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Zernike-like systems in polygons and polygonal facets
(Optical Society of America, 2015)
info:eu-repo/semantics/article,
Zernike polynomials are commonly used to represent the wavefront phase on circular
optical apertures, since they form a complete and orthonormal basis on the unit disk. In
[Diaz et all, 2014] we introduced a new Zernike ...
On a modifcation of Olver's method: a special case
(Springer US, 2016)
info:eu-repo/semantics/article,
We consider the asymptotic method designed by Olver (Asymptotics and
special functions. Academic Press, New York, 1974) for linear differential equations of
the second order containing a large (asymptotic) parameter : ...
Orthogonal basis with a conicoid first mode for shape specification of optical surfaces
(Optical Society of America, 2016)
info:eu-repo/semantics/article,
A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and ...
Generalization of Zernike polynomials for regular portions of circles and ellipses
(Optical Society of America, 2014)
info:eu-repo/semantics/article,
Zernike polynomials are commonly used to represent the
wavefront phase on circular optical apertures, since they form a complete
and orthonormal basis on the unit circle. Here, we present a generalization
of this Zernike ...
Convergent and asymptotic expansions of solutions of differential equations with a large parameter: Olver cases II and III
(Rocky Mountain Mathematics Consortium, 2015)
Artículo / Artikulua,
This paper continues the investigation initiated in [Lopez, 2013]. We consider the asymptotic
method designed by F. Olver [Olver, 1974] for linear differential equations of the second
order containing a large (asymptotic) ...
New series expansions of the 3F2 function
(2015)
Artículo / Artikulua,
We can use the power series definition of 3F2(a1, a2, a3; b1, b2; z) to compute this function for
z in the unit disk only. In this paper we obtain new expansions of this function that are convergent
in larger domains. ...
Orthogonal basis for the optical transfer function
(Optical Society of America, 2016)
info:eu-repo/semantics/article,
We propose systems of orthogonal functions qn to represent optical transfer functions (OTF) characterized by including the diffraction-limited OTF as the first basis function q0 OTF perfect. To this end, we apply a powerful ...
Orthogonal basis with a conicoid first mode for shape specification of optical surfaces: reply
(Optical Society of America, 2016)
info:eu-repo/semantics/article,
We present some comments to the paper 'Orthogonal basis with a conicoid first mode for shape specification of optical surfaces: comment'.