Signal statistics of phase dependent optical time domain reflectometry

The statistics of the phase dependent optical time-domain reflectometer have been analyzed. The optical fiber is modeled by the use of a discrete set of reflectors positioned randomly along the fiber. The statistics of the reflected light from a traveling pulse are derived. The statistics of the signal are used to calculate the characteristics of shot noise in the photodetector, and the probability that noise of certain intensity will occur. An estimation of the backscattered power is made by calculating the fraction of the backscattered power that is captured in a guiding mode. Upper power limits are calculated by considering nonlinear optical effects. An estimation of noise from thermally excited sound waves, amplified by Brillouin scattering, is derived. This noise considers the parameters of a photodetector, giving a model for the noise in the measurable photocurrent. Two models are used to describe the fading probability of the signal. The first model, based on the Fabry-Perot interferometer with a random phase perturbation in the middle, is used to calculate the probability that the whole signal vanishes for any value of phase perturbation. The second model, by calculating the correlation between two signals, one perturbed and one unperturbed, predicts the fading of the signal of interest. The present work gives the theoretical basis for the phase dependant Optical Time Domain Reflectometry, allowing its optimization and setting the fundamental limitations to the performance of the system