  In wavefront characterization, often the combination of a Shack-Hartmann
sensor and a reconstruction method utilizing the Cartesian derivatives of
Zernike circle polynomials (the least-squares method, to be called here Method
A) is used, which is known to introduce crosstalk. In
\citep{janssen2014zernike} a crosstalk-free analytic expression of the LMS
estimator of the wavefront Zernike coefficients is given in terms of wavefront
partial derivatives (leading to what we call Method B). Here, we show an
implementation of this analytic result where the derivative data are obtained
using the Shack-Hartmann sensor and compare it with the conventional
least-squares method.
