Comparison of three methods of integration to obtain the profile from its slope

Leonid P. Yaroslavsky; Juan Campos; A. Moreno; Maria Josefa Yzuel

doi:10.1117/12.530333

19 November 2003 Comparison of three methods of integration to obtain the profile from its slope

Leonid P. Yaroslavsky, Juan Campos, A. Moreno, Maria Josefa Yzuel

Proceedings Volume 4829, 19th Congress of the International Commission for Optics: Optics for the Quality of Life; (2003) https://doi.org/10.1117/12.530333
Event: 19th Congress of the International Commission for Optics: Optics for the Quality of Life, 2002, Florence, Italy

Abstract

In some measurement techniques the profile f(x) of a function should be obtained from the measured slope f'(x) data by integration. The slope is measured in a given set of points x_n = nΔx, n = 1, N[f'(x_n)=f'n] and from these data we should obtain the profile with the highest possible accuracy. In general, all integration methods perform some kind of interpolation between the data: Newton-Cotes quadrature expressions (trapezoidal rule, Simpson rule, ...), spline interpolation, etc. We propose here the integration of the function in the Fourier Domain then the most accurate interpolation is automatically carried out. In section 2 we present the classical methods. In section 3 our proposal is described. Finally, in section 4, a comparison between the different methods is carried out.

Citation Download Citation

Leonid P. Yaroslavsky, Juan Campos, A. Moreno, and Maria Josefa Yzuel "Comparison of three methods of integration to obtain the profile from its slope", Proc. SPIE 4829, 19th Congress of the International Commission for Optics: Optics for the Quality of Life, (19 November 2003); https://doi.org/10.1117/12.530333

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available