10 November 2003 Scattered data beam analyzer
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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.
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Javier Sanchez-Mondragon, Javier Sanchez-Mondragon, Jesus Escobedo-Alatorre, Jesus Escobedo-Alatorre, Ramon Rodriguez-Vera, Ramon Rodriguez-Vera, Roberto Rojas-Laguna, Roberto Rojas-Laguna, Romeo J. Selvas-Aguilar, Romeo J. Selvas-Aguilar, Miguel Basurto-Pensado, Miguel Basurto-Pensado, "Scattered data beam analyzer", Proc. SPIE 5181, Wave Optics and Photonic Devices for Optical Information Processing II, (10 November 2003); doi: 10.1117/12.507399; https://doi.org/10.1117/12.507399

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