Abstract
Rayleigh scattering in an optical fiber has the property that its spectrum shifts in proportion to strain and/or temperature changes, which makes distributed sensing of strain/temperature possible. To estimate the spectral shift, cross-correlation between spectra before and after the shift can be used. However, when the shift is large, the overlap portion of the spectra becomes small and false detection of a correlation peak readily arises. In this paper, we analytically obtain the probability of false alarm for cross-correlation coefficients and determine the threshold that gives a specified constant false alarm rate (CFAR). It is shown that stable estimates of spectral shifts are obtained by using the CFAR threshold.
