Computational multiheterodyne spectroscopy

Dual-comb spectroscopy allows for high-resolution spectra to be measured over broad bandwidths, but an essential requirement for coherent integration is the availability of a phase reference. Usually, this means that the combs' phase and timing errors must be measured and either minimized by stabilization or removed by correction, limiting the technique's applicability. We demonstrate that it is possible to extract the phase and timing signals of a multi-heterodyne spectrum completely computationally, without any extra measurements or optical elements. These techniques are viable even when the relative linewidth exceeds the repetition rate difference and can tremendously simplify any dual-comb system. By reconceptualizing frequency combs in terms of the temporal structure of their phase noise, not their frequency stability, we can greatly expand the scope of multiheterodyne techniques.