## 1 Introduction
(**b**) Simplified model for relative photoionization cross sections for REMPI-time-of-flight mass spectrometry (TOFMS); ions (\(N_{1,\rm J}\)) of the molecules (\(M_{0,\rm J}\)) are formed by REMPI and are guided through the TOFMS with a distinct transmission (\(T\)). Relative photoionization cross sections (relPICS) are calculated by dividing the amount of detected ions for a given number of initial molecules of a single compound by the ratio of detected ions and initial molecules of the reference substance. mostly molecular ions. On the other hand, applying higher laser intensities (above \(10^{8}\) W/cm\({}^{2}\)) will lead to increased fragmentation and the production of much smaller fragments (e.g., C\({}^{+}\) for benzene) compared to electron ionization [17; 20; 21]. The ionization rate depends on the applied laser wavelength, since the cross sections for absorption and ionization vary with the wavelength. This behavior complicates quantification and internal or external standards are only applicable for target screening. Another possibility is the utilization of absolute photoionization cross sections [22]. These parameters neglect thermal effects as well as mass spectrometric parameters and are difficult to determine. Therefore, absolute cross sections may only give an estimation of the ionization rate under certain conditions. However, one possible approach to overcome this drawback is the introduction of relative photoionization cross sections (relPICS). In this approach, the ionization rate of the analytes at a given wavelength is compared with that of a reference substance. Once determined, these relPICS can be used to recalculate the concentrations of compounds in an unknown gas mixture just by measuring the concentration of the reference substance. Therefore, relPICS may be used for a simple and system-independent quantification in REMPI-TOFMS measurements at a given laser wavelength. The principle of relPICS has already been used by [PERSON] et al. [23] and will be shortly described in the following. Based on the scheme given in Figure 1b, the number of ions (\(N_{\text{I,i}}\)) produced by (\(1+1\)) one-color REMPI can be derived from Equation (1). These ions are transferred through the mass spectrometric system with a distinct transmission (T) and are separated based on their mass-to-charge ratio (\(m/z\)). The number of detected ions (\(N_{\text{2,i}}\)) is given by Equation (2). \[N_{\text{2,i}}=N_{\text{1,i}}\cdot T=\frac{\sigma_{1}(\omega)\cdot\sigma_{2}( \omega)}{2}\cdot M_{\text{0,i}}\cdot I^{2}\cdot t_{\text{P}}^{2}\cdot T\, \tag{2}\]  
This expression can be normalized to the ionization behavior of the reference substance, which results in:  
\[\frac{N_{\text{2,A}}}{N_{\text{2,ref}}}=\frac{\sigma_{1,\text{A}}(\omega) \cdot\sigma_{2,\text{A}}(\omega)\cdot M_{\text{0,A}}\cdot I^{2}\cdot t_{\text {P}}^{2}\cdot T}{\sigma_{1,\text{ref}}(\omega)\cdot\sigma_{2,\text{ref}}( \omega)\cdot M_{\text{0,ref}}\cdot I^{2}\cdot t_{\text{P}}^{2}\cdot T}\, \tag{3}\]  
where A--analyte and ref--reference. For time-of-flight mass spectrometers, \(T\) can be approximated as a constant for all ions in a mass range between \(m/z\) 20 and 300. Therefore, Equation (3) simplifies to:  
\[\sigma_{\text{rel, ref}}(\omega)=\frac{\sigma_{1,\text{A}}(\omega)\cdot\sigma_{2,\text{A}}(\omega)}{\sigma_{1,\text{ref}}(\omega)\cdot\sigma_{2,\text{ref}}( \omega)}=\frac{N_{\text{2,A}}}{N_{\text{2,ref}}}\cdot\frac{M_{\text{0,ref}}} {M_{\text{0,A}}}=\frac{r_{\text{A}}}{r_{\text{ref}}}, \tag{4}\]  
Here, \(r_{1}=\frac{N_{\text{2,i}}}{M_{\text{0,i}}}\) is the response factor of a single substance at a distinct wavelength.