All this maths reminds me of where I started this thread - how to calculate diffraction effects with simple maths and elementary physics (Huygens-Fresnel Principle). I am sure all this exotic maths is very beautiful, but I do think running a simple computer model where you sum the wavelets is very transparent and easily understood.
I think trying to put a number to contrast is just a bit of fun, like devising a way to score renaissance paintings from one to ten. My 6 inch newt had mathematically better contrast than my 4 inch mak, but to my eyes at least the newt stars looked hairy and horrible. Compared to the little mak, the newt was a dreadful instrument for viewing double stars, regardless of its theoretically better contrast and resolution.