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The use of optical clocks or oscillators in future ultraprecise navigation, gravitational sensing, coherent arrays, and relativity experiments will require time comparison and synchronization over terrestrial or satellite free-space links. Here, we demonstrate full unambiguous synchronization of two optical time scales across a free-space link. The time deviation between synchronized time scales is below 1 fs over durations from 0.1 to 6500 s, despite atmospheric turbulence and kilometer-scale path length variations. Over 2 days, the time wander is 40 fs peak to peak. Our approach relies on the two-way reciprocity of a single-spatial-mode optical link, valid to below 225 attoseconds across a turbulent 4-km path. This femtosecond level of time-frequency transfer should enable optical networks using state-of-the-art optical clocks or oscillators.

Spectrally resolved photoacoustic imaging is promising for label-free imaging in optically scattering materials. However, this technique often requires acquisition of a separate image at each wavelength of interest. This reduces imaging speeds and causes errors if the sample changes in time between images acquired at different wavelengths. We demonstrate a solution to this problem by using dual-comb spectroscopy for photoacoustic measurements. This approach enables a photoacoustic measurement at thousands of wavelengths simultaneously. In this technique, two optical-frequency combs are interfered on a sample and the resulting pressure wave is measured with an ultrasound transducer. This acoustic signal is processed in the frequency-domain to obtain an optical absorption spectrum. For a proof-of-concept demonstration, we measure photoacoustic signals from polymer films. The absorption spectra obtained from these measurements agree with those measured using a spectrophotometer. Improving the signal-to-noise ratio of the dual-comb photoacoustic spectrometer could enable high-speed spectrally resolved photoacoustic imaging. Spectrally resolved photoacoustic images often require the acquisition of data for each wavelength separately. Here, the authors use dual frequency-comb spectroscopy for photoacoustic measurements, enabling spectrally resolved measurements without the need to scan the illumination wavelength.

Optical frequency combs have revolutionized optical frequency metrology and are being actively investigated in a number of applications outside of pure optical frequency metrology. For reasons of cost, robustness, performance, and flexibility, the erbium fiber laser frequency comb has emerged as the most commonly used frequency comb system and many different designs of erbium fiber frequency combs have been demonstrated. We review the different approaches taken in the design of erbium fiber frequency combs, including the major building blocks of the underlying mode-locked laser, amplifier, supercontinuum generation and actuators for stabilization of the frequency comb.

Quantifying sector‐resolved methane fluxes in complex emissions environments is challenging yet necessary to improve emissions inventories and guide policy. Here, we separate energy and agriculture sector emissions using a dynamic linear model analysis of methane, ethane, and ammonia data measured at a Northern Colorado site from November 2021 to January 2022. By combining these sector‐apportioned observations with spatially resolved inventories and Bayesian inverse methods, energy and agriculture methane fluxes are optimized across the study's ∼850 km2 sensitivity area. Energy sector fluxes are synthesized with previous literature to evaluate trends in energy sector methane emissions. Optimized agriculture fluxes in the study area were 3.5× larger than inventory estimates; we demonstrate this discrepancy is consistent with differences in the modeled versus real‐world spatial distribution of agricultural sources. These results highlight how sector‐apportioned methane observations can yield multi‐sector inventory optimizations in complex environments. Plain Language Summary Improving our knowledge of the locations, magnitudes, and types of methane sources is important for implementing effective emissions mitigation technologies and regulations. Methane emissions are often challenging to quantify because a wide variety of sources can emit methane, and these disparate sources are often intermingled. We demonstrate how a dynamic linear model can use multi‐month time series of two tracer gases, ethane and ammonia, to effectively separate methane emissions from the energy and agriculture sectors. Incorporating these data into a Bayesian inverse analysis refines the magnitude and distribution of methane fluxes from each sector. Our analysis reveals that methane from agriculture is several times higher than inventory estimates. While this is in part due to the spatial distribution of sources, more monitoring is needed to improve agriculture emissions factors. Energy sector emissions factors optimized in this work are consistent with other regional studies of energy sector methane emissions. A synthesis of these works demonstrates a regional decline in energy sector emissions despite a concomitant increase in oil and gas extraction; however, current emissions are similar to 2008 estimates. Key Points A dynamic linear model apportions energy and agriculture methane emissions from multi‐month trace gas measurements in Northern Colorado An estimated 0.4 ± 0.2 kg CH4 are emitted per barrel of oil equivalent produced, yielding a Wattenberg Field emission rate of 15 Mg CH4/hr Optimized agriculture methane emissions are higher than inventory predictions, in part due to mislocated fluxes in the inventory

Mid-infrared dual-comb spectroscopy has the potential to supplant conventional Fourier-transform spectroscopy in applications requiring high resolution, accuracy, signal-to-noise ratio and speed. Until now, mid-infrared dual-comb spectroscopy has been limited to narrow optical bandwidths or low signal-to-noise ratios. Using digital signal processing and broadband frequency conversion in waveguides, we demonstrate a mid-infrared dual-comb spectrometer covering 2.6 to 5.2 µm with comb-tooth resolution, sub-MHz frequency precision and accuracy, and a spectral signal-to-noise ratio as high as 6,500. As a demonstration, we measure the highly structured, broadband cross-section of propane from 2,840 to 3,040 cm−1, the complex phase/amplitude spectra of carbonyl sulfide from 2,000 to 2,100 cm−1, and of a methane, acetylene and ethane mixture from 2,860 to 3,400 cm−1. The combination of broad bandwidth, comb-mode resolution and high brightness will enable accurate mid-infrared spectroscopy in precision laboratory experiments and non-laboratory applications including open-path atmospheric gas sensing, process monitoring and combustion.

The transfer of high-quality time–frequency signals between remote locations underpins many applications, including precision navigation and timing, clock-based geodesy, long-baseline interferometry, coherent radar arrays, tests of general relativity and fundamental constants, and future redefinition of the second 1 , 2 , 3 , 4 , 5 , 6 , 7 . However, present microwave-based time–frequency transfer 8 , 9 , 10 is inadequate for state-of-the-art optical clocks and oscillators 1 , 11 , 12 , 13 , 14 , 15 , 16 that have femtosecond-level timing jitter and accuracies below 1 × 10 −17 . Commensurate optically based transfer methods are therefore needed. Here we demonstrate optical time–frequency transfer over free space via two-way exchange between coherent frequency combs, each phase-locked to the local optical oscillator. We achieve 1 fs timing deviation, residual instability below 1 × 10 −18 at 1,000 s and systematic offsets below 4 × 10 −19 , despite frequent signal fading due to atmospheric turbulence or obstructions across the 2 km link. This free-space transfer can enable terrestrial links to support clock-based geodesy. Combined with satellite-based optical communications, it provides a path towards global-scale geodesy, high-accuracy time–frequency distribution and satellite-based relativity experiments. Using two-way exchange between coherent frequency combs, each phase-locked to the local optical oscillator, optical time–frequency transfer is demonstrated in free space across a 2-km-long link, with a timing deviation of 1 fs, a residual instability below 10 −18 at 1,000 s and systematic offsets below 4 × 10 −19 .

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.

We performed 7.5 weeks of path-integrated concentration measurements of CO2, CH4, H2O, and HDO over the city of Boulder, Colorado. An open-path dual-comb spectrometer simultaneously measured time-resolved data across a reference path, located near the mountains to the west of the city, and across an over-city path that intersected two-thirds of the city, including two major commuter arteries. By comparing the measured concentrations over the two paths when the wind is primarily out of the west, we observe daytime CO2 enhancements over the city. Given the warm weather and the measurement footprint, the dominant contribution to the CO2 enhancement is from city vehicle traffic. We use a Gaussian plume model combined with reported city traffic patterns to estimate city emissions of on-road CO2 as (6.2±2.2)×105 metric tons (t) CO2 yr−1 after correcting for non-traffic sources. Within the uncertainty, this value agrees with the city's bottom-up greenhouse gas inventory for the on-road vehicle sector of 4.5×105 t CO2 yr−1. Finally, we discuss experimental modifications that could lead to improved estimates from our path-integrated measurements.

We present the first quantitative intercomparison between two open-path dual-comb spectroscopy (DCS) instruments which were operated across adjacent 2 km open-air paths over a 2-week period. We used DCS to measure the atmospheric absorption spectrum in the near infrared from 6023 to 6376 cm−1 (1568 to 1660 nm), corresponding to a 355 cm−1 bandwidth, at 0.0067 cm−1 sample spacing. The measured absorption spectra agree with each other to within 5 × 10−4 in absorbance without any external calibration of either instrument. The absorption spectra are fit to retrieve path-integrated concentrations for carbon dioxide (CO2), methane (CH4), water (H2O), and deuterated water (HDO). The retrieved dry mole fractions agree to 0.14 % (0.57 ppm) for CO2, 0.35 % (7 ppb) for CH4, and 0.40 % (36 ppm) for H2O at  ∼  30 s integration time over the 2-week measurement campaign, which included 24 °C outdoor temperature variations and periods of strong atmospheric turbulence. This agreement is at least an order of magnitude better than conventional active-source open-path instrument intercomparisons and is particularly relevant to future regional flux measurements as it allows accurate comparisons of open-path DCS data across locations and time. We additionally compare the open-path DCS retrievals to a World Meteorological Organization (WMO)-calibrated cavity ring-down point sensor located along the path with good agreement. Short-term and long-term differences between the open-path DCS and point sensor are attributed, respectively, to spatial sampling discrepancies and to inaccuracies in the current spectral database used to fit the DCS data. Finally, the 2-week measurement campaign yields diurnal cycles of CO2 and CH4 that are consistent with the presence of local sources of CO2 and absence of local sources of CH4.

Determination of trace gas emissions from sources is critical for understanding and regulating air quality and climate change. Here, we demonstrate a method for rapid quantification of the emission rate of multiple gases from simple and complex sources using a mass balance approach with a spatially scannable open-path sensor – in this case, an open-path dual-comb spectrometer. The open-path spectrometer measures the total column density of gases between the spectrometer and a retroreflector mounted on an uncrewed aerial vehicle (UAV). By measuring slant columns at multiple UAV altitudes downwind of a source (or sink), the total emission rate can be rapidly determined without the need for an atmospheric dispersion model. Here, we demonstrate this technique using controlled releases of CH4 and C2H2. We show an emission rate determination to within 56 % of the known flux with a single 10 min flight and within 15 % of the known flux after 12 flights. Furthermore, we estimate the detection limit for CH4 emissions to be 0.03 g CH4 s−1. This detection limit is approximately the same as the emissions from 25 head of beef cattle and is less than the average emissions from a small oil field pneumatic controller. Other gases including CO2, NH3, HDO, ethane, formaldehyde (HCHO), CO, and N2O can be measured by simply changing the dual-comb spectrometer.