Statistics of coherently detected backscatter and range performance of coherent OTDRs

Abstract

We derive the statistics of a coherently detected backscatter waveform taking into account the effects of polarization. For the first time these statistics are related to measurable parameters. We show that for long-range OTDRs the effects of polarization are statistically small.

In relation to the demodulation process we used our statistical model to show that for long-range operation and with heterodyne detection all types of demodulation provide similar performance. With homodyne detection half-wave demodulation results in a 7 dB lower signal-to-noise ratio than the other types of demodulation which have similar performance. There is the usual 3 dB advantage of homodyne over heterodyne detection. Our results indicate that with the same launched powers, the signal obtained from a coherent OTDR can have up to a 37 dB better signal-to-noise ratio than one obtained from an incoherent pulse OTDR. This results in a 9 dB range advantage.

We verify previously tabulated results which we found apply only for short-range operation. We use our model to predict the limits of long-range performance and to predict the effect of speckle on averaging. Finally, we explain the breakpoint behaviour that can be seen in results already reported and which is characteristic of linear full- or half-wave envelope demodulation.