Deconvolution and compensation of mass spectrometric overlap interferences with the miniRUEDI portable mass spectrometer

Graphical abstract


Method details Background
The miniRUEDI (Gasometrix GmbH, Switzerland) is a portable mass spectrometer system [1,2] , which is widely used in environmental research to study gas/water exchange processes, biogeochemical turnover, and the origin and transport of fluids. The miniRUEDI was designed as a simple and robust system for on-site gas analysis during field work at remote locations and allows quantification of individual gas species in gaseous or aqueous matrices. Since its development during the past decade [1,2] , the system has been used successfully to quantify the partial pressures of He, Ar, Kr, N 2 , O 2 and CO 2 , in lakes, oceans, groundwaters, and a range of gaseous fluids in environmental systems [3][4][5][6][7][8][9][10][11][12][13][14] .
For quantification of the gas species, the miniRUEDI system uses a quadrupole mass spectrometer (Stanford Research Systems RGA200, m / z resolution ≤ 0.5 amu), which is equipped with a Faraday cup (FC) detector and an electron multiplier (EM) detector. The partial pressures of the different gas species are determined from the ion-current peak heights measured with the mass spectrometer by peak-height comparison relative to a reference gas with well known partial pressures of the species of interest [1] . This simple peak-height comparison relies on the assumption that each ion-current peak results from one single species only (the "target species" corresponding to that peak).
However, depending on the target species and the composition of the analysed gas mixture, some of the ion-current peaks involved in the analysis may result from different species contributing to the ion-current at the same m / z ratio ("overlap interference"). Such mass-spectrometric interferences cannot be used for peak-height comparison in a straight-forward way with the miniRUEDI. Unfortunately, avoiding the interferences is often not possible or impractical in many applications. For example, 15 N + , 16 40 Ar ++ and CO 2 ++ ions interfere with the analysis of atmospheric Ne, which is a sensitive natural proxy to study the recharge dynamics and aeration ("excess air" formation) of groundwaters [15] . Table 1 lists further details and other examples of mass-spectrometric interferences that are commonly encountered in miniRUEDI analyses of gases in environmental systems. If such interferences cannot be avoided, they need to be disentangled and quantified before peakheight comparison for calibration of the partial pressures. To this end, the relative fractions of the interfering ion currents are deconvolved in terms of the species involved in the interference [16] . The deconvolution yields the ion-current fractions pertaining to the target species, and therefore allows accurate peak-height comparison even in the presence of mass-spectrometric interferences.
Here, we present an extension to the existing miniRUEDI peak-height comparison technique. This method extension deconvolves and quantifies mass-spectrometric interferences in miniRUEDI analyses, and thereby substantially improves the analytical accuracy in situations where massspectrometric interferences cannot be avoided. To facilitate the adoption of the method in field applications of the miniRUEDI, the procedures for mass-spectrometric deconvolution and interference compensation were integrated in the ruediPy open-source software toolbox for instrument control and data processing with the miniRUEDI [17] .

Deconvolution of mass-spectrometric interferences
Consider the mass spectrum of ion-current peak-heights y ( m / z ) observed with an arbitrary gas mixture consisting of N different gas species. This mass spectrum is modelled as a linear combination ˜ y (m/z) of basis spectra x i ( m / z ) ( i = 1 , . . . , N) [16] . The requirements for the x i are that they are linearly independent and well known from external analysis. While the x i typically correspond to pure gases containing only one single species, it may also be practical to consider gas mixtures containing different species (see Section 4 for examples). For convenience, the x i are defined as dimensionless spectra that are normalised such that max m/z { x i (m/z) } = 1 .
The peak heights ˜ y (m/z) are given by the following equation system ( m/z = μ 1 , . . . , μ M ): If N ≤ M , the relative contributions ( a 1 , . . . , a N ) of the basis spectra to the spectrum observed with an arbitrary gas mixture can be estimated from the above equation system ("spectral deconvolution") [16] . To this end, the best-fit solution of the equation system is determined by minimising the sum χ 2 of the squared error-weighted residuals of the model relative to the observed data (error-weighted least-squares regression) [18] : Note that the y ( μ j ) are determined as the means of repeated peak-height measurements. The y ( μ j ) are therefore, in a first step, estimated from the error of the mean [1] . Note that the error of the mean tends to underestimate the true error because it only captures the random noise during a single measurement, but does not account for additional uncertainties such as those related to instrumental drift or non-linearities of the mass spectrometer. The y ( μ j ) are therefore heuristically enforced to a minimum value of 1 %, which corresponds to the typical peak-height error that can be achieved with the miniRUEDI [1] .
The standard errors a i of the a i are, in a first step, estimated by error propagation of the y ( μ j ) in the χ 2 regression. In a second step, the χ 2 value is used to quantify the overall difference between the modeled and the observed peak heights (i.e., the goodness of the regression fit). If χ 2 M − N, the difference between the modeled and the observed spectra is fully explained by the y ( μ j ). If χ 2 >> M − N, either the model is unsuitable to explain the observed peak heights (i.e., the equation system (1) is incomplete), or the y ( μ j ) were underestimated by a factor χ 2 /χ 2 σ , where χ 2 σ is the χ 2 value corresponding to the 1-σ quantile. In the latter case, the a i are therefore rescaled in a second step to account for the full uncertainty of the data:

Compensation of mass-spectrometric interferences
For analysis of a given target species at a given m/z = μ k , the corresponding interferences need to be quantified and subtracted from the measured ion current at this m / z ratio. The fraction of the ion-current contributed by the target species to the total ion current at μ k is computed from k th line of equation system (1) using the a i and the a i values as determined by the deconvolution procedure ( Section 2 ). Only the ion-current fraction contributed by the target species is used in the peak-height comparison to quantify the partial pressure of the target species.

Demonstration and validation examples
The performance of the deconvolution method for interference compensation is demonstrated using two examples related to typical applications in environmental research.

Example-1: CH 4 analysis on m/z = 15
The analysis of CH 4 in environmental gases is typically affected by mass-spectrometric interferences on m/z = 15 and m/z = 16 (see Table 1 ). The m/z = 16 ion current is commonly dominated by O + and O ++ 2 and is therefore hardly useful for CH 4 analysis. As a way out, CH 4 is analysed via its CH + 3 fragment at m/z = 15 . The ion current at this m / z ratio is affected to a considerably lesser degree by the interferences of 15 N + and peak-tails from m/z = 14 and m/z = 16 .
To illustrate the analysis of CH 4 and interference compensation at m/z = 15 , two test-gas mixtures are considered in this example. The nominal gas compositions of these gases are: • Gas-I: 23.1% (vol) CH 4 in N 2 (Messer AG, Switzerland) • Gas-II: 250 ± (13)ppm (vol) CH 4 in air (Isometric Instruments, Canada) The ion currents measured with these test gases using the detector at m/z = 14 , 15 , 16 , 28 , 32 are listed in Table 2 . These ion-current spectra were deconvolved in terms of the basis spectra of CH 4 , N 2 and clean air ( Table 3 ). The deconvolution is illustrated in Fig. 1 . Note the remarkably good agreement of the deconvolution model results with the measured spectra of Gas-I and Gas-II.
For Gas-I, the relative contribution of CH 4 to the ion current at m/z = 15 as determined by the deconvolution method is 100 ± (2)% ( Table 2 ). It is not surprising that CH 4 dominates the m/z = 15 ion current, because the CH 4 concentration in Gas-I is rather high.
For Gas-II, however, the relative contribution of CH 4 to the m/z = 15 ion current is only 70 ± (3)% ( Table 2 ). The remaining 30 ± (2)% are attributed to the air basis spectrum, which must be subtracted from the m/z = 15 ion current for CH 4 quantification.
To validate these deconvolution results, Gas-II is treated as an unknown sample and Gas-I is used as a reference standard to calibrate the CH 4 analysis. The ratio of the CH 4 concentrations in Gas-I and Fig. 1. Normalised ion-current spectra and deconvolution of Example-1. The yellow bars in panels A-C show the basis spectra used in the deconvolution (CH 4 , N 2 and Air; see Table 3 ). Panels D and E show the spectra of Gas-I and Gas-II as determined in the measurements (blue bars) and by deconvolution in terms of the basis spectra (yellow bars; see Table 2 ). Note the logarithmic scaling of the ion-current data.
Gas-II is equal to the ratio of the respective ion currents. Therefore, with [ CH 4 ] I = 23 . 1 % and using the data in Table 2 , the CH 4 concentration in Gas-II is determined as follows: Raw ion-current peak heights (without interference compensation): [ CH 4 ] II , raw = (0 . 629 ± 0 . 008) pA (394 ± 6) pA × 23 . 1 % = (369 ± 7) ppm 2.6 ± 0.9 271 ± 5 -- The CH 4 concentration value in Gas-II [CH 4 ] II,raw as calculated from the raw m/z = 15 ion currents is not consistent with the nominal CH 4 concentration of (250 ± 13) ppm in Gas-II, because the interferences at m/z = 15 were ignored in the calculation. However, if the interference compensation is applied to the m/z = 15 ion currents, the resulting CH 4 concentration value [CH 4 ] II,comp is in good agreement with the nominal CH 4 concentration of Gas-II. Note that [CH 4 ] II,comp exhibits a slightly larger standard error than [CH 4 ] II,raw . The increase in the error reflects the additional uncertainties introduced with the deconvolution, which must always be taken into account to assess the quality of the interference compensation.

Example-2: Ne analysis on m/z = 20
The analysis of Ne in environmental gases is typically affected by mass-spectrometric interferences on m/z = 20 and m/z = 22 (see Table 1 ). The m/z = 22 ion current is commonly dominated by the omnipresent CO ++ 2 and is therefore not useful for 22 Ne analysis. Ne is therefore quantified via the 20 Ne isotope on m/z = 20 . However, the ion current at this m / z ratio is commonly subject to two interferences by 40 Table 4 . These ion currents were deconvolved in terms of the basis spectra of H 2 O, Ne, and Ar using the basis data given in Table 5 .
Note that Ne analysis at m/z = 20 in air-like gases requires the use of the EM detector, because the FC sensitivity is too low. In contrast, the high ion currents at m/z = 18 (H 2 O main peak) and m/z = 40 (Ar main peak) would saturate the EM detector. However, the FC ion currents at m/z = 18 and 40 were not used in the deconvolution, because mixed EM and FC data were found to be unsuitable for deconvolution due to the drift in the EM/FC sensitivity ratio between different analysis steps. Table 4 shows the deconvolution results for Gas-III, IV and V. For Gas-III, Ne contributes (74 ± 1) % to the ion current at m/z = 20 . For Gas-IV with its increased H 2 O partial pressure, the m/z = 20 ion current is almost twice as high as in Gas-III, and the relative Ne contribution amounts to (42 ± 1) % only. For Gas-V, which exhibits a considerably lower Ne concentration, the Ne contribution to the m/z = 20 ion current amounts to a mere (14 ± 2) %.
To validate these deconvolution results, Gas-IV and Gas-V are treated as unknown samples, and Gas-III is used as a reference to calibrate the Ne analysis (analogous to Example-1): Raw ion-current peak heights (without interference compensation):  Note that H 2 O tends to adsorb onto metal surfaces of the vacuum system and is therefore highly persistent in the miniRUEDI mass spectrometer. While the ion currents of other species is immediately controlled by their concentrations in the gases introduced into mass spectrometer, the H 2 O ion current therefore takes much longer to stabilise after switching the miniRUEDI gas inlet from one gas to another ( Fig. 2 ). The H 2 O ion current must be stable during a given analysis step in order to allow robust compensation of the H 2 O interference. After switching between gas inlets, the H 2 O ion current was therefore allowed to stabilise for 20 min before starting a new measurement in the above example. Depending on the application, such long idle times may conflict with the requirements for the duty cycle and time resolution for the gas analysis.

Implementation in the miniRUEDI software
The deconvolution and interference compensation of the raw ion-current data have been integrated in the ruediPy open-source software [17] . The procedures are implemented as a data pre-processing tool, which can be applied if mass-spectrometric interferences cannot be avoided in the conventional peak-height comparison method. After pre-processing, the interference-corrected ion currents are processed using the existing standard protocol for partial-pressure calibration by peak-height comparison [1] .

Gas analysis
The analysis procedure follows the existing standard procedures implemented for each miniRUEDI analysis step (sample, standard, or blank) in the ruediPy software, whereby the following extensions for the deconvolution tool were added: • In addition to the normal ion-current measurements ( PEAK and ZERO readings), optional "helper" peak-height measurements may be recorded at additional m / z ratios in order to provide further constraints the regression equation system (1) ( Section 2 ). Such "helper" readings are marked by the software as PEAK_DECONV and ZERO_DECONV ; they are not used in the peak-height comparison to calculate the partial pressures ( Section 3 ).
• For every target m / z ratio that requires interference compensation by deconvolution, a data block with the corresponding deconvolution parameters is written to the data file (marked as DECONVOLUTION , see Section 5.2 ).

The DECONVOLUTION block
Each DECONVOLUTION block contains the following data fields (see example below for the data format): • target_mz (integer): the m / z ratio where the ion-current needs to be compensated for massspectrometric interferences.
• target_species (string): name/label of the target gas species for which the partial pressure will be quantified using the compensated ion current at target_mz. Notes: • In the ruediPy data files, the DECONVOLUTION block is written on a single data line.
• The basis spectra are specific to the mass-spectrometer instrument and the electronic settings of the ion source. It is therefore recommended to measure the basis spectra using the same mass spectrometer and ion-source settings as used with the gas analysis. • It is recommended to configure the interference compensation in the software before running the analysis in order to make sure that the correct DECONVOLUTION block is written automatically to the data files. However, it is also possible to add or modify DECONVOLUTION blocks in existing raw data files using an ASCII editor.

Data processing
The data processing procedure implemented in the ruediPy software is as follows (extensions to existing standard procedures are marked in italics ): For each analysis step (sample, standard, blank): • Read the raw data file of the analysis step.
• Determine the main ion-current peak-heights from the PEAK and ZERO readings (mean or median values) • Determine the helper peak-heights from the PEAK_DECONV and ZERO_DECONV helper readings (if any).
• For each DECONVOLUTION block (if any): -Deconvolution ( Section 2 ): deconvolve all ion-current peak-height data according to the DECONVOLUTION parameters and determine the relative contributions of the spectrometric interferences at m/z = target_mz using the peak-height data recorded with the detector specified in the detector field.
-Interference compensation ( Section 3 ): subtract all interferences determined in the deconvolution step from the detector ion-current peak-height determined at target_mz .
Calibration of partial pressures: Convert the (interference-corrected) ion-current peak heights as determined from the PEAK and ZERO data to partial pressures using the existing peak-height comparison procedure [1] .

Conclusions
We present a method to deconvolve and compensate mass-spectrometric overlap interferences in miniRUEDI gas analyses. The procedures for deconvolution and compensation of the interferences were integrated in the open source software for miniRUEDI instrument control and data processing [17] in order to facilitate the adoption of the new method in miniRUEDI field applications.
The method was shown to substantially improve the analytical accuracy in situations where massspectrometric interferences cannot be avoided, and thereby expands the scientific application area for the miniRUEDI. In a first example, we validated the interference compensation for accurate tracelevel CH 4 analysis in air-like gas matrices, which expands the application range of the miniRUEDI in studies on the sources and the dynamics of this important greenhouse gas in environmental systems. In a second example, we demonstrated the compensation of interferences involved in the trace-level analysis of Ne in air-like gas matrices, which expands the analytical potential to study the linkages between groundwater recharge dynamics and the quality of water resources.
Note that the deconvolution method for interference compensation with the miniRUEDI is not conceptually linked to specific types of target gas species or gas matrices. Therefore, as long as the species involved in a given interference are known and the corresponding basis spectra can be measured, the method is in principle applicable to any target gas species or gas matrix, and thereby substantially expands the application range of the miniRUEDI.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.