## 4 Brillouin Optical Correlation Domain Analysis: BOCDA
### Examples of Performance-Improved BOCDA Systems
#### 4.4.1 BOCDA System with Intensity Modulation Scheme  
Figure 21 shows a BOCDA system that includes the three performance improvement schemes: the \"intensity modulation scheme\" [51], the \"time-division polarization diversity scheme\" [57], and the \"beat lock-in scheme\" [66]. Here, the IM scheme is explained in detail. Figure 22a schematically shows the Brillouin gain shape that is generated at each location by the BOCDA principle of the position-selective excitation of the Brillouin gain. At the correlation peak position, the Lorentz-shaped Brillouin signal spectrum is generated. Figure 21: Example of the BOCDA systems that include three performance improvement schemes: the intensity modulation scheme, the time-division polarization diversity scheme, and the beat lock-in detection scheme [51; 57; 66]. sides of the peak position, a broadened spectrum is generated that has large power portions at both edges of the spectrum shape, as shown in Figure 22a. The BOCDA system output is obtained by the integration of all the spectra that are generated at each position along the fiber. Then, the total shape becomes as shown in Figure 22(b-i). The total BOCDA output spectrum consists of two components; one is the signal component corresponding to the correlation peak position, and the other corresponds to the non-correlation portions besides the peak position. When a strain is applied to a short-length fiber portion, whose length is almost the same as the spatial resolution given by Equation (2) or Equation (3), the Lorentz-shaped signal spectrum is slipped down along the skirt of the mountain-shaped background spectrum, as shown in Figure 22(b-ii). When a large strain is applied, the top of the signal spectrum is lower than the top of the mountain-shaped background. This means that a large strain might not be measured correctly. Then, a scheme to reduce the height of the background spectrum was proposed, which is the \"intensity modulation scheme\". In the SOCF research, it has been known that the synthesized coherence function shape is given by the Fourier transform of the time-averaged light source power spectrum shape. In that sense, the amount of the Brillouin gain that is induced as a function of the fiber axis z is thought to be calculated roughly by the Fourier transform of the light source power spectrum shape. Of course, the gain shape is also the function of the frequency difference between the pump and the probe, as shown in Figure 22a. This means that the Brillouin gain distribution is plotted in the two dimensions; one is the frequency difference \(\Delta\
u\), and the other is the fiber position z. When the LD power spectrum has high power portions at both edges, the Fourier transform theorem shows that relatively large side lobes are generated. Then, the mountain-shaped non-desired background spectrum is thought to be generated by the large side lobes. The side lobes have the possibility of being reduced by the so-called \"apodization\" or \"window\" in the Fourier transform theorem, which was exactly true in the case of the simple SOCF. We proposed the \"intensity modulation scheme\" for the BOCDA system, in which the IM modulation is applied by an IM modulator, as shown in Figure 21, which is synchronized to the FM modulation [51]. By the IM modulation, the time-averaged light source power spectrum is  
Figure 22: The spectral shape induced locally along the optical fiber by the BOCDA principle (**a**). At both sides of the correlation peak position, broadened spectra are generated that have large power portions at both edges of the spectrum. The BOCDA output spectrum is obtained by integrating all of the spectra that are generated at each position along the fiber (**b**). At the correlation peak position, a Lorenz-shaped signal spectrum is obtained, and a mountain-shaped background spectrum is generated as the integration of the spectra caused at the non-correlation portion. manipulated, so that both edges of the spectrum shape are reduced to zero.