## 3 Results  
### Characterization of the Circular Multipass Cell  
To implement the MPC-PAS system, the first step was to analyze the cell to define its resonant modes in order to maximize the photoacoustic signal generated inside the cell. These are standing waves that can be formed inside the cell due to multiple reflections of the incident light. These resonant modes are determined by the dimensions and optical properties of the cell, as well as the boundary conditions imposed by the surrounding materials. The resonant modes can have different shapes and spatial distributions depending on the cell geometry and material properties. It is important to note that the proper selection of resonant modes is crucial to optimize the performance of a resonant cell in photothermal spectroscopy. As previously stated, three capacitive microphones were installed inside the cell, spaced 1 cm apart and symmetrically positioned around the center as shown in Figure 5. The laser beam was incident inside the cell and it was modulated by a chopper (MC2000B, BW = 10 kHz, Thorlabs, Newton, NJ, USA). The modulation frequency was varied in a range from 1.5 kHz to 9 kHz with a step of 20 Hz. The results obtained for the microphones are shown in Figure 6, where three main resonance modes can be observed at approximate frequencies: 4000 Hz, 6800 Hz, and 8000 Hz.  
Due to its instability and very poor response, the resonant mode near 8000 Hz was not considered. The first resonant mode (4000 Hz) shows a stable behavior, but it has a  
Figure 6: Resonant modes inside the cell identified by the three microphones.  
lower amplitude compared to the resonant mode at 6800 Hz. This mode has the highest amplitude, stability, and signal-to-noise ratio (SNR). Consequently, and in order to evaluate the position of the microphones inside the cell, two characterizations were performed. Frequency sweeps were performed in the range previously defined for the microphone position parallel and perpendicular to the input beam, rotating the microphones 90\({}^{\circ}\), as shown in Figure 7a, and evaluating the frequency response. As shown in Figure 7b, the behavior in the measurement range is similar in the two configurations. However, in the configuration perpendicular to the input beam, the amplitude of the main resonant mode is slightly higher (6%).  
Finally, as shown in Figures 6 and 7, the microphone with the best response is the M1, positioned precisely at the center of the cell, and, thus, it was selected for further measurements. It is imperative to elucidate that the height at which the sensor was installed within the cell was also subjected to evaluation, with the finding that proximity to the center yielded optimal results.  
The detailed frequency response of the MPC for the M1 and M2 was determined by performing a frequency sweep from 6 kHz to 7.2 kHz, as illustrated in Figure 8, which is in close proximity to the main resonance frequency that had been determined previously, while varying the chopper modulation frequency in steps of 20 Hz. The resonance frequency (_fr_) of the MPC was measured to be approximately 6800 Hz, accompanied by a Q factor of approximately 32 at standard atmospheric pressure and room temperature.