Noise analyses of Vernier-effect-based fiber sensing systems

Vernier-effect-based fiber sensing systems measure physical parameters by tracking the envelope shift in spectral interferograms. However, there is a lack of general understanding of measurement errors caused by various noises, especially the amplitude noise. This paper proposes a model for amplitude noise distribution in Vernier-effect-based spectral interferograms, based on which numerical studies were conducted on the statistical characteristics of errors in identifying extrema of spectral envelopes. Two typical methods were used to identify the extremum of envelope, one of which is to directly locate the extremum in the spectral fringe, while the other determines the extremum by the fitting method that generates an envelope. Numerical results indicate that, for the first method, the standard variance of extremum deviation determined by the fringe linewidth only holds within a limited bandwidth range of the envelope. This range increases with signal to noise (SNR) and the free spectral range (FSR) of the fringe. Significantly, for the second method, the standard variance maintains a small value and almost independent of the envelope bandwidth over the entire bandwidth range. The obtained results provide a theoretically reliable basis for widespread applications of Vernier-effect-based sensors.