In optics usually Zernike polynomials are used to represent the aberration of a lens. As you know Zernike polynomials are defined in the unit disk and there they are orthogonal. The problem is that the lens that I have (a pupil) is $5 \text{mm}$ diameter long, so is not a unit disk. I do not know how to scale the Zernike polynomials so they are valid for disk with radius bigger than one.
Why do you need Zernike polynomials? I need them to calculate the generalized pupil image: $$GP(x,y)=P(x,y)\exp\left(\frac{i2\pi}{\lambda}WA(x,y)\right)$$where $P(x,y)$ is one if $(x,y)$ is inside the pupil and zero if outside, $\lambda$ is the wavelength and $WA(x,y)$ is the aberration defined by Zernike polynomials.
NOTE: I did not post this question in physics forum because I think is more a mathematical question than a physics one.
Thanks!
I think that you overcomplicate things: Zernike polynomials are defined inside the closed unit disk, but nowhere is it said what "unit" means. You are the one who defines the measurement unit, therefore choose one such that $5 \rm{mm}$ should be "one unit".
Alternatively, if you have some function $f : \{ |z| \le 1 \} \to \Bbb C$ and would like to use it to define $g : \{ |z| \le R \} \to \Bbb C$, just define the latter as $g(z) = f \big( \frac z R \big)$ (rescale the argument).