Scattered data beam analyzer

Javier Sanchez-Mondragon; Jesus Escobedo-Alatorre; Ramon Rodriguez-Vera; Roberto Rojas-Laguna; Romeo J. Selvas-Aguilar; Miguel Basurto-Pensado

doi:10.1117/12.507399

10 November 2003 Scattered data beam analyzer

Javier Sanchez-Mondragon, Jesus Escobedo-Alatorre, Ramon Rodriguez-Vera, Roberto Rojas-Laguna, Romeo J. Selvas-Aguilar, Miguel Basurto-Pensado

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Proceedings Volume 5181, Wave Optics and Photonic Devices for Optical Information Processing II; (2003) https://doi.org/10.1117/12.507399
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

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 F_nl(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 F_nl(ρ,θ). In these cases, where the F_nl(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.

Citation Download Citation

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

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KEYWORDS

Zernike polynomials

Beam analyzers

Bessel beams

Bessel functions

Radon

Wavefronts

Interferometry

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