Smooth maps from clumpy data: Covariance analysis

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 \cite{2001A&A...373..359L}, 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.