Fidelity of the dual-pulse phase-OTDR response to spatially distributed external perturbation

Abstract

In the present paper, we perform, for the first time, analysis of the dual-pulse phase-optical time-domain reflectometer (OTDR) response fidelity to spatially distributed external perturbation. The fidelity includes the concepts of response linearity with respect to the external action and the variance of this response as it contains random contributions. Generally, the response of a dual-pulse phase-OTDR configuration to external phase perturbation, provided the demodulation of the backscattered signal has been performed, consists of linear and nonlinear contributions. The linear part of the response is produced due to the difference in the optical paths of the fields backscattered by different scattering fiber segments and is usually considered as a useful signal. The nonlinear part of the response is produced by the scattering fiber segments themselves and is usually considered as random distortions that degrade the phase-OTDR response fidelity. However, in cases when the shape of the external perturbation is known, e.g. the external perturbation is a travelling acoustic wave or uniform stretching of a sensitive fiber, the average characteristics of the random nonlinear part of the phase-OTDR response can be calculated and additional information about the external perturbation can be extracted. In this paper we theoretically calculated the total response of the dual-pulse phase-OTDR to external perturbation in the form of a longitudinal acoustic wave with small amplitude depending on the ratio of the acoustic wavelength and the length of the scattering fiber segment. Due to the influence of the scattering segments, this response always contains random components. Using the theory of speckles, we analyzed the probability density function (PDF) of this random response and its variance. We also performed theoretical and experimental consideration of the important special case of uniform strain distribution along the sensitive fiber occupied by the dual-pulse. It is shown that in this case the contributions of the scattering fiber segments to the phase-OTDR response are linear on average, and therefore the total phase-OTDR response is linear on average; the experimental results are in good agreement with theoretical predictions.