The statistics of ToF‐SIMS data revisited and introduction of the empirical Poisson correction

Generation of time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) data involves two overarching processes: secondary ion production and secondary ion detection. The interpretation of ToF‐SIMS data is facilitated if the intensities of the as‐measured mass spectra are proportional to the abundances of the species under investigation. While secondary ion yield is normally taken to be a linear process, ion detection is not owing to detector dead‐time effects. Consequently, methods have been devised that attempt to linearize, or correct, data that are affected by the dead time. In this article, we review the statistics of ToF‐SIMS data generation and confirm a report in the literature that abundance estimates from so‐called Poisson corrections are biased. We show that these corrections are only unbiased asymptotically and that a rigorous probabilistic analysis can quantitatively account for the observed bias. Two sources of bias are identified, one having a statistical basis and one due to the form of the correction equation at high ion detection rates. Based on insights gained from this analysis, we propose a new correction equation, the empirical Poisson correction, which largely eliminates the statistical bias. The performance of the proposed correction is illustrated by reanalyzing 14 experimentally measured datasets that suffer from varying levels of dead‐time effects. Copyright © 2016 John Wiley & Sons, Ltd.