Orthogonal functions and Zernike polynomials- a random variable interpretation

• Autores: Christopher S. Withers
• Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 50, Nº 3, 2009, págs. 435-444
• Idioma: inglés
• DOI: 10.1017/s1446181109000169
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• Resumen

  • There are advantages in viewing orthogonal functions as functions generated by a random variable from a basis set of functions. Let Y be a random variable distributed uniformly on [0,1]. We give two ways of generating the Zernike radial polynomials with parameter l, {Zll+2n(x), n=0}. The first is using the standard basis {xn,n=0} and the random variable Y1/(l+1). The second is using the nonstandard basis {xl+2n,n=0} and the random variable Y1/2. Zernike polynomials are important in the removal of lens aberrations, in characterizing video images with a small number of numbers, and in automatic aircraft identification.