On the 2D Post-Processing of Brillouin Optical Time-Domain Analysis

Abstract

The benefits and limitations inherent to the 2D postprocessing of measurements from Brillouin optical time-domain analyzers are investigated from a fundamental point of view. In a preliminary step, the impact of curve fitting on the precision of the estimated Brillouin frequency shift is analyzed, enabling a fair comparison between the representative noise-reduction algorithms studied in this article. The performances in terms of signal-to-noise ratio, experimental uncertainty σ B on the Brillouin frequency shift and spatial resolution delivered by advanced image processing methods-such as wavelet transform and non-local means algorithms-are then compared with the impact of a 2D Gaussian filter. The major discrepancies observed when comparing the gain in signal-to-noise ratio to the σ B reduction are then determined by exploiting the separability of the Gaussian filter, which reveals that noise reduction is only effective along 1-D of the 2D array of measurements and originates from a digital reduction of the system analog bandwidth. The signal-to-noise ratio improvement obtained from filtering in the spectral dimension is only illusory, since its action is redundant with the curve fitting procedure to estimate the Brillouin frequency shift. Finally, the maximum σ B reduction achievable by digital post-processing is theoretically given, hence setting a fundamental limit to the improvement brought by data processing.

Study on the signal-to-noise ratio of Brillouin optical-time domain analyzers

“…It must be mentioned that, both the thermal and shot noise bandwidths, i.e. B e and B c , can be optimized (minimized) through proper post-processing (e.g., digital filtering [10]), to match the signal bandwidth B s that is only determined by the targeted spatial resolution. This way the power of noises can be minimized.…”

“…On the other hand, SNR o estimated for PD-350 continues increasing and eventually becomes larger than that of PD-75 at optical powers larger than -12 dBm. After applying a low-pass digital filtering [10] to minimize the noise bandwidths, SNR o for both PDs are represented by the solid lines in Fig. 3.…”

“…In this Appendix, the spectral behavior of the thermal noise is investigated, clarifying the impact of post-processing filtering on the SNR improvement [10]. Firstly, the PSDs of thermal noise for PD-75 and PD-350 are respectively measured, represented by the blue curves in Figs.…”

“…However, the signal power cannot be infinitely increased in classical BOTDA, since the pulse duration is fixed by the required spatial resolution, whilst the maximum powers of the pulse and of the CW probe are limited by the onset of nonlinear effects [6][7][8][9]. On the other hand, the minimum noise bandwidth is determined by the targeted spatial resolution and cannot be further reduced, regardless of the denoising technique used [10]. With the increasing demand for better performance of distributed Brillouin sensors, sophisticated techniques have been proposed to further improve the SNR by enhancing the equivalent signal power, such as distributed Raman/Brillouin amplification [11][12][13][14] and/or optical pulse coding [15][16][17][18][19][20].…”

Genetic-optimised aperiodic code for distributed optical fibre sensors

“…spatial resolution (SR), measurand accuracy, sensing range and measurement time) 1,[22][23][24] . For any conventional time-domain DOFS, the maximum attainable SNR turns out to be limited by fundamental physical constraints: whilst the maximum pulse peak power is limited by the onset of nonlinear effects [25][26][27][28][29] , the minimum noise power is determined by the signal bandwidth thus being irreducible whatever the denoising technique used 30,31 .…”