# Non-Local Effects in Brillouin Optical Time-Domain Analysis Sensors
## 3 Mitigation of Non-Local Effects
### Probe Dithering for ER Impairments Mitigation  
In the description of the BOTDA sensor thus far, it has been assumed that the pump wave is just an ideal optical pulse. However, any practical device that is used to generate the pulse is bound to have a limited extinction ratio (ER). Hence, as shown in Figure 6, in real-world BOTDA sensors there is a CW pump power that leaks and counter-propagates with the probe wave along the fiber. In this way, as shown in Figure 6, there are three regions of interaction with the pump wave that the probe wave finds as it travels along the fiber. The first interaction section extends from the probe entrance in the fiber at \(z=L\) to the location of the pulse at a particular \(z_{0}\). In this region, just the pedestal of the pump pulse and the probe wave interact, leading to Brillouin amplification of the probe wave. Then, the probe wavefront meets the pulse and is amplified during the width \(u\) of the pulse (half the spatial width of the pulse in the fiber, which equals the spatial resolution). Finally, after leaving the pulse location, there is another interaction area, from \(z=z_{0}-u\) to \(z=0\), where the probe wave is again amplified by the pump pedestal. Therefore, the net effect of the presence of the pump wave pedestal is that the probe wave experiences more gain than just that due to the pulse itself. A gain that is not useful for sensing. On the contrary, the extra power amplification of the probe wave aggravates the appearance of pump pulse depletion since the pulse meets a higher probe power along the entire sensing fiber than would be met in the case of no pump pulse pedestal [24]. This effect takes place even in BOTDA setups deploying two probe waves. In this case, the power of the probe waves becomes unbalanced owing to the interaction with the pedestal: one probe wave is amplified while the other one is depleted. Thus, gain and loss processes induced by the probe waves over the pump pulse no longer compensate each other, leading to pulse depletion, which in turn introduces a more stringent limitation of the total probe wave power that can be deployed in the sensor. Figure 7 displays the numerically calculated frequency-dependent depletion factor of the pump pulse in a dual-probe BOTDA configuration for different ER of the pulse. It can be observed that the use of a 25 to 30 dB ER of the pump pulses, which is typical of pulses shaped using electro-optic modulators, seriously increases the depletion factor and, hence, the error in the measurement of the BFS. Figure 6: Schematic description of probe and pulse waveform interaction along the fiber for an extinction ratio (ER) limited pump pulse wave. To obtain a higher ER of the pulses, acousto-optic modulators (AOM), optical switches or cascaded Mach-Zehnder modulators (MZM) can be used. However, AOMs and optical switches are limited in the rise time of the pulses that they can produce so it is not possible to generate short pulses. Furthermore, the use of cascaded MZMs increases the complexity and final cost of the sensor. Thus, in order to use a single MZM, which provides short pulses at a reduced setup complexity and cost of the sensor, we have devised a method to deploy the probe dithering technique to reduce the detrimental effects of the use of limited ER pulses in BOTDA sensors [25]. In this incarnation of the technique, the modulation of the optical frequency of the probe wave is performed by taking advantage of the chirp of the source laser under direct current modulation. The theoretical underpinnings of the method are similar to those of the interaction between pump and probe waves in Brillouin optical correlation domain analysis sensors. As the laser used for generating not only the probe wave but also the pump pulse is FM modulated, the pulse pedestal and the probe wave have their optical frequencies modulated with the same sinusoidal shape.