Fig. 1. Schematic illustration of the chaotic BGS construction. (a) Conventional chaotic BOCDA; (b) definition of pulse ER in chaos-based scheme; (c) time-gated chaotic BOCDA system; (d) definition of the chaos PBR; (e) measurement of the noise floor along the FUT; (f) pure chaotic BGS after differential denoising.

Fig. 2. Optimization of the chaotic BGS in simulation. (a) Time series under different pulse modulation methods; (b) measured BGSs with or without time gating; (c) BGSs at different positions in long-range system; (d) schematic of differential denoising method.

Fig. 3. Experimental setup of the proposed long-range chaotic BOCDA.

Fig. 4. The BGSs under different schemes at two positions along the FUT. (a) 13.80 km and (b) 27.53 km. (c) The SBR as a function of the fiber position.

Fig. 5. The BGS map along (a) the second half of the FUT or (b) the SMF2 without Lorentz fit. The BGS map along (c) the second half of the FUT or (d) the SMF2 with Lorentz fit.

Fig. 6. The BFS accuracy at the SMF2 with different data processing methods. Standard deviation (a1) of single measurement or (a2) of the 30 independent repeated measurements before Lorentz fit; standard deviation (b1) of single measurement or (b2) of the 30 independent repeated measurements after Lorentz fit.

Fig. 7. (a) The BFS distribution near 10 cm strain section under different strains applied; (b) the BFS as a function of the applied strain.

Fig. 8. The BFS distribution at the SMF2 and the zoomed view near the strain section.