Surface Description for Cornea Topography Using Modified Chebyshev-polynomials
نویسندگان
چکیده
The optical behaviour of the (human) cornea is often characterized with the Zernike-coefficients derived via the Zernike-transform of its optical power map. In this paper, a radial transform based on the Chebyshev-polynomials of the second kind is suggested for a surface-based, rather than an optical power map based representation of the cornea. This transform is well-suited for providing compact representations for quasi-hemispherical surfaces, and after appropriate argument-transform applied to these polynomials also for spherical-calotte-like surfaces. Examples illustrating the effect of the argument-transformation are also included in the paper. Copyright c 2005 IFAC.
منابع مشابه
Simulated Crater Degradation Based on Chebyshev Coefficients
Introduction: Impact craters on the Moon (and other bodies) form and degrade over time resulting in a change in crater shape and hence an overall evolution in lunar topography. Modeling of crater erosion (e.g. [1, 2, 3]) enables the tracking of crater shape evolution with time and can be used to estimate the relative age of a particular crater. Intuitively, crater degradation results from the c...
متن کاملIdentification of Corneal Aberrations by using Computer Techniques
The objective was to study the relative contributions of optical aberrations of the cornea and determine the irregularities across its surface area. Corneal topographic imaging data is used and corneal aberrations are computed by using corneal height maps. Mathematical modeling of cornea surface is developed by using Zernike polynomials and they are compared with the patient corneas. Simulation...
متن کاملSolving singular integral equations by using orthogonal polynomials
In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...
متن کاملModified frame algorithm and its convergence acceleration by Chebyshev method
The aim of this paper is to improve the convergence rate of frame algorithm based on Richardson iteration and Chebyshev methods. Based on Richardson iteration method, we first square the existing convergence rate of frame algorithm which in turn the number of iterations would be bisected and increased speed of convergence is achieved. Afterward, by using Chebyshev polynomials, we improve this s...
متن کاملPost-buckling response of thin composite plates under end-shortening strain using Chebyshev techniques
In this paper, a method based on Chebyshev polynomials is developed for examination of geometrically nonlinear behaviour of thin rectangular composite laminated plates under end-shortening strain. Different boundary conditions and lay-up configurations are investigated and classical laminated plate theory is used for developing the equilibrium equations. The equilibrium equations are solved dir...
متن کامل