## 4 Data Processing
### Time Domain Averaging before Normalization  
Here, we describe the processing procedure and the reflectogram calculation when all points of the mode pulse are used for averaging (green circles for the (\(i-1\))-th pulse in Figure 7a,b). The pulse-by-pulse normalization procedure is then performed: \(S_{i}=\frac{I_{i}}{R_{i}}\). As mentioned above, correct pulse-by-pulse division is possible only when the growth rates of the signals in both channels are equal. Finally, the FFT from the final signal is calculated: \(F=\hat{F}(S_{i})\). The optical frequency coordinate (optical detuning) is transformed to the longitudinal coordinate according to the following expression:  
\[z_{k}=\frac{c\cdot k}{2\cdot N\cdot\delta v}, \tag{5}\]  
where \(k\) is the and \(N\) are the FFT vector index and length, respectively, and \(c\) is the speed of light. For correct comparison, different reflectograms were additionally normalized to the level of 0 dB at zero FFT frequency (in other words, the signal levels were normalized to the average transmitted power). It should be noted that absolute values of reflection amplitudes depend on the coupling ratios of couplers used for the MZI [19]. Thus, additional system calibration is required for the absolute values measurements.  
The resulting reflectograms are presented in Figure 8a. In this figure, we tried to trace a dependence of the reflectogram calculation results on the number of averaging points. Thus, we used original data with the maximum sampling rate (green curve in Figure 8a) and reduced the number of points used in calculations. For example, only the first 10 points after the bursts are used for the calculation of blue line in Figure 8a. It should be noted that the legend of Figure 8 indicates, in fact, the number of averaging points \(J\) measured at a fixed optical frequency \(\omega_{i}\) averaged over different pulses. The number of averaging points \(J\) fluctuates with pulse-to-pulse fluctuations of the mode pulses duration. We note that although the average number of points changes by two orders of magnitude, the characteristic features remain in different reflectograms. For example, a sharp decrease in reflectograms is present in all the graphs (except for black and red ones) at the coordinate \(z\)-2.2 m, which corresponds to the end of the LUT. We can conclude that a higher signal level observed at shorter lengths (\(z<2.2\) m) corresponds to RLS, while a lower signal level (at \(z>2.2\) m) corresponds to the NFL. Next, a peak with an amplitude of \(-40\) dB is observed at the coordinate \(z=0.4\) m, which corresponds to the location of a circulator used in the MZI. The peak corresponds to scattered radiation inside the circulator directly from port 1 to port 3. Moreover, a couple of peaks with much smaller amplitudes are noticed in the noise signal at the coordinates \(z=4.4\) and \(z=4.8\) m. However, the positions and amplitudes of these peaks did not depend on the LUT configuration. Thus, we conclude that these peaks are associated with parasitic modulation in the electrical part of the scheme.  
We also note that the appearance of the reflectogram near the noise floor does not remain constant. The useful signal on the reflectograms, which corresponds to the RLS, has the same structure (alternating dips and peaks). However, the NFL and dips and peaks in the noise floor change their positions and amplitudes as the number of averaging points increases (see black squares in Figure 8b). The increase in the number of averaging points from 1 to 430 points results in a significant decrease in NFL of \(\sim\)30 dB (Figure 8b). The red line in Figure 8b corresponds to the RLS level.