# Current Progress in Femtosecond Laser Ablation/Ionisation Time-of-Flight Mass Spectrometry
## 4 Performance of fs-LIMS Instruments in the Element and Isotope Analysis
### Chemometrics and Analysis Protocols  
For better understanding and control of the laser ablation process, the ionisation efficiency of elements can be represented as a function of several parameters characterising the chemical and physical properties of the element. Nonstoichiometric ionisation is caused mostly by matrix effects and these are directly related to the material properties [148]. The matrix effects were investigated in several different samples and the relative sensitivity coefficients (RSCs) of the elements in different matrices were determined [149]. By combining the RSCs values with the physical property values of the matrices, the datasets were analysed by the chemometrics tool of orthogonal partial least-squares (OPLSs) for ns-and fs-laser ablation. RSCs of the elements in different matrices were measured experimentally. A theoretical model was worked out by combining the laser-solid interaction and plasma expansion processes to predict the RSCs involved in the study. RSCs were derived based on Fe concentration as reference (see also Section 4.3 for definition). The theoretical expression for an RSC\({}_{\text{i}}\) for species \(I\) was developed with the parameters characterising the physical and chemical properties of the relevant element, including specific heat capacity, absorption coefficient, surface absorbance, fusion heat, vaporisation heat, boiling point, thermal conductivity and first ionisation potential; in plasma expansion. Moreover, the temperature and electron number density of the ablation plasma were calculated. The model predicts the influence of thermal properties on ionisation efficiency by ns-ablation. The non-thermal properties (e.g., ionisation potentials, IPs) contributed almost equally to the models for ns- and fs-laser ablation. This model was used to compare the predicted RSC\({}_{\text{i}}\) with that derived from the measurement results conducted on several geological standard research samples. Overall, a good agreement between theoretical and experimental RSCs was reported [150]. In our group, the data analysis protocol was developed specifically for the LIMS application supporting the automatic analysis of a large amount of data [151], typically in the context of 2D and 3D chemical imaging. The developed software allows fast and precise quantitative data analysis of time-of-flight mass spectrometric data. The quantitative analysis of isotopes, using automatic data analysis, yields results with an accuracy of isotope ratios up to 100 ppm for a signal-to-noise ratio (SNR) of \(10^{4}\). The accuracy of isotope ratios was found to be inversely proportional to both SNR and mass resolution (m/\(\Delta\)m). Follow-up studies by our group identified that the individual spectral degradation can significantly affect the mass resolution and quantification while accumulating the spectra for improvement of the signal-to-noise ratio (SNR) in LIMS [112]. These are spectra not only suffering from accidental surface and space charging, but also detector saturation. Spectral degradation of the overall spectrum can occur if some individual mass spectra, affected by peak broadening, are included in the accumulation process. The studies present the method to automatically identify individual spectra subjected to peak broadening and a filtering method capable of systematic and reproducible exclusion of such spectra from the accumulation process. Improvements in the isotope accuracy of Si, Ni, and Cr by factors between 1.6 and 7.7 were demonstrated [112]. In very recent studies, the data analysis protocols based on the isotope intensity correlation and depth profiling data were developed in the same group. High-quality depth profiling data allowed a high-degree correlation between the isotope signals. The isotope ratio (\(\delta\)-notation) can be derived from linear regression with accuracy and precision at the per mille level [152]. The data used for precise isotope measurements are improved using a spectrum cleaning procedure that ensures the removal of low-quality spectra.