We provide an analysis of a data beam fitting method of N data points on a circular pupil that corresponds to its
best rms fit that uses an orthogonal vectorial basis of the N data points. The solutions of many physical problems often result on finding specific solutions of basic functions Fnl(ρ,θ) with polar symmetries that also can be easily treated numerically. Unfortunately, in some other cases, the analytical
solution loss its orthogonality by the experimental data discretization, therefore become inadequate for a best rms fit
data. On the other hand, by introducing the Schmidt orthogonalization, we can get the best rms fit for the solution in the coefficients of the expansion and in Fnl(ρ,θ). In these cases, where the Fnl(ρ,θ) has a cumbersome convergence, we develop the rms fit based on Zernike like Polynomials and establish the proper transformation. We illustrate in more detail the method by developing a beam analyzer as an application.