## 2 Theoretical Part
It is known that the maximum length of LUT \(L_{max}\) corresponding to the highest frequency modulation is limited through the frequency tuning step \(\delta\
u\) in the following way:  
\[L_{max}=\frac{c}{4n\delta\
u}, \tag{2}\]  
where \(n\) is the refractive index in the LUT. In turn, spatial sampling \(\delta l\) in the reflectogram was limited to the maximum probe laser tuning range \(\Delta\
u\), i.e., by the product of frequency tuning step and the number of mode pulses used in the reflectogram calculation, as follows [21]:  
\[\delta l=\frac{c}{2n\Delta\
u}. \tag{3}\]  
A key feature of the self-sweeping laser used in the study was the strict discreteness of the optical frequencies of the sequentially generated mode pulses, which was defined through the fixed length of the laser cavity. For such a source, the dependence of the optical frequency on the pulse number was a linear function. For this reason, the problem of tuning non-linearity compensation observed in the time domain and described in the introduction was solved automatically during the transition from time to mode pulse numbers. It should be mentioned that the window function could be properly selected for processing measured signals with the FFT in OFDR systems, especially when a strong reflector presents in a LUT. We illustrate this issue with a numeric example. According to Expression (1), the model signal was the sine sampled at discrete coordinates (black line in Figure 3a). To evaluate a reflectogram corresponding to this signal, we performed the FFT with a rectangular window (black solid line in Figure 3b). The reflectogram had a single peak with an amplitude of 0 dB centered at the modulation frequency. It had wide wings corresponding to the instrument. The wings were located at a relatively high level of \(\sim-35\) dB. However, it was known from [22] that the sinusoid length had to be properly selected to meet the condition of periodicity over the considered sampling interval and reduce the wings' amplitudes in this way. Thus, the number of sampling points was reduced to be closer to a multiple of the sine period (see the red line in Figure 3a), and a sharp decrease in the instrument function wings level down to \(-70\) dB (red solid line in Figure 3b) was observed. This behavior related to the spectral leakage effect [22]. Another approach to reduce the level of the instrument function wings was to change the shape of the FFT window function. The Hann window is one of the most commonly used window functions [22; 23]. When the Hann window was used, the level of the instrument function wings decreased down to \(-100\) dB at a large distance from the central peak (black dashed line in Figure 3b). However, a significant broadening of the central peak occurred in this case. It was noted that despite the use of a different window, the proper selection of the sinusoid length worked similarly in this case. The red dashed line in Figure 3b corresponded to the FFT with the Hann window in the case where the number of points became closer to the multiple of the sine function period. However, in this case, the wings level did not decrease as significantly as in the previous case. Moreover, the instrument function stayed wider compared to the FFT rectangular window function. Thus, when selecting the window function, it was necessary to maintain balance between the width of the central peak and the level of the instrument function wings. When processing the experimental signals, we further used FFT with Hann window function.