Mitigating the effects of the gain-dependence of the Brillouin line-shape on dynamic BOTDA sensing methods

It has been recently shown that in stimulated Brillouin amplification (pulsed pump & CW probe) the line-shape of the normalized logarithmic Brillouin Gain Spectrum (BGS) broadens with increasing gain. Most pronounced for short pump pulses, a linewidth increase of ~3 MHz (~1.5 MHz) per dB of additional gain was observed for a pump pulse width of 15 ns (30 ns), respectively. This gain-dependency of the shape of the BGS compromises the accuracy of the otherwise attractive, highly dynamic and distributed slope-assisted BOTDA techniques, where measurand-induced gain variations of a single probe, are converted to strain/temperature values through a calibration factor that depends on the line-shape of the BGS. A previously developed technique with built-in compensation for Brillouin gain variations, namely: the Ratio Double Slope-Assisted BOTDA (RDSA-BOTDA) method, where both slopes of the BGS are interrogated, fails to meet this new challenge of the gain-induced shape dependence of the BGS, resulting, for instance, in significant measurement errors of ~5% per dB of gain change for a 15 ns pump pulse. Here, we propose and demonstrate an extension of the RDSA-BOTDA method, which now offers immunity also to Brillouin gain-dependent line-shape variations. Requiring a prior characterization of the gain-induced line-shape dependency of the fiber and pump-pulse-width in use, this mitigation technique takes advantage of the fact that the sum of the measured logarithmic gains at judiciously chosen two fixed frequency points of the BGS can be used to determine the local peak gain, via a pre-established calibration curve. Based on the deduced correct peak gain, its associated BGS shape can now be used in the application of the previously introduced RDSA-BOTDA technique to obtain error-free results, independent of the gain dependence of the line-shape. The proposed technique has been successfully put to test in an experiment, involving a RDSA-BOTDA measurement of a fiber segment, vibrating at 50 Hz with a constant, peak-to-peak amplitude of 640 microstrain. As the Brillouin gain was manually varied from 1 to 3.5 dB, classical data processing, based on a single gain value, predicted amplitudes which varied by as much as 90 microstrain, while the proposed mitigation technique produced the correct constant amplitude, regardless of the gain changes. This restored accuracy of the RDSA-BOTDA technique is of importance, especially for monitoring real-world dynamic scenarios, where high Brillouin gains, which often locally vary due to dynamically introduced losses, can successfully achieve fast gain-independent double-slope-assisted Brillouin measurements (many kHz's of sampling rates over hundreds of meters), with enhanced spatial resolution and signal to noise ratio.