  A recurring question arises when trying to characterize, by means of
measurements or theoretical calculations, the zenithal night sky brightness
throughout a large territory: how many samples per square kilometer are needed?
The optimum sampling distance should allow reconstructing, with sufficient
accuracy, the continuous zenithal brightness map across the whole region,
whilst at the same time avoiding unnecessary and redundant oversampling. This
paper attempts to provide some tentative answers to this issue, using two
complementary tools: the luminance structure function and the Nyquist-Shannon
spatial sampling theorem. The anaysis of several regions of the world, based on
the data from the New world atlas of artificial night sky brightness (Falchi et
al 2016, Sci. Adv. 2, e1600377) suggests that, as a rule of thumb, about one
measurement per square kilometer could be sufficient for determining the
zenithal night sky brightness of artificial origin at any point in a region to
within 0.1 magV/arcsec2 (in the root-mean-square sense) of its true value in
the Johnson-Cousins V band. The exact reconstruction of the zenithal night sky
brightness maps from samples taken at the Nyquist rate seems to be considerably
more demanding.
