Free-form dual-comb spectroscopy for compressive sensing and imaging

Time-programmable frequency combs enable new measurement paradigms for dual-comb spectroscopy (DCS) that are free of many of the constraints found in traditional DCS. As opposed to fixing the repetition rate offset between combs, free-form DCS uses full control of the temporal offset between the dual-comb pulse trains, thereby enabling user-selectable sampling patterns that optimize resolution, signal-to-noise ratio, species selectivity or acquisition time. Here we show that free-form DCS enables compressive sensing and demonstrate compression factors of up to 155, with an up to 60-fold reduction in acquisition time, while maintaining identical spectral point spacing and comparable signal-to-noise ratio to traditional DCS. We also demonstrate molecular recurrence sampling (an extreme case of compressive sensing) for methane detection at 22× higher sensitivity than traditional DCS at the cost of requiring a priori knowledge of the probed species. Finally, free-form DCS can enable fast species-selective imaging since its radio frequency signal is narrow band, in contrast to traditional DCS, and therefore compatible with limited camera read out rates. We demonstrate imaging of methane plumes across a 128 × 64-pixel focal plane array at a 250 Hz rate. In the future, this flexible free-form approach can enable applications ranging from rapid open-path spectroscopy to nonlinear multidimensional comb-based spectroscopy. By incorporating time-programmable frequency combs, free-form dual-comb spectroscopy enables compressive sensing at factors of up to 155, with a corresponding reduction in acquisition time without sacrificing spectral resolution.