# Phase-Coded and Noise-Based Brillouin Optical Correlation-Domain Analysis
## 2 Phase-Coded Brillouin Optical Correlation-Domain Analysis
### Double Pulse-Pair Analysis  
The remainder of Section 2 relates to phase-coded B-OCDA protocols that use a single pump pulse along the lines of Section 2.3. The effective stimulation of the acoustic wave requires that the duration \(T_{p}\) of the pump pulse is several times longer than the Brillouin lifetime \(\tau\). The period of the phase code \(NT\), in turn, must be longer still. These considerations suggest that the minimum number \(N\) of correlation peak position scans equals several multiples of \(\tau/T\). For high-resolution setups that involve short phase code symbols, that number is between 50 and 200.  
Figure 6: (**a**) Measured normalized Brillouin gain as a function of correlation peak position and frequency offset between the pump and signal waves [19]. The fiber under test was 8.8 km long. Measurements were performed with a spatial resolution of 2 cm. All 440,000 resolution points were successfully addressed. The Brillouin pump and signal waves were jointly phase-modulated by a repeating perfect Golomb code of 211 symbols period and a bit duration of 200 ps. The pump wave was also amplitude-modulated by a sequence of 9785 pulses with symbol duration of 20 ns. (**b**) Magnified view of the Brillouin gain map in a 2-m-long section located towards the output end of the fiber under test [19]. A 7-cm-long heated region is identified by the Brillouin analysis. Reproduced with permission from [19], IEEE, 2016  
A variant of phase-coded B-OCDA with a reduced number of position scans was proposed in 2016 [23]. In that system, the phase code period was deliberately chosen to be shorter than \(T_{p}\). Consequently, the Brillouin amplification events of the signal wave in multiple correlation peak positions overlap in time, and the Brillouin interactions at individual locations cannot be separated directly. To work around this difficulty, each trace is acquired twice with pump pulse durations of \(T_{p}\) and \(T_{p}+\Delta T_{p}\), respectively. While \(T_{p}\) exceeds the phase code period \(NT\), the differential pulse width \(\Delta T_{p}\) does not. The two measurements of the output signal power are subtracted, and the difference trace unambiguously retrieves the Brillouin interactions at individual correlation peak positions.  
The measurement technique combines double pulse-pair analysis, which is often used in B-OTDA [12], and correlation-domain analysis. The detection bandwidth that is necessary in the double pulse-pair B-OCDA case corresponds to \(\Delta T_{p}\gg\Delta z/v_{g}\). That bandwidth is narrower than that of double pulse-pair time-domain analysis, which corresponds to the shorter time intervals \(\Delta z/v_{g}\). On the other hand, double pulse-pair B-OTDA maps the entire fiber under test with only a single pair of scans per choice of \(\Omega\).  
Figure 7 shows an example of double pulse-pair, phase-coded B-OCDA analysis [23]. The fiber under test was 43 m long, and the spatial resolution of the analysis was 2.7 cm. Only 11 pairs of correlation peak position scans were necessary for addressing all 1600 resolution points. The durations of the pair of pulses were 29 ns and 30 ns, whereas the period of the phase code was only 2.9 ns. The double pulse-pair analysis successfully removes the ambiguity introduced by the short code period. Three 8-cm-wide hot-spots are clearly seen in the measurements.