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Optics Letters

Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Vol. 27, Iss. 22 — Nov. 15, 2002
  • pp: 1986–1988

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

J. Campos, L. P. Yaroslavsky, A. Moreno, and M. J. Yzuel  »View Author Affiliations


Optics Letters, Vol. 27, Issue 22, pp. 1986-1988 (2002)
http://dx.doi.org/10.1364/OL.27.001986


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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

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/ol/abstract.cfm?URI=ol-27-22-1986


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References

  1. S. C. Irick, R. Krishna Kaza, and W. R. McKinney, Rev. Sci. Instrum. 66, 2108 (1995).
  2. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1987).
  3. C. Elster and I. Weingärtner, “High-accuracy reconstruction of a function f(x) when only df(x)/dx is known at discrete measurement points,” Proc. SPIE 4782 (to be published).
  4. L. Yaroslavsky and M. Eden, Fundamentals of Digital Optics (Birkhauser, Boston, Mass., 1996).
  5. J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB (Prentice-Hall, Englewood Cliffs, N.J., 1999).
  6. L. Yaroslavsky, Proc. SPIE 4667, 120 (2002).

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