Noise Sensitivity of Differential Interferometry

In differential interferometry, two interferometers are used to characterize signals that have a fluctuating common phase, but a constant differential phase that is of interest. To extract the differential phase, the data points can be plotted against each other to form an ellipse. The eccentricity of the ellipse then determines the differential phase. However, noise in the data will lead to uncertainty in the differential phase, and different ellipse-fitting techniques will have different sensitivities to such noise. We have investigated algebraic, geometric, and Bayesian fits to compare the average errors in the differential phase estimate when different types of noise are present. We find that algebraic fits are generally the most sensitive to noise, while the efficacy of the geometric and Bayesian fits depends on the type of noise present. Additionally, we have studied how the standard deviation of phase error (𝜎_φ) depends on the number of data points used (𝑁), and finding that generally that 𝜎_φ = 𝐶𝑁^-0.5 , where 𝐶 depends on the fitting method and type of noise. Finally, we describe a variant of the geometric fit, called the reciprocal fit, which performs better than the conventional geometric fit.