EDP Sciences
Free access
Volume 392, Number 3, September IV 2002
Page(s) 1153 - 1174
Section Instruments, observational techniques and data processing
DOI http://dx.doi.org/10.1051/0004-6361:20020965

A&A 392, 1153-1174 (2002)
DOI: 10.1051/0004-6361:20020965

Smooth maps from clumpy data: Covariance analysis

M. Lombardi and P. Schneider

Institüt für Astrophysik und Extraterrestrische Forschung, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
(Received 23 January 2002 / Accepted 27 June 2002)

Interpolation techniques play a central role in Astronomy, where one often needs to smooth irregularly sampled data into a smooth map. In a previous article (Lombardi & Schneider 2001, hereafter Paper I), we have considered a widely used smoothing technique and we have evaluated the expectation value of the smoothed map under a number of natural hypotheses. Here we proceed further on this analysis and consider the variance of the smoothed map, represented by a two-point correlation function. We show that two main sources of noise contribute to the total error budget and we show several interesting properties of these two noise terms. The expressions obtained are also specialized to the limiting cases of low and high densities of measurements. A number of examples are used to show in practice some of the results obtained.

Key words: methods: statistical -- methods: analytical -- methods: data analysis -- gravitational lensing

Offprint request: M. Lombardi, lombardi@astro.uni-bonn.de

SIMBAD Objects in preparation

© ESO 2002