

• Read coordinates of  max. pupil coordinate point of max. field in OPD plot. (both in mm for example)
• calculate coefficient “a” of function   OPD-value = a * pupil-coord. ^2    (since its a pure defocus)
• Calculate derivative of quadratic OPD function  (which gives me the linear ray fan function)
• Calculate value of derivative of OPD function at max. pupil coordinate
• → should agree with value in ray fan plot at the same pupil coordinate

Thanks a lot for your help