Elliptical polarization from circular and linear components

Two coherent waves with common propagation direction and frequency can combine into a polarization ellipse. Take circular components $E_x=A\cos \psi$, $E_y=A\sin \psi$ and add $B\cos \psi$ along $x$. The resulting semiaxes are $|A+B|$ and $|A|$. Choosing positive $A,B$ gives a nondegenerate ellipse with unequal axes. Uncorrelated relative phases do not describe the same fixed pure polarization.