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

Characterizing the zenithal night sky brightness in large territories: How many samples per square kilometer are needed?