## 1 Introduction  
Theoretical and experimental development of methods for measuring the ultra-low absorption of ultrapure materials is carried out in many laboratories around the world. One of the most sensitive methods are photothermal methods--in particular, photothermal common-path interferometry [1, 2, 3, 4, 5, 6, 7, 8] and laser-induced deflection techniques [4, 9, 10, 11]. Achievements in the development of these methods can be assessed using data from Heraeus, a manufacturer of some of the world's purest quartz glasses. According to the presented data [12], the optical absorption (\(\lambda\approx 1\) um) in Suprasil 3001 glass is below the detection limit of the methods used (~1 ppm/ cm for bulk absorption). Increasing the sensitivity of ultra-low absorption measurements in quartz materials to \(10^{-9}\) cm\({}^{-1}\) is a general problem with important applications. In particular, it will make it possible to measure absorption variations introduced by impurities against the background of the fundamental absorption of quartz glass and the absorption of the OH group (\(1\div 5\times 10^{-8}\) cm\({}^{-1}\)/ppm) [13]. Such measurements open up the possibility of monitoring the concentrations of the most common metal impurities (Fe, Ti, etc.) at a uniquely low level of 1 ppt in quartz glasses [14]. Its relevance is confirmed by the manufacturers' data [15, 16], in which the detection limit value of the measurement method used is indicated as the impurity concentration value in the purest glasses (for example, <0.5 ppb for iron in SK-1300 glass [16]). In [17], we presented a new method for measuring ultra-low absorption (with a sensitivity of \(\sim\)10\({}^{-6}\) cm\({}^{-1}\) achieved at the moment with a signal-to-noise ratio \(\approx\)100/1 for quartz glass), called time-resolved photothermal common-path interferometry (TPCI). The TPCI scheme is a modified version of the thermal lens scheme [18; 19] and the photothermal common-path interferometry scheme [1; 2; 3; 4; 5; 6; 7; 8]. Differences between these schemes are discussed in [20; 21]. We have developed a theory that relates the values of the measured signals with the absorption coefficients of isotropic [17] and anisotropic solid dielectrics of some classes of symmetries [20]. In [22], a modified optical part of the TPCI scheme, which provided a Gaussian-like shape of laser beams in the volume of the tested samples, was presented, bringing the experimental conditions as close as possible to the theoretical description. In addition, the effect of ambient air on absorption measurements was studied. This paper discusses the problem of measuring absorption under conditions of developed heat diffusion. Until now, the problem of measuring absorption using a TPCI scheme has been considered in the absence of heat diffusion in the region of the heating beam, since the duration of its pulse, \(\tau_{\text{pulse}}\), was much less than the characteristic time of heat diffusion, \(\tau_{\text{diff}}=\text{C}\rho a_{\text{h}}^{2}/\Lambda\). For example, for quartz glass, \(\tau_{\text{pulse}}\approx 100\) us and \(\tau_{\text{diff}}\approx 2600\) us. Here, C is the heat capacity, \(\rho\) is the density, \(\Lambda\) is the heat conductivity coefficient, and \(a_{\text{h}}\) is the heating beam waist radius at the 1/e intensity decay level. One of the ways to improve the sensitivity of measurements is to increase the energy of the heating pulse by increasing its power. However, there is a limit related to the dependence of the refractive index on the radiation power density of the heating laser in the sample volume, which finally masks the absorption signal [1]. On the other hand, the heating energy can be increased without increasing the field intensity but by increasing the pulse duration. It follows from the calculations presented below that this way of increasing sensitivity also has its limits.