Based on Rayleigh backscattering in optical fibers, distributed acoustic sensing (DAS) can detect and locate vibration information at any position along a long-distance optical fiber. However, due to the complexity of the environment and events in practical applications, more information is required for accurately diagnosing events. Meanwhile, Rayleigh backscattering can provide rich information like strain and temperature about the testing object and its surrounding environment. However, the existing DAS systems have difficulty in measuring temperature and strain because of their limited measurement range. Thus, we propose a spectrum extension algorithm based on the Rayleigh spectrum method. During the measurement, the algorithm dynamically extends the frequency range of the spectrum as the strain or temperature changes, solving the limited measurement range of the Rayleigh spectrum method. In the experiment, the measurement range of the system is increased by 65 times compared to the non-extension algorithm, with stable demodulation achieved.

The experimental system is based on the time-gated digital optical frequency domain reflectometry (Fig. 1). The collected Rayleigh backscattering signals are subjected to segmented matched filtering to obtain the Rayleigh scattering intensity spectra at each position on the optical fiber. The Rayleigh spectrum method is employed to calculate the spectral shift between the measured spectrum and the reference spectrum via cross-correlation under the strain occurrence (Fig. 2), and then the corresponding strain or temperature variation is obtained. Generally, the measurement range is limited by the frequency range of the chirped probe pulse, and to overcome this limitation, we put forward a spectrum extension algorithm (Fig. 3). Considering that non-uniform strain will result in spectral distortion, the algorithm dynamically splices and extends the spectrum via adopting the weight average of the existing spectrum and the new spectrum by the raised cosine window based on the spectral shift. This method both increases the frequency range of the spectrum and ensures the high correlation between the extended spectrum and the measured spectrum, thus extending the system measurement range. In the experiments, the positive and negative sidebands are employed for probing by an intensity modulator. The two sidebands are demodulated separately and then averaged to obtain the final spectrum. The superposition of positive frequency cross-correlation and negative frequency cross-correlation is utilized to suppress cross-correlation noise and optimize the cross-correlation calculation performance (Fig. 4), thereby improving the demodulation stability of the system.

The capability of the algorithm to demodulate large-amplitude strain signals and the measurement range improvement are verified under a chirped pulse frequency range of 1 GHz, corresponding to an actual demodulation range of ±3 με. By adopting the spectrum extension algorithm to measure the strain changes applied by piezoelectric ceramics (PZT) (Fig. 5), successful static strain measurement is achieved after extending the reference spectrum by 1.8 GHz. Compared to the cumulative method, it has the ability for discontinuous signal measurement with a measurement range of up to 12 με. The strain resolution is 10.7 nε with sound linearity. By applying a larger strain signal through an electric translation stage, the spectrum is extended by 30 GHz, and a strain up to 198 με is demodulated steadily (Fig. 6).

We propose a spectrum extension algorithm based on the Rayleigh spectrum method, which can improve the measurement range of the time gated digital-optical frequency domain reflectometer (TGD-OFDR)-based DAS system. This algorithm detects the frequency shift of the measured spectrum and dynamically extends the reference spectrum. The influence of spectrum deformation on the spectrum extension is well suppressed to break through the limitation of the probe pulse sweep range in the TGD-OFDR system. In the demonstrational experiment, the measurement range is increased by 65 times compared to the non-extension algorithm, which realizes a strain measurement range of 198 με and a strain measurement resolution of 10.7 nε. By employing the extended reference spectrum, the limitations between the two measurements in this method are eliminated, thereby enabling the system to perform discontinuous measurements.