The reliability of observational measurements of column density probability distribution functions

Probability distribution functions (PDFs) of column densities are an established tool to characterize the evolutionary state of interstellar clouds. Using simulations, we show to what degree their determination is affected by noise, line-of-sight contamination, field selection, and the incomplete sampling in interferometric measurements. We solve the integrals that describe the convolution of a cloud PDF with contaminating sources and study the impact of missing information on the measured column density PDF. The effect of observational noise can be easily estimated and corrected for if the root mean square (rms) of the noise is known. For $\sigma_{noise}$ values below 40% of the typical cloud column density, $N_{peak}$, this involves almost no degradation of the accuracy of the PDF parameters. For higher noise levels and narrow cloud PDFs the width of the PDF becomes increasingly uncertain. A contamination by turbulent foreground or background clouds can be removed as a constant shield if the PDF of the contamination peaks at a lower column or is narrower than that of the observed cloud. Uncertainties in the definition of the cloud boundaries mainly affect the low-column density part of the PDF and the mean density. As long as more than 50% of a cloud are covered, the impact on the PDF parameters is negligible. In contrast, the incomplete sampling of the uv plane in interferometric observations leads to uncorrectable distortions of the PDF of the produced maps. An extension of ALMA's capabilities would allow us to recover the high-column density tail of the PDF but we found no way to measure the intermediate and low column density part of the underlying cloud PDF in interferometric observations.