Hi Alicia,

The convention chosen by Zemax is “arbitrary”, but it does not mean it is random or fluctuating. It is described in the sentence(s) before the one you highlighted (perhaps not clearly enough).

In practice, different groups of people (and consequently the software they use) may use different conventions that are well justified. A common example is for defining the sign of surface coefficients: An optical engineer may define the sag coefficients with respect to an imaginary axis oriented from the “object” towards the “image” (AKA the optical axis). On the other hand, manufacturing or metrology engineers may define these coefficients with another axis (usually linked to the physical lens surface --the normal pointing from the inside of the lens to the outside--  or to the manufacturing/metrology machine). Both conventions make sense.

In practice, I would second the suggestion of the last sentence of your screenshot, that you test a simple case first: You can try with a Zernike phase with 4 Zernike coefficients and use the 4th (parabolic) to see that a negative coefficient gives a positive power (a collimated beam is made convergent) and vice versa.