## 4 IR Signal Occurring during Endovasal Laser Treatment of a Vein with TOTFC  
In the EVLT process, as a result of the absorption of laser radiation, TOTFC is heated to a high temperature, the value of which depends on the average power of laser radiation (see Figure 2). Heated bodies are known to emit of radiation in a wide spectral range. This radiation is called a thermal or an IR signal [19]. Let us assume that TOTFC is a completely  
Figure 7: The dependence of \(\Delta P\_80\) on \(\Delta T_{TOTFC\_80}\) at various \(\Delta\
u\) (the wavelength of laser radiation is 980 nm, the inner vein diameter is 5 mm). blackbody. The spectral luminosity density of a blackbody (\(u\)(\(\lambda\),\(T\))) at a certain temperature is described by the formula [20]:  
\[u(\lambda,\,T)=\frac{2\textit{h}\cdot c^{2}}{\lambda^{5}}\cdot\frac{1}{exp\left( \frac{\hbar c}{\lambda kT}\right)-1} \tag{5}\]  
where \(\lambda\) is the wavelength (m), \(c\) is the speed of light (3 \(\times\) 10\({}^{8}\) m/s), \(h\) is the [PERSON]'s constant (\(\textit{h}\) = 6.626 \(\times\) 10\({}^{-34}\) J\(\cdot\)s), \(k\) is the Boltzmann constant (\(k\) = 1.380649 \(\times\) 10\({}^{-23}\) J/K), \(T\) is the temperature of a blackbody in degrees Kelvin (in this case, \(T\) = \(T_{TOTFC}\)). The distributions of the spectral luminosity density of TOTFC in the wavelength range 0.2-20 \(\upmu\)m at an average laser power \(P\) = 10 W for traction speeds \(\
u\) in the range 1-7 mm/s and at \(\
u\) = 2 mm/s for an average laser power \(P\) in the range 8-14 W are shown on Figure 8.  
The spectral luminosity density of TOTFC mainly depends on the average power of laser radiation (see Figure 8b), and the change in the traction speed does not significantly affect the spectral luminosity density of TOTFC (see Figure 8a). The maximum spectral luminosity of TOTFC is in the wavelength range of 1-6 \(\upmu\)m. With a decrease in the traction speed and with an increase in the average power of laser radiation, the wavelength of the maximum spectral luminosity density of TOTFC shifts to the short-wavelength region, which, following [PERSON]'s law [22], is associated with an increase in the temperature of TOTFC. In the EVLT model shown in Figure 1b, thermal radiation (IR signal) occurs in TOTFC, then propagates along with the optical quartz fiber, is reflected by a beamsplitter, and then PD is recorded. In this case, the spectral luminosity density TOTFC at the output of PD (\(\sigma\)) is described as follows:  
\[\sigma=\int_{\lambda_{1}}^{\lambda_{2}}u(\lambda,T)\cdot S_{F}(\lambda)\cdot S _{BS}(\lambda)\cdot S_{PD}(\lambda)d\lambda \tag{6}\]  
where \(\lambda\)1, \(\lambda\)2 are the smallest and the largest wavelengths under study, respectively, \(S_{F}(\lambda)\) is the transmission spectrum of the optical quartz fiber, \(S_{BS}(\lambda)\) is the reflection spectrum of the beamsplitter, \(S_{PD}(\lambda)\) is the spectral sensitivity of PD. When choosing PD, it is to be taken into account that its spectral sensitivity is to lie in the range corresponding to the maximum spectral luminosity of TOTFC, that is, in the wavelength range of 1-6 \(\upmu\)m. In addition, after passing through the optical quartz fiber, the intensity of the IR signal in the region of wavelengths above 2 \(\upmu\)m will be greatly  
Figure 8: Spectral luminosity densities TOTFC (\(u\)(\(\lambda\),\(T\))) at an average laser radiation power \(P\) = 10 W for traction speeds (\(\
u\)) in the range 1-7 mm/s (**a**) and at \(\
u\) = 2 mm/s for \(P\) in the range 8–14 W (**b**) (the wavelength of laser radiation is 980 nm, the inner vein diameter is 5 mm). weakened [23; 24]. PD is to be particularly sensitive in the range 1-2 \(\upmu\)m. According to [25], these conditions are satisfied by an uncooled Germanium (Ge) photodiode, an uncooled PbS\({}_{295}\) photoresistor, and a cooled PbS\({}_{78}\) photoresistor. In the current study, continuous laser radiation was used. In this case, the problem of the high noise level of PbS photoresistors may be important [26].