Broadband Phase Spectroscopy over Turbulent Air Paths

Broadband atmospheric phase spectra are acquired with a phase-sensitive dual-frequency-comb spectrometer by implementing adaptive compensation for the strong decoherence from atmospheric turbulence. The compensation is possible due to the pistonlike behavior of turbulence across a single spatial-mode path combined with the intrinsic frequency stability and high sampling speed associated with dual-comb spectroscopy. The atmospheric phase spectrum is measured across 2 km of air at each of the 70 000 comb teeth spanning $233{\mathrm{cm}}^{-1}$ across hundreds of near-infrared rovibrational resonances of ${\mathrm{CO}}_2$, ${\mathrm{CH}}_4$, and ${\mathrm{H}}_2\mathrm{O}$ with submilliradian uncertainty, corresponding to a ${10}^{-13}$ refractive index sensitivity. Trace gas concentrations extracted directly from the phase spectrum reach 0.7 ppm uncertainty, demonstrated here for ${\mathrm{CO}}_2$. While conventional broadband spectroscopy only measures intensity absorption, this approach enables measurement of the full complex susceptibility even in practical open path sensing.

Figure 1

Phase-sensitive, turbulence-compensated dual-comb spectrometer. The signal comb is transmitted across the 2 km turbulent path, recollected in a single-mode fiber, and heterodyned against the LO comb. The instantaneous turbulence phase noise is extracted from the data and used to self-compensate the measured complex spectrum, which is then normalized by the reference complex spectrum to retrieve the atmospheric molecular phase (and absorbance) spectrum. Gray, fiber; red, air path.

Figure 2

(a) Phase spectrum averaged for 5 min without compensation (gray) and with turbulence compensation (black), where the molecular phase signatures are evident (see inset). (b) Power spectral density of the timing correction $t_C$ (green) and a power-law scaling of $\sim f^{-2.4}$ (red).

Figure 3

(a) Phase $\beta (\nu )L$ (green, left axis) and absorbance $\alpha (\nu )L$ (gray, right axis) over an expanded $83{\mathrm{cm}}^{-1}$ window centered on the ${\mathrm{CO}}_2$ band. Spectral data points are acquired at individual comb teeth spaced at $0.003{\mathrm{cm}}^{-1}$. (b) Fit residuals for phase (5 mrad standard deviation) and absorbance. (c) Same spectra after a more aggressive piecewise baseline fit. (d) Corresponding fit residuals (offset) for phase (0.6 mrad standard deviation) and absorbance ($1.3\times {10}^{-3}$ standard deviation). (e) Similar data to (c) but for a spectral window centered to include ${\mathrm{CH}}_4$ and water resonances. (f) Corresponding fit residuals (offset).

Figure 4

Expanded view of the phase spectrum (green) and fit (dashed red) along with the individual contributions from ${\mathrm{CO}}_2$ (black) and water (blue).

Figure 5

Extracted ${\mathrm{CO}}_2$ concentration from the phase (green) and amplitude (gray) spectra as well as from a nearby calibrated point sensor (orange).