Adaptive Cornea Modeling from Keratometric Data

Ophthalmic Physiologic Optic

et al. 2013

Section: Introductionmentioning

confidence: 99%

Zernike vs. Bessel circular functions in visual optics

Treviño¹,

Gómez-Correa²,

Ophthalmic Physiologic Optic

et al. 2013

“…This has connections with other successful approximation schemes, such as the adaptive least squares (see e.g. [18,Chapter 21], and also [33]), the moving least squares [18,, and others.…”

Section: Approximation By Radial Basis Functionsmentioning

confidence: 89%

“…In this paper we develop an alternative technique for calculating integrals of the form (1) by combining the essence of the ENZ approach with the approximation power of the radial basis functions (RBF), which are standard tools in the approximation theory and numerical analysis, appearing in applications ranging from engineering and artificial intelligence to solutions of partial differential equations, see for example [18]. The Gaussian radial basis functions (GRBF) have been also used in the context of ophthalmic optics [32,33,34].…”

Section: Introductionmentioning

confidence: 99%

Computation of 2D Fourier transforms and diffraction integrals using Gaussian radial basis functions

Martínez–Finkelshtein

Ramos-López

Applied and Computational Harmonic Analysis

2017

We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we obtain a rapidly converging series expansion for the integrals, allowing for their accurate calculation. We apply this idea to the evaluation of diffraction integrals, used for the computation of the through-focus characteristics of an optical system.We implement this method and compare its performance in terms of complexity, accuracy and execution time with several alternative approaches, especially with the extended Nijboer-Zernike theory, which is also outlined in the text for the reader's convenience. The proposed method yields a reliable and fast scheme for simultaneous evaluation of such kind of integrals for several values of the defocus parameter, as required in the characterization of the through-focus optics.

“…Recently, they also found application in the context of ophthalmic optics [26]. A more general version of this type of functions (using the socalled anisotropic radial basis functions) was developed for fitting corneal elevation data [27,28]. Each GRBF is determined by its center, given by polar coordinates (q, α), and by its shape parameter L > 0; the expression which evaluates it at a point with polar coordinates (ρ, θ) is…”

Section: Methodsmentioning

confidence: 99%

Computational aspects of the through-focus characteristics of the human eye

Ramos-López

Martínez–Finkelshtein

2014

J. Opt. Soc. Am. A

Calculating through-focus characteristics of the human eye from a single objective measurement of wavefront aberration can be accomplished through a range of methods that are inherently computationally cumbersome.A simple yet accurate and computationally efficient method is developed, which combines the philosophy of the extended Nijboer-Zernike approach with the radial basis function based approximation of the complex pupil function. The main advantage of the proposed technique is that the increase of the computational cost for a vector valued defocus parameter is practically negligible in comparison to the corresponding scalar valued defocus parameter.