  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), 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.
