## 2 Materials and Methods  
### The BILLI System  
A lidar, also known as an optical radar, is an active range-resolving optical remote measurement system whose main components are composed of a transmitter (laser) and the receiver (telescope, optical analyzer/detector, data acquisition/computer). The principle of operation is the following [43; 44]: the laser emits a light pulse into the atmosphere and its photons are scattered in all directions from molecules and aerosols (particles, droplets, etc.) present in the air. Part of the light is backscattered toward the telescope. Then, by means of a detector and computer, it is possible to analyze the detected signal vs. The time elapsed between the emission and detection (t). This makes it possible to characterize the chemico-physical properties of air along the beam. In fact, if R is the distance from the lidar of the backscattering layer and \(c\) is the speed of light, we can write R = ct/2. Going back and forth from the backscattering layer, the laser pulse undergoes attenuation by air, as expressed by its extinction coefficient, linked to the light absorption of its species. Often, the absorption lines of molecules are narrow, making it possible to employ DIAL to retrieve their concentration. This technique uses the idea of differential-absorption measurement in which two light pulses with slightly different wavelengths (ON: the light is strongly absorbed by the species under investigation, OFF: the light is not absorbed at all or at least much less) are emitted into the atmosphere, and two corresponding backscattered signals are detected concurrently. The difference between the two profiles is directly linked to the molecule abundance and this technique allows one to determine and map the concentrations of selected molecular species in ambient air [43; 44]. BILLI (whose technical scheme and experimental setup are reported in Figure 1) is a monostatic-biaxial DIAL-Lidar system mounted in a small laboratory truck and is composed of a transmitter and receiver equipment [21; 37; 38; 39; 40; 41; 42]. The transmission sub-system is based on a double grating dye-laser optically pumped by an injection seeded Nd:YAG laser (powerful, tunable and narrow-linewidth), a device for the frequency generation (i.e., difference frequency mixing, DFM), and an optical parametric amplifier operating in the NIR (Near IR) band (OPANIR). The limited tunability (few tenths of nm) of Tm, Ho:YLF, and fiber lasers was the main reason of their exclusion (from the transmission sub-system during the implementation stage) given the difficulties in choosing the best absorption line [36]. Instead, due to the harsh environment near degassing craters that can cause burns on the surface of nonlinear crystals, OPOs (optical parametric oscillators) have been discarded [37; 38; 39]. This transmitter was used to generate laser radiation at \(\approx\)2 \(\upmu\)m, a region of the electromagnetic spectrum absorbed by atmospheric CO\({}_{2}\), with negligible cross-sensitivity to H\({}_{2}\)O [36]. The laser source of BILLI has the following characteristics [39]:  
* 10 pm wavelength stability corresponding to about 0.2 cm\({}^{-1}\) wavenumber stability;
* enhanced beam profile amplifier (EBPA);
* dynamic mode option (DMO); and
* piezo wavelength control (PWC). The receiver sub-system is based on a Newton telescope and a detection system, which consists of a thermoelectric-cooled InGaAs PIN photodiode, directly linked to the analog-to-digital converter (ADC). Two large motorized elliptical mirrors (major axis: 450 mm) make it possible to scan all of the  
Figure 1: **(a)** Technical scheme of the BILLI DIAL system extrapolated and rearranged from the Figure 2 reported in [37]); **(b)** Experimental setup of the system during the Stromboli campaign (the volcano summit is visible above the two inset pictures). The scanning mirrors and the laser system are visible in the top and bottom inset picture, respectively. angles above the horizon.