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.

A new method of analytical representation and numerical simulation of multimode fiber interferometer signals is developed. A system of averaged normalized characteristics, called amplitude and spectral characteristics, is introduced for this end. Interferometer signals generated by fiber length variation or laser frequency modulation were investigated at various parameters of the fiber. Joint usage of amplitude and spectral characteristics proved to substantially broaden the dynamical range of measurements of weak and strong external disturbances of the fiber. The method may be used for analysis and design of various optical sensor schemes with multimode fiber interferometers. It is also usable for estimating modal noise characteristics in optical systems with undesirable effects of intermodal interference.

The Rayleigh backscattering produced by an incident fundamental mode in a multimode step-index optical fiber was analyzed using a recently developed diffraction technique. The complete set of backward propagating modes, both radial and azimuthal, was determined and regarded. For this type of fiber, normalized mode functions were constructed in an explicit form, thus providing a unified power scale to characterize the relationships between various excited modes. The dependencies of the mode excitation efficiencies on the technical parameters of the fiber and the frequency of the launched radiation were studied. A comparison of the mode excitation efficiencies was performed with those in the fiber with quadratic refractive index profiles.