Statistical analysis of temperature measurement errors in a Brillouin scattering-based distributed temperature sensor

There is currently considerable interest in the development of distributed fibre sensors based on Brillouin scattering in optical fibres as this approach has been shown to offer the possibility of long range sensing of temperature (and strain) with good spatial resolution. The accuracy with which temperature (or strain) can be measured is not only related to the system signal to noise ratio but also on the frequency separation between sampling points over the Brillouin spectrum. In our experimental systems, the Brillouin frequency is measured by manually adjusting the laser frequency difference until the Brillouin interaction is optimized at the fibre segment of interest. However, in an automated system, it is likely that the Brillouin interaction would be monitored while the laser frequency difference is scanned over a number of discrete values and the Brillouin frequency determined by curve fitting to this data. In this paper we describe a statistical method for analyzing the accuracy in measuring the Brillouin frequency when such an automated routine is used. We use Gaussian statistics to simulate a noisy Brillouin spectral profile and fit a Lorentzian line shape to the noisy data. We compare error distributions in the Brillouin frequency from two fitting algorithms. The first is a numerical approach using an iterative algorithm based on the Newton-Raphson method. In the second method an analytic approach is followed that involves the transformation of the Lorentzian line-shape to a linear function; fitting then being carried out using the least squares technique. Results from both approaches are compared with a very simple analytic expression.