Two-dimensional Legendre polynomials as a basis for interpolation of data to optimize the solution of the irradiance transport equation analyzed as a boundary problem on surfaces testing
| Autor: | M. M. Morín-Castillo, J. A. Arriaga-Hernández, J. Oliveros-Oliveros, B. Cuevas-Otahola |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Surface (mathematics)
Wavefront business.industry Zernike polynomials Differential equation Mathematical analysis Boundary problem 01 natural sciences Atomic and Molecular Physics and Optics 010309 optics symbols.namesake Optics 0103 physical sciences symbols Electrical and Electronic Engineering business Convection–diffusion equation Engineering (miscellaneous) Legendre polynomials Interpolation Mathematics |
| Zdroj: | Applied Optics. 58:5057 |
| ISSN: | 2155-3165 1559-128X |
| DOI: | 10.1364/ao.58.005057 |
| Popis: | In this paper, we give a solution to the irradiance transport equation (ITE) using the two-dimensional (2D) Legendre polynomials (LPs) and an interpolator (i-LP) based on the LP. In the first place, we analyze the experimental data; subsequently, we proceed to fit the most probable 2D LPs’ surface to the data in order to obtain the wavefront surface (W(x,y) of the elements under test) as a solution of the ITE differential equation associated with a boundary problem; and finally, we interpolate the resulting fitting. The interpolation is built from LP to increase the resolution and sharpness of the data. We apply the ITE to these results in order to obtain the wavefront as a nondeterministic solution that increases the resolution of the ITE as an optical test, and we compare our results regarding the obtained aberration surfaces (AS(x,y)). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|