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

M3 - מאמר

AN - SCOPUS:0037113271

VL - 27

SP - 1986

EP - 1988

JO - Optics Letters

JF - Optics Letters

SN - 0146-9592

IS - 22

ER -