Integration in the Fourier domain for restoration of a function from its slope: Comparison of four methods

Juan Campos, L. P. Yaroslavsky, A. Moreno, M. J. Yzuel

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19 Citations (Scopus)

Abstract

In some measurement techniques the profile, f(x), of a function should be obtained from the data on measured slope f′(x) by integration. The slope is measured in a given set of points, and from these data we should obtain the profile with the highest possible accuracy. Most frequently, the integration is carried out by numerical integration methods [Press et al., Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1987)] that assume different kinds of polynomial approximation of data between sampling points. We propose the integration of the function in the Fourier domain, by which the most-accurate interpolation is automatically carried out. Analysis of the integration methods in the Fourier domain permits us to easily study and compare the methods' behavior. © 2002 Optical Society of America.
Original languageEnglish
Pages (from-to)1986-1988
JournalOptics Letters
Volume27
DOIs
Publication statusPublished - 15 Nov 2002

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