Improvement in signal-to-noise ratio of Rayleigh backscattering measurement using optical low coherence reflectometry

I have calculated the signal-to-noise ratio (S/N) of fluctuations remaining in Rayleigh backscattered signal distributions obtained after performing moving and frequency averaging with an optical low coherence reflectometer (OLCR). From the calculation, I obtained the number of measurements needed for each averaging that achieves the required S/N with the minimum sampling data. Specifically, I derived the numbers of measurements numerically for Gaussian and Lorentzian light spectra, respectively. The result was successfully applied to diagnosis on long silica-based waveguides by using an OLCR with a high-power narrow-band light source