High-accuracy reconstruction of a function f(x) when only df(x)/dx or d(2)f(x)/dx(2) is known at discrete measurement points

Clemens Elster; Ingolf Weingartner

doi:10.1117/12.450459

24 December 2002 High-accuracy reconstruction of a function f(x) when only df(x)/dx or d²f(x)/dx² is known at discrete measurement points

Clemens Elster, Ingolf Weingartner

Author Affiliations +

Proceedings Volume 4782, X-Ray Mirrors, Crystals, and Multilayers II; (2002) https://doi.org/10.1117/12.450459
Event: International Symposium on Optical Science and Technology, 2002, Seattle, WA, United States

Abstract

The task of reconstructing a function f(x) from a set of measurements of the first or second derivative is considered. Methods for numerical integration are briefly outlined and discussed with regard to their potential application to the current task. Furthermore, cubic spline interpolation of the data followed by integration of the interpolation spline is proposed, and the influence of noise on the accuracy of the reconstructed function f(x) is examined. Results of numerical simulations for several test problems are presented for both noiseless and noisy data, and the efficiency of different methods is compared. Best results were obtained by cubic spline interpolation and subsequent integration of the spline function. The examples presented demonstrate that the reconstruction of a function f(x) from a set of measurements of the first or second derivative can be performed with high accuracy.

Citation Download Citation

Clemens Elster and Ingolf Weingartner "High-accuracy reconstruction of a function f(x) when only df(x)/dx or d²f(x)/dx² is known at discrete measurement points", Proc. SPIE 4782, X-Ray Mirrors, Crystals, and Multilayers II, (24 December 2002); https://doi.org/10.1117/12.450459

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