## 2 Materials and Methods  
### Photoacoustic Effect and Multipass Cell  
The photoacoustic effect was discovered by [PERSON], who detected an acoustic signal by modulating a light source and causing it to impinge on a sample contained in a closed cell. It consists of the absorption of modulated light by the sample, leading to an increase in its internal energy. This energy is transferred to adjacent molecules, which are heated and undergo a process of expansion and contraction. This generates pressure variations, producing acoustic waves [16], which can be detected by sensors such as microphones. This process is illustrated in Figure 1.  
The photoacoustic effect can be explained in three fundamental processes: first, the absorption of light radiation, which depends on the properties of the material, such as the absorption coefficient and the length of the optical path; second, transformation of electromagnetic energy into heat, which depends on the quantum efficiency of the sample; and finally, the diffusion of heat up to the threshold at which acoustic waves are produced is the result of the interplay between diffusivity, conductivity, and specific heat capacity. While several authors have described in detail the photoacoustic effect inside a cavity, the photo-induced signal can be expressed generally as follows:  
\[S\propto\frac{P*\alpha}{f*V} \tag{1}\]  
where \(P\) is the optical power of the light source, \(f\) is the modulation frequency, \(\alpha\) is the absorption coefficient of the gas molecules, and \(V\) is the interaction volume. As described in Equation (1), there are different ways to improve the photoacoustic signal. One of the options is to increase the optical path by using multipass cells. The MPC-PAS technique has been shown to offer a significant advantage in terms of enhancing the sensitivity and accuracy of gas detection [29; 30; 31; 32]. By having the light beam pass multiple times through the sample, the total amount of energy absorbed by the gas molecules is increased, leading to the generation of a more intense acoustic signal. This capability enables the detection of extremely low gas concentrations, thereby improving the signal-to-noise ratio of the system. MPC, a key component of the system, enhances efficiency without necessitating an increase in laser power, rendering it well-suited for applications that demand high precision and trace detection, such as environmental monitoring and industrial process detection. The multipass cell's enhanced optical lengthens the effective optical path, making it particularly advantageous for dilute or low-concentration samples, where the photothermal signal may be weak. Additionally, this cell's extended optical path enhances selectivity by increasing interaction time and suppressing undesired background signals. The MPC-PAS is implemented by a multipass cell (Figure 2), which is characterized by its small size (10 cm diameter) and its composition of 45 parabolic mirrors inside the cell [29; 33]. These mirrors facilitate multiple reflections, thereby increasing the optical path of the system and enhancing its advantages. The cell's stability, attributable to its resistance to thermal expansion, surpasses that of alternative photoacoustic cell types, rendering it particularly well suited for environments where temperature control is challenging [30]. This cell's attributes include its small size, adaptable path length, straightforward alignment, and versatility in sensing techniques. The reduction in size and volume of the cell offers significant advantages for the development of rapid and portable gas detection systems. Conventional cells typically exhibit stringent requirements regarding distance, axial flip angle, and mirror tilt to meet operational conditions. In contrast, the optical cell depicted in Figure 2 allows for straightforward modification of the optical path length by adjusting the orientation angle of the input laser beam, rendering it well suited for the analysis of gaseous species with distinct absorption lines.