To give the background of my question, I am studying Zernike moments and need to work with magnitude only. Since my understanding of polar and cartesian coordinates is limited, I am failing to understand what would be basic for a person of related field.
The complex Zernike polynomials be represented as $V_{nm}(x,y)$ in the cartesian coordinates. Equivalently in $\left(\rho, \theta\right)$ polar coordinates they can be decomposed into the product of a radial polynomial $R_{nm}(\rho)$ and a phase term depending on $\theta$. Thus: $$ V_{nm}(x, y) = V_{nm}(\rho, \theta) = R_{nm}(\rho) e^{- \mathrm{j} m \theta} $$
The moments can then be computed as: $$ A_{nm} = \frac{n+1}{\pi}\sum_x \sum_y f(x,y) V_{nm}^{*}(\rho, \theta), \; x^2 + y^2 \leq 1 $$
I have no idea what the $*$ is :( Since magnitude and phase collectively give the value, I need to confirm that if we are interested only in magnitude, can we remove the whole $e^{- \mathrm{j} m \theta}$ term. Conversely, can we replace $V_{nm}(\rho, \theta)$ with $R_{nm}(\rho)$ in the last equation?
Thanks in advance for any guidance.