## Statistical precision of the intensities retrieved from constrained fitting of...

*Atmos. Meas. Tech., 8*, 2333-2345, doi:10.5194/amt-8-2333-2015.

Least-squares fitting of overlapping peaks is often needed to separately quantify ions in high-resolution mass spectrometer data. A statistical simulation approach is used to assess the statistical precision of the retrieved peak intensities. The sensitivity of the fitted peak intensities to statistical noise due to ion counting is probed for synthetic data systems consisting of two overlapping ion peaks whose positions are pre-defined and fixed in the fitting procedure. The fitted intensities are sensitive to imperfections in the m/Q calibration. These propagate as a limiting precision in the fitted intensities that may greatly exceed the precision arising from counting statistics. The precision on the fitted peak intensity falls into one of three regimes. In the “countinglimited regime” (regime I), above a peak separation χ ∼ 2 to 3 half-widths at half-maximum (HWHM), the intensity precision is similar to that due to counting error for an isolated ion. For smaller χ and higher ion counts (∼ 1000 and higher), the intensity precision rapidly degrades as the peak separation is reduced (“calibration-limited regime”, regime II). Alternatively for χ < 1.6 but lower ion counts (e.g. 10–100) the intensity precision is dominated by the additional ion count noise from the overlapping ion and is not affected by the imprecision in the m/Q calibration (“overlapping-limited regime”, regime III). The transition between the counting and m/Q calibration-limited regimes is shown to be weakly dependent on resolving power and data spacing and can thus be approximated by a simple parameterisation based only on peak intensity ratios and separation. A simple equation can be used to find potentially problematic ion pairs when evaluating results from fitted spectra containing many ions. Longer integration times can improve the precision in regimes I and III, but a given ion pair can only be moved out of regime II through increased spectrometer resolving power. Studies presenting data obtained from least-squares fitting procedures applied to mass spectral peaks should explicitly consider these limits on statistical precision.