Integration in the Fourier domain for restoration of a function from its slope: comparison of four methods
Optics Letters, Vol. 27, Issue 22, pp. 1986-1988 doi:10.1364/OL.27.001986
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- OCIS Codes:
- (120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
- (120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
- (200.3050) Optics in computing : Information processing
Citation
J. Campos, L. P. Yaroslavsky, A. Moreno, and M. J. Yzuel, "Integration in the Fourier domain for restoration of a function from its slope: comparison of four methods," Opt. Lett. 27, 1986-1988 (2002)
http://www.opticsinfobase.org/abstract.cfm?URI=ol-27-22-1986
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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
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