Self-Correction Limits in Dual-Comb Interferometry

Self-sufficient correction algorithms have recently been developed to estimate and compensate the relative frequency noise between two free-running frequency combs using only their dual-comb interferograms (IGMs). However, such algorithms are limited by the relatively low observation rate of the frequency noise, equal to the IGM repetition rate. In this paper, we analyze the effectiveness of estimation methods based on the cross-correlation function and the ambiguity function. We derive estimators and obtain their theoretical variances as a function of the IGMs' measurable parameters to later establish criteria that verify the success rate of each method for the correction and coherent averaging of successive IGMs. Finally, we present different cases of both real and simulated dual-comb systems and assess their compatibility with these estimation methods.