## 2 Materials and Methods
The maximum (the red and black curves) and minimum (the blue curve) of the oscillograms correspond to the end of the heating pulse. the oscillograms demonstrate similar shapes over the time interval of the heating pulse. These forms depend on heat diffusion times, thermo-optical parameters, and absorption coefficients, which determine the processes of heating and heat diffusion. To correctly calculate the absorption coefficient under conditions of developed heat diffusion, we proposed a method [22] based on the processing of experimental oscillograms of the time-varying component of the probe radiation power. To do this, a tangent to the oscillogram obtained for the sample under study was first constructed at the point corresponding to the moment the pulse started. The ratio between two values, namely, the value of the tangent line at the end of the heating pulse (this corresponded to the oscillogram value in the absence of heat diffusion) and the experimentally obtained value of the maximum pulse amplitude of the time-varying component, was calculated. This ratio determines the correction factor. The correction factor obtained in this way took into account the decrease in the amplitude of the time-varying component as a result of the heat diffusion process. This coefficient was employed as a correction multiplier, which was included in the formula for the linear dependence of the signal amplitude on the heating pulse energy, which is valid for short heating pulse durations. This procedure for the Suprasil 311 calibration sample was not performed due to the smallness of the correction. As a result, the absorption coefficient of the crystal was calculated using the obtained correction and the known value of the thermo-optical parameter of crystalline quartz, as well as the known absorption of quartz glass. In [22], the resulting correction factor was equal to 1.7. The disadvantage of this method is the ambiguity of constructing tangent lines, which is related to both the noisiness of the oscillograms and the finite duration of the leading edge of the heating pulse due to the transient generation of the heating laser, as well as the finite resolution of the measuring system. These factors lead to great ambiguity in the results obtained during measurements in crystals with low absorption (\(\sim\)10\({}^{-7}\) cm\({}^{-1}\)). The theoretical calculation presented below is intended to increase the accuracy of calculations and eliminate the mentioned ambiguity when measuring absorption coefficients \(\alpha\)\(\sim\)10\({}^{-7}\) cm\({}^{-1}\) in crystalline quartz. Moreover, this is also topical for measurements in synthetic ultrapure quartz glasses, the absorption of which can drop to the level of the fundamental absorption of SiO\({}_{2}\) material, which, according to theoretical estimates, is \(\alpha\)\(\sim\)5 \(\times\) 10\({}^{-8}\) cm\({}^{-1}\)[27] at wavelengths of 1000 nm. Figure 4: Oscillograms U(t) of the time-varying component of the probe radiation power, which were obtained for SCQ (red), Suprasil 311 quartz glass (black), and ambient air (blue). The oscillograms are functions of time, which are normalized to the corresponding \(\tau_{\rm diff}\) for each oscillogram; the height of the oscillograms is normalized to the products of the corresponding absorption coefficients and thermo-optical parameters.