TY - JOUR
T1 - Integration in the Fourier domain for restoration of a function from its slope
T2 - Comparison of four methods
AU - Campos, Juan
AU - Yaroslavsky, L. P.
AU - Moreno, A.
AU - Yzuel, M. J.
PY - 2002/11/15
Y1 - 2002/11/15
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0037113271&partnerID=8YFLogxK
U2 - 10.1364/OL.27.001986
DO - 10.1364/OL.27.001986
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AN - SCOPUS:0037113271
SN - 0146-9592
VL - 27
SP - 1986
EP - 1988
JO - Optics Letters
JF - Optics Letters
IS - 22
ER -