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Proceedings Paper

Comparison of three methods of integration to obtain the profile from its slope
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Paper Abstract

In some measurement techniques the profile f(x) of a function should be obtained from the measured slope f'(x) data by integration. The slope is measured in a given set of points xn = nΔx, n = 1, N[f'(xn)=f'n] and from these data we should obtain the profile with the highest possible accuracy. In general, all integration methods perform some kind of interpolation between the data: Newton-Cotes quadrature expressions (trapezoidal rule, Simpson rule, ...), spline interpolation, etc. We propose here the integration of the function in the Fourier Domain then the most accurate interpolation is automatically carried out. In section 2 we present the classical methods. In section 3 our proposal is described. Finally, in section 4, a comparison between the different methods is carried out.

Paper Details

Date Published: 19 November 2003
PDF: 3 pages
Proc. SPIE 4829, 19th Congress of the International Commission for Optics: Optics for the Quality of Life, (19 November 2003); doi: 10.1117/12.530333
Show Author Affiliations
Leonid P. Yaroslavsky, Tel Aviv Univ. (Israel)
Juan Campos, Univ. Autonoma de Barcelona (Spain)
A. Moreno, Univ. Autonoma de Barcelona (Spain)
Maria Josefa Yzuel, Univ. Autonoma de Barcelona (Spain)

Published in SPIE Proceedings Vol. 4829:
19th Congress of the International Commission for Optics: Optics for the Quality of Life
Giancarlo C. Righini; Anna Consortini, Editor(s)

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