An Exact Probability Density Function for Intensity-Based Output Noise Propagating Through a Fiber Optic Sensor Demodulation Process

Fiber optic interferometry is a common architecture in many optical sensing strategies and typically requires a demodulation scheme for phase (signal) extraction. For sensing applications, signal-to-noise and other statistical metrics are of great importance in characterizing system performance. In the context of a specific demodulation algorithm employing three-channel inputs, we analytically compute a probability density function of the demodulator output noise, given an arbitrary distribution of input intensity noise and arbitrary noise correlation among the three channels. We compare the analytical formulations with previously validated simulation data from a fiber Bragg grating sensor system, and we find excellent agreement within the specific example of Gaussian input noise.