## 2 Materials and Method
As previously mentioned, the sensitivity of the measurement was limited by the absorption of the air located on the path of the co-propagation of the heating and probe beams. This led to the fact that the measurement results were rather estimative at values of the absorption coefficient in the quartz crystal of \(\sim\)10\({}^{-7}\) cm\({}^{-1}\). Figure 1: Time-resolved photothermal common-path interferometry (TPCI) electro-optical scheme (argon cells not shown). In previous papers we have already pointed out the need to exclude the influence of air. The simplest theoretically but technically complicated solution is to organize vacuum space in the areas of the sample location and co-propagation of laser beams. Such a solution would greatly complicate the experimental work. Therefore, a simpler solution to the problem was found. We assumed that the absorption of ambient air at 1071 nm is mainly determined by energetic transitions in the infrared region at frequencies (and overtones of these frequencies) of vibrational-rotational energy levels of various two-atomic and multi-atomic molecules included in the air. In accordance with this assumption, the absorption of pure one-atomic gas, for example, argon, is determined by electronic transitions whose frequencies are located, as in quartz materials, closer to the UV range of the spectrum. And at near-atmospheric gas pressures, this absorption will be significantly lower due to the gas density, three degrees of magnitude lower than the density of the samples under study. This assumption was confirmed to a large extent in the subsequent experiments. Figure 2 shows a part of the optical scheme modified in this work, with details of the cell arrangement to explain the observed residual disturbances. The cells with an inner diameter of 0.5 cm and a length of 9 cm supplied with argon of 99.99% purity had open ends. Such a decision was caused by the necessity to eliminate the influence of windows in closed cells when measuring ultra-low absorption in quartz glasses at the level of \(\sim\)10\({}^{-8}\) cm\({}^{-1}\). The rate of argon flow into the cells was \(\sim\)3 L/min at a pressure of \(\approx\)1.033 atm at the cell input. The flow rate was selected experimentally by observing single (i.e., without averaging) waveforms of the time-varying component, which allowed us to fix the flow rate at which a jump in the amplitude of low-frequency noises occurred (Figure 3). These noises are apparently caused by the unsteadiness of the gas flow in the cells. The operating pressure of argon at the input of the cells was chosen to be somewhat lower than the threshold of these noises. We should pay attention to the value \(\approx\)0.05 s of the characteristic time of change of the noises arising due to the unsteadiness of the argon flow. The measurement of the absorption coefficient at the level of \(\sim\)10\({}^{-8}\) cm\({}^{-1}\) requires a significant increase in the number of averaged waveforms from 10\({}^{4}\) to 5 \(\times\) 10\({}^{4}\) to average these slow oscillations. This increases the measurement time from 6 min to 30 min. The peculiarity of this simple design was the presence of areas of co-propagation of the heating and probing beams located near the mirrors, which were filled with air mixed with an outgoing unsteady argon flow. The total length of these regions was about 3 cm. The distance between the M\({}_{2}\) and M\({}_{3}\) elements was 50 cm. The optical elements were made of quartz glasses having a large absorption coefficient \(\sim\)10\({}^{-4}\) cm\({}^{-1}\), relatively to the values measured in the samples. As in [14], the measurements were performed in a sample of synthetic crystalline quartz (LLC Quartz Technologies [39]). Figure 4 shows the geometry of the mutual arrangement of the crystallographic axes of the crystal (C, a\({}_{i}\), i = 1, 2, 3), the polarization vector of the heating radiation (E\({}_{h}\)), and the wave vector of the heating beam (k\({}_{h}\)).