## 2 Theoretical Part  
An optical scheme of a typical OFDR system is shown in Figure 1. Radiation from a tunable laser source entered a Mach-Zehnder interferometer (MZI) formed of two couplers: a circulator and a LUT. The tunable probe laser radiation was split at coupler 1 between the reference and probe arms of the MZI. In the former arm, radiation was directed to coupler 2, while in the latter arm, it passed through the circulator. After passing through the circulator, the probe radiation entered the LUT, and the scattered/reflected signal passed through the circulator again and interfered with the other signal from the reference arm at the coupler 2. In the case of distributed measurements, the LUT was represented as a set of many local reflectors. We noted, however, that every particular position of a reflector corresponded to a fixed difference between the lengths of the reference and probe arms of the interferometer \(\Delta L\). The interference signal measured at output of the MZI \(E_{out}(v)\) is given via the following expression:  
\[E_{out}=E_{1}^{2}+E_{2}^{2}+2\sqrt{E_{1}E_{2}}\cdot sin\left(\frac{2\pi v \Delta L}{c}\right), \tag{1}\]  
where \(E_{1}\), \(E_{2}\) are the amplitudes of the probe and reference radiation electric fields at output of coupler 2, \(c\) is the speed of light, and \(v\) is the probe laser optical frequency. In the case of the point reflector, the output signal has the sine function dependence on the laser frequency \(v\). If many local reflectors are present and distributed along the LUT, the output signal becomes a superposition of such sine functions with different amplitudes and periods. An example of a local reflector placed at three different positions in the LUT is demonstrated in Figure 1, together with corresponding sinusoidal transmission functions shown in red, green, and blue for near, middle, and far positions, respectively. The FFT was applied to the spectral transmission function to find the MZI arms difference (time delay) associated with each reflector. In this case, the amplitude of each sine function corresponding to the reflection amplitude for each local reflector was reconstructed. In the case of OR based on RLS, the scattering centers acted as such local reflectors. Here we describe the situation that occurred when a continuous-wave self-sweeping laser [20] was used as a tunable radiation source. The tuning process occurred in a stepwise manner (Figure 2a). In this case, the consecutive horizontal sections with duration \(T\) were divided by a fixed value in the frequency domain--frequency tuning step \(\delta\
u\)--which was determined through the parameters of the laser cavity. In this case, optical frequency within each horizontal section could be considered constant (its fluctuation within each section did not exceed 50 kHz [20]). The duration of each section was equal to the duration of the mode pulse \(T\) and was of the order of several ms. Confirmation of these results was presented in [20], where a detailed analysis of the laser mode dynamics was carried out. When the radiation with stepwise change in the optical frequency passed through the MZI, an amplitude modulation appeared at the output with stepwise modulation in the transmitted power (Figure 2b). The signal from the MZI output was then digitized. The number of points per unit of time in the resulting signal was the signal sampling rate. As a result, sets of amplitudes of the incident transmitted through the MZI waves were recorded for each optical frequency. Figure 1: Typical OFDR system scheme. Figure 2: Illustration of model: (**a**) laser frequency dynamics; (**b**) MZI output signal; (**c**) reflectogram. To calculate the reflectograms (Figure 2c), FFT was applied to the MZI output signals plotted as a function of the pulse number.