Genetic-optimised aperiodic code for distributed optical fibre sensors

Abstract

Distributed optical fibre sensors deliver a map of a physical quantity along an optical fibre, providing a unique solution for health monitoring of targeted structures. Considerable developments over recent years have pushed conventional distributed sensors towards their ultimate performance, while any significant improvement demands a substantial hardware overhead. Here, a technique is proposed, encoding the interrogating light signal by a single-sequence aperiodic code and spatially resolving the fibre information through a fast post-processing. The code sequence is once forever computed by a specifically developed genetic algorithm, enabling a performance enhancement using an unmodified conventional configuration for the sensor. The proposed approach is experimentally demonstrated in Brillouin and Raman based sensors, both outperforming the state-of-the-art. This methodological breakthrough can be readily implemented in existing instruments by only modifying the software, offering a simple and cost-effective upgrade towards higher performance for distributed fibre sensing.

Fig. 1. Principle of the proposed coding and decoding process.

The upper row shows the procedure to generate an N_c-point discrete-time signal c(n) representing the digitally coded pulse sequence from a N_u-point unipolar sequence u(n). This procedure involves three steps: (1) generate an N_p-point single-pulse signal p(n) depending on the target spatial resolution Δz, as N_p = 2Δzf_s/v_g where v_g is the pulse group velocity in the fibre and f_s is the sampling rate; (2) generate an N_d-point sequence d(n) by performing an N_x-point upsampling on u(n), so that N_d = N_xN_u, where N_x = N_p for NRZ format and N_x > N_p for RZ format. Note that an RZ format must be used in given DOFS with a sufficiently long bit duration (=N_x/f_s) to get rid of undesired crosstalk effects that can be imposed by the acoustic inertial response in Brillouin sensing or by the amplified spontaneous forward Raman scattering in ROTDR; and (3) linearly convolve d(n) with p(n), i.e. c(n) = d(n)⊗p(n), where the sign ⊗ denotes linear convolution so that the number of points in the code sequence c(n) is N_c = N_d + N_p − 1. The king the energy of each pumiddle row shows the actual optical sequence launched into the sensing fibre, denoted as c_f(n), which exhibits an uneven amplitude envelop imposed by a function f(n) determined by the EDFA gain saturating response. By taking the energy of each pulse in c_f(n), an N_d-point sequence d_f(n) that is equal to f(n)d(n) can be retrieved and is used for decoding. The bottom row shows the simulated coded fibre response $r_c^m\left(n\right)$ and the decoded single-pulse response $r_s^d\left(n\right)$.

Fig. 2. Theoretical results of the coding gains in logarithmic scale.

a Theoretical maximum and b genetic-optimised G_c/G_r as a function of m. c Coding gains of the genetic-optimised code and Simplex code (left-hand side vertical axis) and their difference (right-hand side vertical axis) as a function of the energy enhancement factor F_E for m = 3.

Fig. 3. Experimental results of GO-coded and single-pulse BOTDA.

a A 136-bit normalised coding sequence c_f(n) measured at the fibre input (blue) and the retrieved d_f(n) (red). Inset: Zoom-in of normalised c_f(n) and d_f(n) over a time span from 12 to 12.2 μs. b Temporal BOTDA gain traces at fibre Brillouin resonance. c SNR profiles over the entire sensing fibre. d Measured BFS profiles around a 5-m-long hotspot located near the fibre far-end. e, f BFS uncertainty profiles along with the sensing fibre for 2 and 1 m SRs, respectively.

Fig. 4. Experimental results of GO-coded and single-pulse ROTDR.

a A 177-bit normalised coding sequence c_f(n) measured at the fibre input (blue) and the retrieved d_f(n) (red). Inset: Zoom-in of normalised c_f(n) and d_f(n) over a time span from 12 to 12.2 μs. b Retrieved temperature profiles over the entire sensing fibre, for single-pulse (blue) and GO-coded (red) schemes. c SNR profiles over the entire sensing fibre, for single-pulse (blue) and GO-coded (red) schemes. d Retrieved temperature profiles around a 5-m-long hotspot located near the fibre far-end. e, f Temperature uncertainty profiles along with the sensing fibre for 2 and 1 m SRs.

Fig. 5. Experimental results of on-line real-time measurement for the temperature of water under heating.

a 2D map of the retrieved temperature as a function of time and fibre position. For the sake of clarity, the figure only shows fibre positions from 10.12–10.2 km. b Evolution of the retrieved temperature at the hotspot. c Error on the retrieved temperature at the hotspot as a function of time, obtained by subtracting the temperature measured by a thermometer to that from a single-pulse scheme (blue) and GO-coded scheme (red), respectively.

Fig. 6. Experimental setup for both GO-code and single-pulse BOTDA.

RF radio frequency, EOM electro-optic modulator, Is. isolator, Cir. circulator, TA tuneable attenuator, PSc polarisation scrambler, SOA semiconductor optical amplifier, FBG fibre Bragg grating, PD photodetector, Acq. acquisition.

Fig. 7. Experimental setup for GO-code and single-pulse ROTDR.

SOA semiconductor optical amplifier, WDM wavelength division multiplexer, APD avalanche photodiode, TIA transimpedance amplifier, Acq. acquisition.