## 4 Data Processing
### Frequency Domain Averaging  
In all approaches described in the above text, the reflectograms are obtained using the data from a fixed-frequency tuning range \(\Delta\
u\) of the probe laser. We conclude that the structure of the signal corresponding to the LUT remains constant and does not depend on the nature of averaging. Moreover, we consider thr influence of the laser tuning range position (the central optical frequency position within a scan) on the reflectogram at a fixed length of the spectral range (window length). In this case, we consider a longer scan and  
Figure 9: Time domain averaging after normalization: (**a**) spectrogram illustrating dependence of the reflectogram on interval of mode pulse; (**b**) average of reflectograms corresponding to different intervals of mode pulse (red curve) in comparison with full mode pulse (black curve, identical to the green curve from Figure 8).  
move the position of the data range used for processing. For this purpose, the data were first averaged over each mode pulse and pulse-by-pulse normalized, as described above. The windowed (short-time) Fourier transform was then applied to the normalized signal:  
\[F_{k}(m)=\hat{F}(S_{i}), \tag{8}\]  
where \(m\) is the window number. The window length is chosen to be 256 points, corresponding to the tuning range \(\Delta\
u\)\(\sim\)2.5 GHz with a frequency tuning step between neighboring points of 9.7 MHz. The overlap of the windows was set to 255 points to observe point-by-point variation in the reflectograms. Thus, the sweeping of the central frequency with a fixed value for the frequency tuning range is effectively carried out. The result is shown as a heat map in Figure 10a. The horizontal and vertical axis correspond to the coordinate along the measuring line (\(z\)) and the detuning of the central frequency. As before, a sharp decrease in amplitude is present at \(z=2.2\) m. However, the amplitude of the signal corresponding to the LUT (\(z<2.2\) m) now depends on the central optical frequency. We conclude that the results of such a line interrogation can be used for sensing tasks, similarly to the distributed temperature measurements performed using a pulsed self-sweeping laser [19]. In addition, the third type of averaging becomes possible: averaging of reflectograms corresponding to different central frequencies (i.e., averaging in the frequency domain). Figure 10b shows a comparison between the original reflectogram (black line) and the result of frequency domain averaging (red line). It can be seen that the fast signal fluctuations now decrease in both regions of reflectogram corresponding to the LUT and the noise floor. It can be expected that with a further variation in the central frequency (vertical axis in the Figure 10a), the reflectogram will become even more smooth, becoming similar to measurement results usually observed in conventional incoherent RLS reflectometry.  
Figure 10: Frequency domain normalization: (**a**) spectrogram showing spectral dependence of reflectogram; (**b**) smoothing through performing frequency domain averaging (black curve is identical to green curve in Figure 8 and red curve is averaging result).