Output noise analysis of optical fiber interferometric sensors using a 3 × 3 coupler

The output noise in a digital passive demodulation scheme for optical fiber interferometric sensors using a 3 × 3 coupler is investigated both theoretically and experimentally. In such a scheme, the measured signal is recovered by the linear combination of the three outputs and a digital arctangent approach. The impact of the additive noise (AN), multiplicative noise (MN) and square-root noise (SN) on the output noise is analyzed. Equations to calculate the output noise variance from the inputs AN, MN and SN are derived for both symmetric and asymmetric 3 × 3 couplers. According to our study, the initial phase and the correlation of different input noise also have great impact on the output noise level. Simulations show that the theoretical analysis is of high accuracy. The noise transfer function (NTF) defined as the ratio of output noise and mean input noise variances is proposed to describe the noise performance of a digital passive demodulation scheme using a 3 × 3 coupler. In our experiment, the distribution of the output noise variance as a function of the initial phase is observed. A method was proposed to predict the distribution of the output noise variance by estimating the variances and the correlation coefficients of the input noises using the non-negative least-squares method and polynomial fitting. The distribution of the output noise variance estimated by this method agrees well with the experimental results