## 4 IR Signal Occurring during Endovasal Laser Treatment of a Vein with TOTFC
To solve this problem, it is necessary to modulate continuous laser radiation or use a pulsed laser. For modern PbS photoresistors, the operating modulation frequency can be 2-3 kHz, and the pulse duration is 50-100 \(\upmu\)s.  
Considering the dependence of \(T_{TOTFC\_80}\) on \(P\_80\) (Figure 5), assuming that TOTFC is a completely blackbody and the beamsplitter reflects the entire incident IR signal without any distortion (i.e., \(S_{BS}(\lambda)=1\)), it is possible to describe the dependence of the spectral luminosity density of TOTFC \(\sigma\) within the framework of the developed EVLT model for the wavelength range 1-6 \(\upmu\)m from \(T_{TOTFC\_80}\) and \(P\_80\) excluding \(S_{F}(\lambda)\) and \(S_{PD}(\lambda)\), and taking into account \(S_{F}(\lambda)\) and \(S_{PD}(\lambda)\). These dependencies are shown in Figure 9.  
With an increase in the temperature \(T_{TOTFC\_80}\) and the average power of the laser radiation \(P\_80\), the value of \(\sigma\) increases non-linearly and these dependences are described by smooth curves. Taking into account \(S_{F}(\lambda)\) and \(S_{PD}(\lambda)\) leads to a decrease in the recorded spectral luminosity density TOTFC. The highest spectral luminosity density of the IR signal transmitted through an optical quartz fiber is recorded using an uncooled PbS\({}_{295}\) photoresistor. Taking into account the dependences presented in Figures 6, 7 and 9, it is possible to plot the dependence of the change in the spectral density of radiation TOTFC \(\Delta\sigma\) on \(\Delta P\_80\) for the wavelength range 1-6 \(\upmu\)m (see Figure 10) without taking into account \(S_{F}(\lambda)\) and \(S_{PD}(\lambda)\) and considering \(S_{F}(\lambda)\) and \(S_{PD}(\lambda)\). Figure 9: The dependence of the spectral luminosity density TOTFC \(\sigma\) (in the wavelength range 1–6 \(\upmu\)m) on \(T_{TOTFC\_80}\) (**a**) and \(P\_80\) (**b**) without taking into account \(S_{F}(\lambda)\) and \(S_{PD}(\lambda)\) and considering \(S_{F}(\lambda)\) and \(S_{PD}(\lambda)\) for varied PD (the wavelength of laser radiation is 980 nm, the inner vein diameter is 5 mm). The analysis of the dependencies represented above shows that for S\({}_{F}\)(\(\lambda\)) = 1 and S\({}_{PD}\)(\(\lambda\)) = 1 in the change in the spectral radiation density \(\Delta\sigma\) in the wavelength range 1-6 \(\upmu\)m is associated with a change of temperature \(\Delta T_{TOTFC\_80}\), which in turn, is related to a change of the traction speed. The change in the spectral radiation density \(\Delta\sigma\) can be compensated by a proportional change in the average power of the laser radiation \(\Delta P_{\_80}\), following the equation:  
\[\Delta P_{\_80}=0.0046(\Delta\sigma)^{3}-0.083(\Delta\sigma)^{2}+1.1812\Delta\sigma \tag{7}\]  
Thus, in this part of the study, a relationship between a change in the spectral density of radiation \(\Delta\sigma\) associated with a change of temperature \(\Delta T_{TOTFC\_80}\) required to maintain the temperature of TOTFC at \(T_{TOTFC\_80}\) and with a change in the average power of laser radiation \(\Delta P_{\_80}\) was established. Equation (7) can be used to create a feedback system that ensures uniform coagulation of the vein wall during EVLT with wavelength of laser radiation equal 980 nm. It should be noted that the numerical coefficients as shown in Equation (7) can vary depending on the size of the vein, the range of the recorded wavelengths of the IR signal, the parameters of laser exposure and the materials of the optical fiber and the photodetector. The investigation of the effects of these changes on \(\Delta P_{\_80}\) would be the subject of a separate research, depending on the technical features of a laser system used for EVLT and may be a target for further studies.