# Current Progress in Femtosecond Laser Ablation/Ionisation Time-of-Flight Mass Spectrometry
## 4 Performance of fs-LIMS Instruments in the Element and Isotope Analysis
### Time of Flight, Mass Range, and Mass Resolution  
The mass spectrum is measured on a linear time scale \(t\) by the ADC data acquisition system. For the miniature instruments, the TOF spectrum of elements from atomic mass 1 to about 235 is recorded within about 20 \(\upmu\)s. These times are longer for large laboratory systems and can exceed 1 ms. Figure 7 displays the mass range typically used in fs-LMS-GT and shows example of three high mass resolution mass spectra measured on three NIS standards. The transformation into a mass scale is made with two calibration factors using an equation with quadratic dependence of mass \(m\) [atomic mass unit], on time of flight {s} via \(\rm m=k_{0}(t-t_{0})^{2}\). The coefficients \(k_{0}\) and \(t_{0}\) are the calibration constants. They can be calculated using parameters obtained from linear regression using the flight times for at least two isotope masses identified in the spectrum. They can also be determined from the ion optical parameters of the mass analyser. The mass scale accuracy (average absolute mass accuracy) can be calculated using the absolute values of individual mass \(\rm m_{i}\) errors and is given in part per million (ppm) [142]. This value for a miniature TOFMS is a few hundredths of ppm and lies in ppm or sub-ppm range for high mass resolution TOFMS. In the earlier LIMS systems, the mass resolution (\(\rm m/\Delta m\)) was limited, rarely exceeding 300 (LIMA 2A, LAMMA, LAMAS 10M, LAMAS, LAZMA, MB TOF) [132; 143; 144; 24; 145; 24]. Current high laser fluence LIMS designs have significantly improved mass resolution. For LMS, an instrument with about a 30 cm flight path, the mass resolution close to 700  
Figure 7: (**a**) Typical spectrum recorded with LMS-GT for three NIST SRM steel samples. The applied mass range is compatible with the applied data acquisition card to optimally use the sampling range of the card; (**b**) At the mass \(\rm m/z=44\) both isotopic \({}^{44}\)Ca and diatomic \({}^{32}\)S-\({}^{12}\)C mass peaks can be measured; (**c**) At the mass peaks 142, 143 and 144 in addition to isotopic Nd also diatomic mass peaks are observed [141]. in ablation mode [11; 21; 132] and 1100 in desorption mode [12] was obtained, whereas the measurements with LMS-GT can be conducted with the mass resolution of 15,000 and higher [24]. A new strategy to reduce temporal ion spread produced during laser ablation was applied in high irradiance LI-O-TOFMS instrument with inert gas cooling and orthogonal extraction [23; 129]. While applying high irradiance laser ablation ion source, ion concentrations and ion kinetic energies are far too large to be analysed by the TOFMS directly. However, in this system, only part of the produced ions is analysed. The ions are extracted orthogonally and after cooling the selected ions in a low-pressure collision cell to temperatures of the cooling gas. Subsequently, the ions are transported by the lens system into the ion extraction region, where again a part of the incoming ions is used for mass spectrometric analysis. With this system, the mass spectrometric analysis is conducted with a mass resolution close to 2200 [23; 129]. In miniature TOFMS systems, the mass resolution can be raised to m/\(\Delta\)m \(\approx\) 800 for the isotope ratio measurements by optimising the voltages applied to the ion optical system by specially developed \"swarm particle algorithm\" [132; 147]. The dependence of the mass resolution on the laser irradiance is one of the most critical factors for miniature LIMS systems and is related to the space charge of the ablated plume (coulombic repulsion) and surface charging, both influencing the ion spreads [112].