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

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Abstract

In some measurement techniques the profile, fx, of a function should be obtained from the data on measured slope fx 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

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