The paper develops a statistical model for the signals received in phase-sensitive optical time domain reflectometry (OTDR) probed by highly coherent sources. The backscattering process is modelled by a set of discrete scatterers with properly chosen parameters. Explicit equations for calculating the amplitude and the phase of the backscattered signal are obtained. The developed model predicts spectral and autocorrelation characteristics of the amplitude signals that are validated by experimental results. Characteristics of the phase signals, practicable for studying the sensing applications of the OTDR system, are presented and studied as well, demonstrating good correspondence with experiment. A more detailed modelling of distributed vibration sensing systems and their response to disturbances along an optical fiber will be possible as an extension of the developed formalism. Index Terms-Optical fiber devices, optical fiber sensors, Rayleigh scattering, reflectometry, time domain analysis. 0733-8724

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The factors limiting the resolution of displacement sensors based on the extrinsic Fabry-Perot interferometer were studied. An analytical model giving the dependency of extrinsic Fabry-Perot interferometric (EFPI) resolution on the parameters of an optical setup and a sensor interrogator was developed. The proposed model enables one to either estimate the limit of possible resolution achievable with a given setup, or derive the requirements for optical elements and/or a sensor interrogator necessary for attaining the desired sensor resolution. An experiment supporting the analytical derivations was performed, demonstrating a large dynamic measurement range (with cavity length from tens of microns to 5 mm), a high baseline resolution (from 14 pm), and good agreement with the model.

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Unlike conventional sensors that measure the passage of seismic waves at a single position, distributed vibration sensing systems, also known as distributed acoustic sensing systems, detect the passage of seismic waves by averaging a measurement of strain over a section of fibre‐optic cable. Distributed vibration sensing systems work by transmitting pulses of light down the fibre and measuring the phase of the Rayleigh backscatter. At random positions along the fibre, however, fading occurs; this is where the amplitude of the backscattered signal is very small due to cancellation of the scattered electric fields, resulting in anomalously noisy traces in a common source gather.This paper addresses the problem of fading in a particular form of distributed vibration sensors: a new optical arrangement of the instrumentation is described that allows the measurement to be carried out quasi‐simultaneously at multiple optical interrogation frequencies. The interrogation frequencies are chosen to be sufficiently different that their fading properties are distinct and the diversity thus obtained is used to aggregate the data obtained to substantially reduce the noise caused by fading. As well as reducing the effects of fading, the aggregation of the independent results can also help to reduce the overall noise of the measurement and improve the linearity of the distributed vibration sensing system.

In the current paper, distortions in digital demodulation schemes with harmonic phase modulation for interferometric optical sensors are considered. In particular, the influence of target signal variations on phase demodulation errors is theoretically evaluated. An analytical expression describing the phase error magnitude dependence on the first derivative and mean value of the measured signal and amplitude of the phase modulation in the case of a simple 4-point demodulation algorithm is derived. After that, an approach for synthesizing algorithms with suppressed sensitivity to target signal variations is developed. Based on this approach, a novel 4+1 demodulation algorithm is proposed. It is shown analytically that the demodulation error of the new 4+1 algorithm is proportional to the second derivative of the target signal, and therefore, is typically several orders of magnitude smaller than in the case of the 4-point algorithm. The correspondence between analytical expressions and real phase errors induced by target signal variations is verified by means of numeric simulation.

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