Laser absorption spectroscopy as a powerful tool for detecting trace gases has been widely used in the monitoring of atmospheric greenhouse gases, pollutions, and respiration processes, including human breath analysis. The detection is based on the light absorption when it propagates through a medium. Most inorganic and organic molecules have characteristic absorption lines in the mid-infrared (mid-IR), which correspond to fundamental vibrational modes and in the near-IR (first overtones) presenting their absorption fingerprints. Here, we summarize the recent developments of the three techniques, namely, wavelength modulation spectroscopy (WMS), cavity ringdown spectroscopy (CRDS), and frequency comb spectroscopy (FCS), and describe their main features as well as possible applications, illustrated by recent experimental results. Emphasis is made on methane detection as applied to breath analysis and atmospheric monitoring. For the WMS technique, we consider local measurements with a multipass cell and also kilometer long open-path configurations for the near-IR and mid-IR spectral regions. The results of measurements of methane in exhaled breath with the CRDS technique in the near-IR are presented for a group of subjects of different ages. We consider various schemes of the FCS that enable fast broadband detection, including direct spectroscopy, dual FCS, and Vernier FCS, and review numerous applications of this approach that revolutionized the field of absorption spectroscopy. The current trends and possible future developments and applications are also discussed.

Laser absorption spectroscopy (LAS) as a powerful tool to detect trace gases was widely used in atmospheric environment monitoring and studies of air-related phenomena, such as anthropogenic processes and the greenhouse effect, atmospheric chemical reactions, respiration of flora and fauna, and combustion processes. The basic principle of LAS relies on the Beer–Lambert law. When the light propagates through a medium, it is absorbed due to transitions from lower to higher energy levels of the atomic or molecular system. Most inorganic (oxygen, nitric oxide, hydrogen sulfide, etc.) and organic molecules (methane, acetylene, etc.) have characteristic absorption lines in the mid-infrared (mid-IR) spectral region, corresponding to fundamental vibrational modes of molecules and in the near-IR region, where molecular first overtones are located, although with much smaller optical absorption cross sections. From these characteristic absorption molecular lines, presenting spectral fingerprints, the molecules can be uniquely identified. The laser spectroscopy detection of gases also provides a fast and real-time means for online monitoring. In atmospheric monitoring, researchers use laser spectroscopy to detect trace gases to understand the status, origin, and evolution of atmospheric pollution. As such, the concentrations of ammonia1 and carbon monoxide2 were measured. In breath analysis, some volatile organic compounds (VOCs) have been established as biomarkers. Measuring their concentrations in exhaled breath aids in disease diagnosis.3 For example, a laser spectroscopic system can be used for the detection of acetone in breath, which correlates with an abnormal metabolic status, indicative of diabetes.4 Compared to other methods, such as gas chromatography with mass spectroscopy, the LAS approach can substantially reduce the analysis time, employs less expensive and bulky equipment, and simplifies or does not require any sample preparation at all. Another technique, labeled electronic nose, is so far in its infancy and needs further development before it can compete in terms of sensitivity and specificity, especially when several compounds should be detected. In this paper, we will describe several LAS techniques, including wavelength modulation spectroscopy (WMS),5,6 cavity ringdown spectroscopy (CRDS), and frequency comb spectroscopy (FCS). The progress in the LAS field critically depends on the development of new laser sources and detectors, which are employed in all these methods. Recent advances in the generation and detection of infrared radiation7 have a considerable impact on the development of sensitive detection methods of gases. Many exciting new opportunities came about with the development of frequency comb laser sources,8 enabling fast capturing of broadband spectra without the need for scanning the optical wavelength. Of course, this paper provides only a partial overview of the field. In recent years, a variety of sensitive spectroscopic techniques were developed, in particular, the progress in photoacoustic spectroscopy (PAS),9,10 quartz-enhanced PAS,11,12 and integrated cavity output spectroscopy (ICOS)13 was described in recent reviews. Applications to combustion diagnostics14 and standoff chemical detection15 were also reviewed.

The WMS with the typical detection limit from ppm to ppb level is relatively easier to implement compared to the CRDS and the FCS techniques. For cavity ringdown spectroscopy, the complexity and cost of a typical system is higher, while the detection limit can be improved from ppb to ppt level. Although the FCS detection limit is roughly similar to the WMS, it has several advantages, including possibilities of fast and multispecies detection. In addition, combining the FCS with a multipass or resonant cavity provides both the possibility of a local measurement and a long interaction path allowing us to achieve high sensitivity in the ppb range.

In this paper, we summarize the recent developments of the three mentioned techniques and describe their features, as well as possible applications, illustrated by recent experimental results obtained in the group of Schuessler and Kolomenskii at Texas A&M University in collaboration with the groups of Zhang and He (Shandong University) and Zhu (Sun Yat-sen University).

The WMS as a highly sensitive and relatively simple technique was widely used in atmospheric monitoring, breath analysis, and for locking the laser frequency to a specific molecular transition frequency. Its basic principle is as follows. The laser radiation from a diode laser is pumped by the injection current modulated simultaneously with a low frequency oscillation of triangular shape and high amplitude (for scanning of the optical wavelength) and a high-frequency sine-wave oscillation (for high-frequency modulation of the optical wavelength). This radiation is transmitted through an absorbing medium, gas or liquid, and the detected signal is then processed by a lock-in amplifier, so that the demodulated harmonic signal reflects the unknown concentration. We assume that the incident laser intensity and frequency are modulated as described by the following equations:
(1)
(2)
Here, I ¯ is the average laser intensity, Δ I is the modulation amplitude, ω = 2 π f, where f is the modulation frequency, v ¯ is the running average of the scanning laser frequency, Δ v is the frequency modulation amplitude, and ψ is the phase shift between the frequency and intensity modulation. The harmonics retrieved with a lock-in amplifier can be expressed through the components H k ( k = 1 , 2 , 3 , ) of the Fourier series expansion,6 
(3)
where θ = ω, S and φ are the spectral line strength, mainly dependent on the gas temperature T, and the line shape function, respectively, P is the pressure of the gas mixture, χ is the mole fraction of the absorbing species, and L is the effective optical path length.

A WMS setup is generally composed of the following main parts (Fig. 1): a modulated laser source, a multipass absorption cell (or an optical system for sending and receiving the laser beam over a long open-path), a detector, a lock-in amplifier, as well as a data acquisition and processing unit (including possible digital filtering as described in the following).

FIG. 1.

Schematic of a WMS sensor.

FIG. 1.

Schematic of a WMS sensor.

Close modal

Most efforts so far were directed at improving the performance of sensors by upgrading the mentioned main parts. For the laser source, as a core part of the WMS instrument, a distributed feedback (DFB) laser, an interband cascade laser (ICL), a quantum cascade laser (QCL), a vertical-cavity surface-emitting laser (VSCEL), and a difference frequency generation (DFG) source were commonly used. The employed multipass cells were mostly of Herriot16 or White17 types achieving the interaction length of tens of meters. Some novel cells, such as a mini-multi-pass cell18 and a specially designed record-breaking confocal cell19 with the effective path of hundreds of meters, also emerged in recent years. The compactness and robustness of the lock-in detection were realized with digital lock-in amplifiers implemented via digital signal processing (DSP) or using a field-programmable gate array (FPGA),20 which replaced bulky stand-alone commercial lock-in amplifiers, while still preserving competitive performance. Often, various filtering algorithms were applied in signal processing to improve the signal-to-noise ratio. Overall, being relatively simple and cost-efficient, the WMS approach shows high potential in many application fields.

Various WMS sensors were implemented for detecting H2O,21 H2S,22 NH3,23 N2O,24 and CH4.25,26 In terms of cost and performance, the sensors in the near-IR and mid-IR are quite different. Generally, the absorption cross sections of molecules in the mid-IR are larger by about two orders of magnitude compared to those in the near-IR; thus, a sensor in mid-IR potentially has a higher sensitivity. However, the components in the mid-IR, such as laser sources and detectors, are generally more expensive. Therefore, the sensor detection limit, cost, and sensor performance need to be taken into account for the sensor design. We present sensors for different trace gases in Table I, indicating laser wavelength, cell length, and the achieved detection limit. To illustrate the typical sensor design, we describe below sensors for methane and acetone, which are two important target gases in environmental monitoring and breath analysis, respectively. Xia et al.27 reported an ultra-sensitive sensor for methane, which we show schematically in Fig. 2. For this sensor, a confocal multipass cell (MPC) with an effective interaction length of 580 m was developed. The performance of the sensor was evaluated in a series of measurements with two spectroscopic methods, namely, direct absorption spectroscopy (DAS) and WMS. Different digital filtering algorithms were implemented to improve the signal-to-noise ratio in the DAS operation mode. The WMS sensor showed a better performance with the detection limit of 560 ppt achieved at 290 s integration time.

FIG. 2.

The layout of the methane sensor. ICL laser with a wavelength of 3.2 um was coupled to a multipass cell (MPC); after 579 reflections, the laser beam exited the MPC and was focused on a Vigo MCT detector. The whole sensor was controlled by a LabVIEW program, which performed laser modulation, signal demodulation, signal analysis, and displaying.

FIG. 2.

The layout of the methane sensor. ICL laser with a wavelength of 3.2 um was coupled to a multipass cell (MPC); after 579 reflections, the laser beam exited the MPC and was focused on a Vigo MCT detector. The whole sensor was controlled by a LabVIEW program, which performed laser modulation, signal demodulation, signal analysis, and displaying.

Close modal
TABLE I.

Spectroscopic (WMS) sensors used for detection of various trace gases.

GasesLaser wavelengthOptical pathDetection limitReference
Methane 7503 nm 76 m 40 ppb 42  
1653 nm 10 cm 5.8 ppm 43  
1653 nm 290 m 1.2 ppb 25  
1653 nm 100 cm 0.1 ppm 44  
1654 nm 145 cm 130 ppb 45  
1653 nm 20 m 90 ppb 46  
3.3 μ58 m 1.4 ppb 47  
3.3 μ1.3 m 0.505 ppm 48  
1653 nm 26.4 m 79 ppb 49  
Carbon monoxide 2.3 μ10 cm 2 ppm 50  
2.3 μ14.5 m 6 ppb 51  
2.3 μ2 m 1.29 ppm 52  
4.69 μ399 cm 9 ppb 53  
1578 nm 55.1 m 0.29 ppm 54  
4.6 μ76 m 0.5 ppb 55  
Ammonia 1512 nm 100 cm 26 ppbv 56  
9.56 5 m 63.2 ppb 57  
10.39 μ179 cm 2.8 ppm 58  
1531 nm 30 m 53 ppb 59  
Acetylene 1530 nm 40 cm 0.12 ppm 60  
1.53 um 21.9 m 76.75 ppb 61  
1530 nm 10 m 14.3 ppb 62  
1530 nm 52.2 m 0.2 ppm 44  
1553 nm 30 cm 0.54 ppm 63  
Carbon dioxide 2004 nm 27.5 m 68 ppm 64  
2004 nm 12 m 10 ppm 65  
4.319 μ1 cm ∼0.3% 66  
4.319 μ29.8 m 0.72 ppb 67  
1572 nm 16 m 2.7 ppb 68  
1579 nm 20 m 769 ppm 69  
Nitrogen oxide 5.26 um 100 m 124 ppt 70  
5.3 μ3 m 0.1 ppm 71  
5.26 μ310 mm unknown 72  
Formaldehyde 3.43 μ100 m 1.6 ppb 73  
3.59 μ3.75 m 1.5 ppb 74  
3.59 μ50 m 0.58 ppb 75  
GasesLaser wavelengthOptical pathDetection limitReference
Methane 7503 nm 76 m 40 ppb 42  
1653 nm 10 cm 5.8 ppm 43  
1653 nm 290 m 1.2 ppb 25  
1653 nm 100 cm 0.1 ppm 44  
1654 nm 145 cm 130 ppb 45  
1653 nm 20 m 90 ppb 46  
3.3 μ58 m 1.4 ppb 47  
3.3 μ1.3 m 0.505 ppm 48  
1653 nm 26.4 m 79 ppb 49  
Carbon monoxide 2.3 μ10 cm 2 ppm 50  
2.3 μ14.5 m 6 ppb 51  
2.3 μ2 m 1.29 ppm 52  
4.69 μ399 cm 9 ppb 53  
1578 nm 55.1 m 0.29 ppm 54  
4.6 μ76 m 0.5 ppb 55  
Ammonia 1512 nm 100 cm 26 ppbv 56  
9.56 5 m 63.2 ppb 57  
10.39 μ179 cm 2.8 ppm 58  
1531 nm 30 m 53 ppb 59  
Acetylene 1530 nm 40 cm 0.12 ppm 60  
1.53 um 21.9 m 76.75 ppb 61  
1530 nm 10 m 14.3 ppb 62  
1530 nm 52.2 m 0.2 ppm 44  
1553 nm 30 cm 0.54 ppm 63  
Carbon dioxide 2004 nm 27.5 m 68 ppm 64  
2004 nm 12 m 10 ppm 65  
4.319 μ1 cm ∼0.3% 66  
4.319 μ29.8 m 0.72 ppb 67  
1572 nm 16 m 2.7 ppb 68  
1579 nm 20 m 769 ppm 69  
Nitrogen oxide 5.26 um 100 m 124 ppt 70  
5.3 μ3 m 0.1 ppm 71  
5.26 μ310 mm unknown 72  
Formaldehyde 3.43 μ100 m 1.6 ppb 73  
3.59 μ3.75 m 1.5 ppb 74  
3.59 μ50 m 0.58 ppb 75  

To measure fugitive methane emissions, a portable sensor with both high sensitivity and fast response time was developed recently by Oliaee et al.28 with a continuous-wave thermoelectrically cooled GaSb-based distributed feedback diode laser emitting at a wavelength of 3.27 μm (Fig. 3.). The effective optical path length of the multipass cell used in the sensor was 6.8 m. The sensor was evaluated with the DAS and WMS techniques. Under the WMS operation, the detection limit was better than 1 ppb at the integration time of 1 s.

FIG. 3.

A view of the compact methane sensor and its schematic. A GaSb-based DFB laser emitting at 3.27 μm was coupled to a multipass cell with an effective length of 6.8 m. After many passes, the transmitted beam is detected by a TE-cooled photovoltaic MCT photodetector and demodulated by a software-based lock-in amplifier. Reproduced with permission from Oliaee et al., ACS Sensors 7, 564 (2022). Copyright 2022 American Chemical Society.

FIG. 3.

A view of the compact methane sensor and its schematic. A GaSb-based DFB laser emitting at 3.27 μm was coupled to a multipass cell with an effective length of 6.8 m. After many passes, the transmitted beam is detected by a TE-cooled photovoltaic MCT photodetector and demodulated by a software-based lock-in amplifier. Reproduced with permission from Oliaee et al., ACS Sensors 7, 564 (2022). Copyright 2022 American Chemical Society.

Close modal

The interest in detection of acetone as a biomarker for breath analysis and diagnostics has stimulated the development of several sensors. The acetone molecule has four strong fundamental absorption bands in the mid-IR: 3–4, 5.5–6, 7–7.5, and 8–8.5 μm, and different research groups developed acetone sensors in these wavelength intervals. Schwarm et al.29 developed a calibration-free acetone sensor for detection in exhaled breath with the interference correction method based on the WMS near 8.2 μm achieving the detection limit of 0.11 ppm. Nadeem et al.30 reported the acetone sensor employing WMS and a single-mode widely tunable (∼300 cm−1) external-cavity quantum cascade laser operating around 8 μm. In this sensor, the compact multipass cell was used to improve the detection limit to 15 ppbv with an integration time of 10 s, which yielded the noise-equivalent absorption (NEA) sensitivity of 1.9 × 10−8 cm−1 Hz−1/2. Xia et al.31 carried out acetone measurements at a laser wavelength near 3 μm using a Herriot cell with an effective optical path of 24 m and achieved the detection limit of 0.58 ppm in 1 s. We have depicted the schematic diagram of such a sensor in Fig. 4(a). A mid-IR frequency comb was used to characterize the DFB-ICL emission line by observing the beating signal between the two lasers. Due to the choice of the absorption lines, the influence of water and CO2 was minimized. The Allan deviation analysis of the sensor showed that the sensor detection limit was about ∼0.12 ppm with the integration time of 60 s [Fig. 4(b) ]. Overall, the WMS-based sensitive detection of acetone is a feasible and practical approach.

FIG. 4.

(a) Schematic of the acetone WMS sensor in the mid-IR. The ICL-DFB laser beam with the center wavelength of 3.367 μm was split into two beams: one was coupled to a Herriot cell with the effective length of 24 m for acetone measurement and the other was used for detection of the beat-signal with a mid-IR comb to retrieve the laser linewidth. (b) The Allan deviation of the sensor vs time, showing that the sensor detection limit was about ∼0.12 ppm with the integration time of 60 s. Adapted with permission from Xia et al., OSA Contin. 2, 640 (2019). Copyright 2019 The Optical Society.

FIG. 4.

(a) Schematic of the acetone WMS sensor in the mid-IR. The ICL-DFB laser beam with the center wavelength of 3.367 μm was split into two beams: one was coupled to a Herriot cell with the effective length of 24 m for acetone measurement and the other was used for detection of the beat-signal with a mid-IR comb to retrieve the laser linewidth. (b) The Allan deviation of the sensor vs time, showing that the sensor detection limit was about ∼0.12 ppm with the integration time of 60 s. Adapted with permission from Xia et al., OSA Contin. 2, 640 (2019). Copyright 2019 The Optical Society.

Close modal

WMS was also used in the long-path sensing of trace gases, such as methane, carbon dioxide, etc. Michel et al.32 used a quantum cascade laser at ∼8 μm with a power of 40 mW to monitor methane over a 458 m path with the detection limit of 10 ppb at a 1 Hz acquisition rate. In this system, an in-line N2O gas cell was used for system stabilization. The sensor endured quite well harsh environmental conditions, including snow, rain, wind, and changing temperatures.

Xia et al. developed an open-path remote sensing optical system with a near-IR laser source operating close to two wavelengths of ∼1654 and ∼1602 nm for measuring methane and carbon dioxide, respectively.33 The schematic of the system is shown in Fig. 5. The in-line gas cell with a calibrated methane or carbon dioxide gas of 1% and 100% concentrations, respectively, was utilized in the reference channel to retrieve in real time the actual gas concentration from comparison with the signal channel. The sensor was evaluated first indoor, and then it was set up on an airport runway with a 2.6 km round trip path to measure the path-averaged concentration of methane for more than 10 h. The detection limit of the sensor for methane determined by the Allan deviation analysis of the data was 20 ppb.

FIG. 5.

Schematic of the open long-path remote sensing system. A 1.65 μm DFB laser beam was split and used in two channels: one for system calibration by measuring the calibration gas and another for the long-path measurement with aligning by a green laser pointer. The reflected signal was collected by a telescope and focused on an InGaAs avalanche photodiode. The detected signal was demodulated by a digital lock-in amplifier based on a LabVIEW code, and the latter also implemented the current modulation of the DFB laser. Pressure and temperature sensors monitored the parameters of the atmosphere. Reproduced with permission from Xia et al. Opt. Lasers Eng. 117, 21 (2019). Copyright 2019 Elsevier.

FIG. 5.

Schematic of the open long-path remote sensing system. A 1.65 μm DFB laser beam was split and used in two channels: one for system calibration by measuring the calibration gas and another for the long-path measurement with aligning by a green laser pointer. The reflected signal was collected by a telescope and focused on an InGaAs avalanche photodiode. The detected signal was demodulated by a digital lock-in amplifier based on a LabVIEW code, and the latter also implemented the current modulation of the DFB laser. Pressure and temperature sensors monitored the parameters of the atmosphere. Reproduced with permission from Xia et al. Opt. Lasers Eng. 117, 21 (2019). Copyright 2019 Elsevier.

Close modal

The system was designed for the detection of methane over a kilometer long distance with only 10 mW of the optical power from the laser source. In such a long-distance experiment, two key factors should be considered to get better performance. First, the laser scanning and modulation frequencies should be optimized. The transmission signal within the frequency interval of the atmospheric turbulence is strongly suppressed, which can be seen from the calculated by Fourier transform power spectral density of the signal. Therefore, by modulating the wavelength above the cut-off frequency the influence of random variations due to turbulence can be effectively reduced. In our case, the scanning frequency was set to 100 Hz and the modulation frequency was set to be 25 kHz. The second point is that the influence of the signal power fluctuations caused by the laser itself should be minimized as much as possible. Thus, a 1f signal was also demodulated and used for the normalization of the 2f-signal to decrease the effect of the laser power fluctuations. For the data processing, the distance between the telescope and the retroreflector needs to be measured independently to be a known parameter. With the laser power enhanced by a fiber amplifier, even longer detection distances can be reached. A combination of multiple laser sources can increase the bandwidth for the detection of multiple trace gases, which for remote sensing can be a feasible alternative to a more cost and power consuming frequency comb spectroscopy.34 

Zhang et al. developed an open-path gas sensor adopting a QCL as a laser source with the center wavenumber at 2203.73 cm−1 for the detection of atmospheric N2O.35 In this sensor, the 1f-normalization of the WMS signal was also employed to suppress the influence of the laser power fluctuations. A 20 ppm N2O standard gas was used for calibration. With the Allan deviation analysis, the detection limit for the sensor was determined to be 1.1 and 0.14 ppb with the integration times of 1 and 95 s, respectively. In the mentioned works, the distance between the receiver and the reflector had to be accurately measured with a rangefinder or other instrument. Yang et al. developed the phase retrieval approach of the first harmonic signal (1f phase) in the WMS technique to measure the gas concentration and the path length simultaneously.36 This approach has been experimentally validated by measuring CO2 concentration in the open-path configuration. The sensor was evaluated by a long-path (over 700 m) 7-day continuous measurement. The detection limit of about 2 ppm with an averaging time of one second was achieved.

We note that for remote sensing of gas concentrations, a continuous wave integrated path differential absorption (IPDA) LIDAR can be used, which however, unlike WMS, uses intensity modulation. Such a system employs two lasers with the wavelength of the first (online) laser at the center of the absorption line and the wavelength of the second (offline) laser selected to be outside of the absorption line. The concept of the CW system37 designed for CO2 IPDA measurements is as follows. The online and offline seed laser radiations with spectral properties chosen for CO2 detection are intensity modulated (each at its own frequency) and combined using fiber coupler and then are simultaneously amplified to increase the transmitted power by a single erbium doped fiber amplifier (EDFA). A small fraction of power inside of the EDFA is sent to a reference detector for power normalization. The backscattered signals of the lasers from the target surface are collected with a telescope, optically filtered with a narrow band optical filter, and detected by a single detector. Both channels are amplified, electronically filtered, and then digitized to retrieve the CO2 column with the detection limit of better than 0.3 ppm. We note that the WMS technique can also be used in such LIDAR systems.

To get a better signal-to-noise ratio, some novel digital filtering algorithms were implemented for data processing, such as Kalman filtering, wavelet filtering, and neural network algorithms.38–41 Zheng et al.38 developed a wavelet-denoising method to suppress the noise in the 2f-signal of methane sensor at 1.654 μm. With wavelet-denoising method, the minimum detection limit was reduced from 4 to 1 ppm.

Xia et al.39 used the Kalman filter technique to improve the open-path sensor performance. Zhu et al.40 used an improved Savitzky–Golay filtering algorithm to denoise online measurement of an oxygen content in a pharmaceutical vial. This method can match the efficacy of the wavelet analysis and is even faster with a 300 ms response time, showing that it was suitable for online measurement of the gas concentration. Tian et al.41 used a trained on an extensive data set neural network algorithm to denoise the signal. In terms of algorithm complexity, the Kalman filter is a simpler choice for real time online monitoring, which is also suitable to be implemented in a microcontroller unit or with other data processing approaches.

In summary, the advantages of WMS that was realized in various sensors (see Table I) are as follows: (1) It can be adapted to a desired detection sensitivity range since detection limits from ppm to ppt were reported. (2) It is relatively easy to implement and has been commercialized for some trace gases avoiding the strict requirements for optimal optical alignment as compared to cavity ringdown spectroscopy. (3) WMS technique has wide range of applications and has been used in combustion studies, lidar systems to retrieve the temperature, pressure, etc. WMS has also some disadvantages compared to other techniques. Due to commonly narrow tunability of the laser wavelength, a single laser source often can detect only one species. The simultaneous detection of several species requires a combination of lasers with the required wavelength intervals. Thus, for a multi-component gas analysis, a combination of sensors working in different spectral intervals (like near-IR and mid-IR) is a possible direction for future work. Reaching the high sensitivity in the range of ppt can require the increase of the multipass cell length resulting in the sensor becoming heavy and bulky. Consequently, the development of a compact, robust, and sensitive sensor is currently another research direction.

The near-IR continuous-wave cavity ringdown spectroscopy (CW-CRDS) technique is applied to determine methane concentration in human breath samples. Methane is the biomarker indicative of colon and digestive problems. A narrow-linewidth distributed feedback (DFB) diode laser was used to achieve sensitive detection with a high-finesse cavity by employing high reflectivity mirrors. The laser output wavelength is tuned across the absorption line peaks in the near-IR region by adjusting the temperature and current of the DFB diode laser. The experimental setup has a 172 cm long cavity and a decay time of ∼420 μs for the empty cavity corresponding to a path of ∼132 km. The experimentally measured absorbance spectra are fitted with spectroscopic data from the HITRAN database.76 CH4 concentrations were measured for an exhaled breath of 22 volunteers with different health conditions.

Cavity ringdown spectroscopy (CRDS) is a sensitive technique that can directly measure small absorbance and allows inferring the absorber concentration. CRDS has high sensitivity; however, it requires a precise alignment since otherwise higher order modes are excited that preclude accurate measurements.77 

The basic concept of the CRDS technique involves the utilization of a high-finesse cavity with high reflectivity mirrors. The laser light is transmitted into a resonator and reflects back and forth, causing intensity build-up at resonant conditions. After reaching high intensity, the laser radiation is turned off with an acousto-optic modulator (AOM), which results in intensity temporal decay. This decay is measured as the ringdown signal on a photodetector. The ringdown time is registered for each wavelength, which is changed in small increments through the wavelength range corresponding to the absorption peaks of interest.

The idea of the CRDS appeared in the early 1980s. CRDS was developed to measure the reflectivity of highly reflective mirrors in an optical cavity.78 Romanini et al. in 1997 demonstrated CRDS employing a tunable CW single frequency laser source and achieved the detection limit of 10−9 cm−1 or 5 × 10−8 per pass through the sample.79 Their experimental setup was similar to that of Anderson et al.78 except that they used an AOM. Gatti et al. in 2015 introduced a comb-locked cavity ringdown spectrometer in the near-IR from 1.5 to 1.6 μm with a high-finesse passive cavity containing a gas sample by employing flat mirrors of 99.9975% reflectivity and achieved the detection limit of 5.7 × 10−12 cm−1 over a 75 s long spectral acquisition of a single absorption feature.80 In 2016, McHale et al.81 used open-path CRDS with mirror reflectivity of better than 99.996% for methane measurements in ambient air at a wavelength of 1742 nm. The fast development of CRDS stimulated its employment in many applications. CRDS was utilized in analytical and atmospheric chemistry, medical and biological applications, etc., in particular, for analysis of exhaled breath.82 As a diagnostic tool, the measurement of breath can provide specific information on the health status of the subject; it is non-invasive, fast, intact, and undemanding for a patient.77,83

The exhaled breath contains different compounds, and the major components (with typical concentration values indicated for the end phase of exhaling) include nitrogen (78%), oxygen (13%–16%), carbon dioxide (4%–5%), inert gases (∼0.9%), and water vapor (5%–6%). In addition, it contains inorganic trace gases, such as nitric oxide (10–50 ppb), nitrous oxide (1–20 ppb), ammonia (0.5–2 ppm), carbon monoxide (0–6 ppm), and hydrogen sulfide (0–1.3 ppm), and organic VOCs, such as methane (2–10 ppm), acetone (0.3–1 ppm), ethanol, isoprene (∼100 ppb), ethane (0–10 ppb), etc.83 

Here, we consider measurements of methane in exhaled breath with CRDS. Methane is a natural bioproduct that can be detected in the expired air. Methanogenic bacteria found in the colon can produce methane in anaerobic conditions. Methane is normally seen in human breath at concentrations near 2 ppm (close to the atmospheric concentration); however, its excessive production during metabolism and some abnormal conditions can lead to much higher concentrations.84,85 Obesity, irritable bowel syndrome, inflammatory bowel illnesses, anorexia, and other ailments are correlated with abnormal methane production.86,87 Here, after considering the theoretical background of CRDS and its experimental arrangement, we present our results on methane measurements in the breath of volunteers of different ages and health conditions.

The transmitted intensity (It) of the laser is given by the equation88 
(4)
where I 0 is the incident intensity of light; for a single absorbing species, the absorption coefficient α = σ n , σ is the absorption cross section of the species at a particular wavelength, L is the path length of the radiation interaction with the sample, and n is the number density of the absorbing molecules.
In the case of an empty cavity, the main losses are due to reflections and diffraction. Ignoring the effects of the diffraction, the intensity of light in an empty cavity after interruption of the laser source will decay exponentially according to the expression
(5)
The transmitted intensity of laser light for an empty cavity can be written as I ( t ) = I 0 exp ( t / τ 0 ) with the rate determined by the cavity ringdown time,
(6)
where t r = 2 L / c 0 is the travel time for a round trip and c 0 is the speed of light in the empty cavity. With a gaseous sample inside the cavity, the molecules of the sample absorb the laser beam that is injected into the cavity, so the intensity decays faster due to the absorption loss,
(7)
where c is the speed of light in the cavity filled with the gas. The ringdown time (decay time constant) in this case is given by
(8)
The absorption coefficient at a given wavelength can be evaluated from the known ringdown time in the empty cavity and the one for the cavity filled with the absorbing species, and assuming c = c 0, we obtain
(9)
with τ 0 and τ 1 determined by Eqs. (6) and (8), respectively.
For the determination of concentrations of N s constituent components of a gas mixture, we equate for each measured wavelength experimentally determined absorption coefficients to the sum of the simulated contributions of the components to the absorption,
(10)
where n l are the molecular densities and σ l are known absorption cross sections of the gas components that are determined from a database, such as HITRAN.76 Using the formulas n l = P C l / ( k B T ) , where P is the pressure of the gaseous sample and C l = n l / n are unknown fractional concentrations, Eq. (10) can be presented in the form
(11)
where n is the overall molecular density of the gas sample and T and P are the gas temperature and pressure. Here, we introduced the vector B = { B 1 , B N } that is determined by the results of measurements at N wavelengths λ m (m = 1, …, N) and the matrix A with elements A m l ( m = 1 , , N and l = 1 , , N s ) that is calculated from the spectral database. Provided that the number of measurements N is larger than the number of species N s, the vector of unknown concentrations C = { C 1 , , C N s } that gives the least squares deviation of the left and right parts of Eq. (11) can be determined as89 
(12)
where A T is the transpose of matrix A.

The schematic of our CRDS setup is shown in Fig. 6. The measurements were performed at 70 Torr by utilizing a DFB laser at 1653 nm and a 172 cm long cavity with 99.9987% high reflectivity mirrors (Layertec, GmbH). The calculated finesse of the cavity is F = π R / ( 1 R ) 242 000.90 A He–Ne laser was used for the system alignment.

FIG. 6.

Schematic diagram of the experimental setup. The first order diffraction of the laser beam is directed to the optical cavity, while zeroth order beam is used for monitoring the wavelength. A He–Ne laser was used for the system alignment. Drierite and Ascarite are optionally used for filtering out H2O and CO2 when they interfere with the measurement. OF1 and OF2 are optical fibers, CL1 is a collimating lens and CL2 is a coupling lens, OAPM is an off-axis parabolic mirror, and PZT driver actuates a piezoelectric transducer to scan the cavity length.

FIG. 6.

Schematic diagram of the experimental setup. The first order diffraction of the laser beam is directed to the optical cavity, while zeroth order beam is used for monitoring the wavelength. A He–Ne laser was used for the system alignment. Drierite and Ascarite are optionally used for filtering out H2O and CO2 when they interfere with the measurement. OF1 and OF2 are optical fibers, CL1 is a collimating lens and CL2 is a coupling lens, OAPM is an off-axis parabolic mirror, and PZT driver actuates a piezoelectric transducer to scan the cavity length.

Close modal

The beam deflected with the acousto-optic modulator (AOM) is sent to the cavity, so the AOM can work as a fast-optical switch to turn the beam on and off. A piezoelectric transducer (PZT) is actuated by a triangular shape voltage and is connected to the concave mirror of the cavity, thus modulating the cavity mode frequencies. When the resonance frequency of the cavity mode is matched with the laser frequency, high intensity inside the cavity builds up. After the incident beam is shut off, the decaying signal on an InGaAs photodetector is registered. The signal from the photodetector is sent to the FPGA device, which enables the recording of the ringdown time as the measurement progresses and the wavelength is changing. A Python software code allows the user to set the temperature and the laser current and enables scanning over the desired wavelength range.

In general, the exhaled breath samples contain significant amounts of carbon dioxide and water, as can be seen in Fig. 7, which depicts the ringdown time vs wavelength clearly showing the absorption transmission dips of 12CH4, 13CH4, CO2, and H2O in measured at different pressures exhaled breath samples. These measurements were done without filters containing Drierite and Ascarite that can be used to reduce the content of CO2, and H2O, and the sufficiently high spectral resolution allowed us to clearly observe different absorption peaks without their overlap. As Fig. 7 shows, at low pressure, the signals are small. However, achieving higher pressure requires larger samples and leads to the broadening of the spectral lines. Considering both factors, 70 Torr was chosen as the optimal pressure. The total scan time was 1 h and 20 min per 1000 data points.

FIG. 7.

Ringdown time vs wavelength measured for exhaled breath of one of the subjects at different pressures; from top to bottom, different colors represent: 0 (black, empty cavity), 20 (red), 30 (blue), 40 (magenta), 50 (green), 70 (orange), and 80 Torr (mint).

FIG. 7.

Ringdown time vs wavelength measured for exhaled breath of one of the subjects at different pressures; from top to bottom, different colors represent: 0 (black, empty cavity), 20 (red), 30 (blue), 40 (magenta), 50 (green), 70 (orange), and 80 Torr (mint).

Close modal

After the full scan in the range (1652.75–1654.25 nm), the data are fitted using HITRAN database76 with a Python script. The concentration of each type of molecule is determined by the procedure presented by Eqs. (11) and (12).

Figure 8(a) reports the absorption peaks and concentrations of 12CH4, 13CH4, CO2, and H2O in a 70 Torr sample of a healthy 28-year-old individual. The concentration of methane of 1.87 ppm was obtained by fitting the measured absorption spectrum with the data from the HITRAN database.76 For a subject with suspected intestinal bacterial overgrowth [Fig. 8(b)], a much higher methane concentration of 11.54 ppm was observed. The absorption peak of 12CH4 is significantly larger than that of 13CH4 since the natural abundances of 12C and 13C are 98.9% and 1.1%, respectively. In these measurements, the filters with Drierite and Ascarite were not used. With the Allan deviation analysis of the presented here CRDS setup, the detection limit was determined to be 2.5 × 10−11 cm−1 with averaging over 70 ringdown events91 with an estimated fractional detection limit for 12CH4 with the absorption line near 1653.73 nm of about 0.3 ppb. The measured lower values of the CO2 concentration in Figs. 8(a) and 8(b) are due to the used method of the exhaled breath collection by blowing up a balloon. The air that gets into the airways leading to the lungs (in capnography this volume is called “dead space”) at the end of the inhaling process is expelled first when the exhaling starts.92 Since this air does not flow through lungs, it is not enriched with CO2, and as a result, the exhaled air in the balloon is diluted with the air from the dead volume having the CO2 concentration close to the atmospheric one (which is about 400 ppm). The concentration of methane in ambient air is about 1.9 ppm; therefore, when methane is not added to the exhaled breath the concentration close to this atmospheric value is measured. However, for several individuals much higher methane concentrations were registered.

FIG. 8.

Absorption spectra: (a) of a healthy 28 years old individual (J-subject) and (b) of a 53-year-old individual with a suspected intestinal bacterial overgrowth (S-subject), showing much higher methane concentration. Data are fitted with the HITRAN database. Larger 12CH4 peaks and much smaller peaks of 13CH4 can be seen.

FIG. 8.

Absorption spectra: (a) of a healthy 28 years old individual (J-subject) and (b) of a 53-year-old individual with a suspected intestinal bacterial overgrowth (S-subject), showing much higher methane concentration. Data are fitted with the HITRAN database. Larger 12CH4 peaks and much smaller peaks of 13CH4 can be seen.

Close modal

The concentrations of 12CH4 present in the exhaled breath samples of 22 volunteers measured at a pressure in the cavity of 70 Torr are presented in Fig. 9. A concentration above 10 ppm of methane is considered positive in the diagnosis of small intestinal bacterial overgrowth.93 The results of Fig. 9 indicate that 3 out of 22 participants had this criterion fulfilled. Two subjects had somewhat elevated level of methane but below 10 ppm. For all other subjects, the 12CH4 concentration was within 1.8–2 ppm.

FIG. 9.

12CH4 concentrations for 22 volunteers of different ages. Concentration values above the red dashed line can indicate abnormal gastrointestinal condition.

FIG. 9.

12CH4 concentrations for 22 volunteers of different ages. Concentration values above the red dashed line can indicate abnormal gastrointestinal condition.

Close modal

Mid-IR systems being able to exploit high absorption cross sections encounter restraints, such as lower performance and higher costs of required components compared to the near-IR. Cavity ringdown spectra of ammonia at 10 ppbv were recorded with a CW DFB QCL at 8.5 μm with a detection limit for ammonia reaching 0.25 ppbv.94 A CRDS instrument based on a widely tunable between 6 and 8 μm optical parametric oscillator was developed for the detection of vapor-phase explosives with the detection limit down to 75 ppt.95 Another CRDS system with a DFB QCL near 4.5 μm actively stabilized to a given cavity mode achieved the minimum detectable absorption of 2.3 × 10−11 cm−1.96 A linewidth reduction as well as the locking of a DFB QCL wavelength near 4.527 μm with an optical frequency comb via optical feedback with a CRDS setup targeting radiocarbon detection using 14C16O2 absorption line proved a 100 kHz resolution bandwidth and the ability to detect radiocarbon at 14C/12C isotope ratio of ∼10−8.97 

A frequency-stabilized CRDS technique with combined high-bandwidth locking of a continuous-wave probe laser and a frequency-stabilized cavity leads to a significant improvement of the SNR98 and a better limit of detection (1.7 × 10−11 cm−1 after averaging 170 ringdown events requiring 21 ms at an acquisition rate of 8 kHz).99 The introduction of an optical feedback frequency-stabilized CRDS100 allowed us to reduce the baseline noise to 5 × 10−12 cm−1. Maity et al. utilized a quantum cascade laser tunable in the mid-IR range 7.5–8 μm with a power ∼100 mW coupled with a CRDS setup to obtain the detection limit of methane isotopes in air ∼13 ppb and ∼0.0003 cm−1 resolution.101 The advantage of locking the probe laser frequency to a self-referenced femtosecond optical frequency comb and a high acquisition rate was recently demonstrated,102 resulting in the reduced noise-equivalent absorption coefficient of 2 × 10−12 cm−1 Hz−1/2. A way to overcome the CRDS limitation of measuring only one resonant cavity mode at a given time by realizing a broadband dual frequency comb CRDS was proposed by Lisak et al.103 Further development of this trend of combining the advantages of the CRDS and frequency comb techniques can be expected also in the future.

Back in the 1970s, Eckstein et al. identified the comb structure of the Fourier transformed spectrum from a picosecond laser pulse train and used it to study the atomic spectra.104 Near the end of the 1990s, with the invention of the self-referencing technique, the femtosecond frequency comb was first demonstrated in the Kerr lens mode-locked Ti:sapphire laser and revolutionized the field of optical metrology following pioneering works by two research groups of Hänsch and Hall.105–107 The frequency comb coherently unites the electromagnetic spectrum from the radio frequency to the optical frequency with a simple expression fn = nfr + f0, where optical frequencies fn are the equally spaced comb teeth, which are under the broad spectrum of a single pulse; fr is the frequency gap between the adjacent comb teeth and is equivalent to the pulse repetition rate or the reciprocal of the pulse interval; and f0 is the carrier-envelope offset frequency, related to the pulse-to-pulse carrier-envelope phase slippage of the phase-coherent pulse train.108 For ordinary mode-locked lasers, fr is usually in the range between 50 MHz to 1 GHz, which is determined by the optical length of the round trip in the laser resonator. With pulse picking or cavity filtering techniques, fr can be extended to the range of the order from 0.001 to 10 GHz. f0 is in the range between 0 to fr due to the offset between the comb teeth and the integer number multiplied by the repetition rate. Hence, if the coherent laser pulse train is in the near infrared, the integer n is of the order of 104–107 to bridge the gap from the radio frequency to the near infrared optical frequency. With a commercially available radio frequency reference, such as the Rb standard, and the precise control of the fr and f0 by phase locked loops, the clockwork mechanism of the frequency comb transfers the stability of the frequency standard from the radio frequency to the optical frequency. Hence, for a Ti:sapphire femtosecond laser emitting the pulse train of a 100 MHz repetition rate with 10 fs pulse duration, the corresponding frequency comb covers about 100 THz spectral range containing 106 comb teeth, and each comb tooth can be regarded as a narrow-linewidth continuous-wave laser.

The mode-locked laser sources have played a major role in the developments and applications of the frequency comb. Various types of the mode-locked solid-state lasers and fiber lasers have been stabilized to radio frequency standards to serve numerous applications.109 With the implementation of nonlinear wavelength conversion techniques such as supercontinuum, second or high harmonic, sum or difference frequency generation, four-wave mixing, etc., frequency combs based on mode-locked lasers cover the electromagnetic spectrum from the extreme ultraviolet to the terahertz range, enabling the bidirectional phase-coherent conversion between these frequencies and radio frequencies and continuously finding new applications, such as ultrastable clock, ultrasensitive sensing, and ultraprecise spectroscopy.109 

In addition to the mode-locked lasers as the workhorses for the optical frequency comb community, the electro-optic combs and microresonator frequency combs are being developed fast.110,111 Usually, both latter techniques employ a continuous-wave seed laser with a narrow linewidth. For an electro-optic comb, a seed laser beam is modulated by an electro-optic modulator in phase or both in phase and amplitude to generate a series of sidebands with equal frequency spacing.110 The bandwidth of the modern commercial electro-optic modulators can reach 40 GHz and above. Thus, this method provides wider spacing comb teeth than the mode-locked laser, but the comb bandwidth is usually limited by the electro-optical properties of the modulator. For a microresonator frequency comb, a seed laser beam is coupled into an optical microcavity of high-quality factor to generate the frequency comb by the nonlinear Kerr effect, i.e., four-wave mixing. Due to the interplay between the nonlinearity and dispersion, a stable soliton can circulate in the microresonator with a round trip time in the range of 1–100 ps.111 Thus, in the frequency domain, this method can provide a 10 GHz to 1 THz comb spacing and a small volume for the on-chip integration and has already been demonstrated in the sensing and LIDAR applications.112,113

Since the invention at the end of the 20th century, stabilized frequency combs have been widely used for optical clocks,114 frequency metrology,115 laser spectroscopy,116 astronomical spectrum calibration,117 optical communication,118 absolute ranging,119 and other fields. In the field of spectroscopy, frequency combs not only provide super-accurate references for tunable narrow-linewidth lasers by measuring beating signals but also serve as broadband light sources with accurate comb mode frequencies, which simultaneously enable the broadband and high-frequency resolution spectral measurements. There are a large number of optical frequency combs as light sources advancing research on new types of spectroscopic methods such as direct optical frequency comb spectroscopy, broadband cavity-enhanced frequency comb spectroscopy, Fourier transform spectroscopy with a frequency comb, dual comb spectroscopy, frequency comb Vernier spectroscopy, etc.

As a coherent broadband source, a frequency comb can be used to replace an incoherent broadband source in a traditional absorption spectroscopy setup, which usually consists of a light source, an absorbing sample, and a spectrometer,116 as is illustrated in Fig. 10. In this direction, considerable progress has been achieved and still is underway in the development of the spectrometer capable of high-resolution, high-sensitivity, and broadband spectral measurements with a short acquisition time.

FIG. 10.

Scheme of the direct frequency comb absorption spectroscopy.

FIG. 10.

Scheme of the direct frequency comb absorption spectroscopy.

Close modal

Limited by the spectral resolutions of the traditional spectrometers, such as the Czerny–Turner type monochromator120 and the Fourier transform spectrometer,121 the comb structures of the light sources were difficult to resolve below the 0.5 GHz repetition rate. However, in many gas sensing applications at ambient conditions, the linewidths of the target transitions are larger than 1 GHz. Thus, the requirement of high resolution is relaxed, and sometimes free running frequency combs can be used to achieve reasonable results at a low cost. Moreover, the practical applications can benefit from the coherence of these sources with such properties as low divergence, high brightness, long coherence time, etc. Following the Beer–Lambert law, to increase the sensitivity of the trace gas detection, the usual approach of increasing the interaction length between the light and the absorption sample can be used. In the field applications, with the low divergence of the coherent frequency comb laser beams, the ranging distances of up to several kilometers were demonstrated.122–125 This distance scale is complimentary to the satellite remote sensing of many hundred kilometers range and the laboratory scale investigations in the range of a few meters, enabling a more detailed middle range gas sensing, which is critical for many applications, such as pollution studies, atmospheric science, etc. In the laboratory, usually a multi-pass cell or a high-finesse resonator can be used to increase the interaction length. The Herriott cell or specially designed multipass cells provide a convenient way to increase the interaction length, but the achieved effective interaction lengths are usually limited by the number of reflections allowed by the design and typically are less than 1 km.120 

We built a confocal multipass cell with about 580 m path length120 and used it with a mid-IR comb source126 to analyze the human breath. The experimental setup and the spectroscopic results are presented in Fig. 11. It can be seen that the breath from a patient with colon cancer in Fig. 11(c) contained much more methane than that of a healthy person in Fig. 11(d). The mole fractions retrieved from the fittings of Figs. 11(c) and 11(d) are 12.90 ± 0.04 and 1.97 ± 0.04 ppm for CH4 and 6500 ± 200 and 16 700 ± 200 ppm for H2O, respectively. The significant reduction of the H2O mole fraction in the breath of the colon cancer patient is due to the use of a dry ice-cold trap to reduce the water vapor. Further, the detection limit of methane in human breath is estimated to be about 40 ppb in the experiments within standard deviation. The double pass Czerny–Turner monochromator in the Yokogawa analyzer has a resolution of about 0.10 nm and was set at a measurement speed of about 1.00 nm/s.

FIG. 11.

Direct mid-IR FCS with a multipass cell for breath analysis: (a) Schematic of the experimental setup. A flip mirror is used to let red (He–Ne) laser pass to align the multipass mirror getting the spot patterns, which are shown in the upper left corner. (b) The raw spectrum of the breath from a colon cancer patient was measured by Yokogawa optical spectrum analyzer. Because the signals of many absorption peaks reach the noise floor of −50 dBm/nm determined by the spectrometer and result in large errors in the absorbance calculation, we disregard the absorption peaks above the absorbance value of ∼3.4 for the HITRAN76 simulations and in the concentration retrieving process. (c) and (d) show the normalized absorption spectra (black solid lines) of the exhaled breath from a colon cancer patient and a healthy person, respectively. The methane (red dotted lines) and water vapor (blue dashed lines) are HITRAN simulations presented with the absorption spectra. The CH4 mole fractions retrieved from the fittings of (c) and (d) are 12.90 ± 0.04 and 1.97 ± 0.04 ppm, respectively. The significant increase of the methane absorption peaks can be seen in (c) at the wavelengths of ∼3368 and ∼3380 nm.

FIG. 11.

Direct mid-IR FCS with a multipass cell for breath analysis: (a) Schematic of the experimental setup. A flip mirror is used to let red (He–Ne) laser pass to align the multipass mirror getting the spot patterns, which are shown in the upper left corner. (b) The raw spectrum of the breath from a colon cancer patient was measured by Yokogawa optical spectrum analyzer. Because the signals of many absorption peaks reach the noise floor of −50 dBm/nm determined by the spectrometer and result in large errors in the absorbance calculation, we disregard the absorption peaks above the absorbance value of ∼3.4 for the HITRAN76 simulations and in the concentration retrieving process. (c) and (d) show the normalized absorption spectra (black solid lines) of the exhaled breath from a colon cancer patient and a healthy person, respectively. The methane (red dotted lines) and water vapor (blue dashed lines) are HITRAN simulations presented with the absorption spectra. The CH4 mole fractions retrieved from the fittings of (c) and (d) are 12.90 ± 0.04 and 1.97 ± 0.04 ppm, respectively. The significant increase of the methane absorption peaks can be seen in (c) at the wavelengths of ∼3368 and ∼3380 nm.

Close modal

Even higher sensitivity can be achieved with the cavity-enhanced FCS,127–131 employing resonance enhancement with a high-finesse Fabry–Pérot cavity. By actively controlling the length of the Fabry–Pérot cavity, the longitudinal modes of the cavity must be precisely matched with the frequency comb modes, i.e., the pulse interval matches the round trip time for the cavity. Hence, after the round trip in the cavity, the pulse overlaps with the subsequent pulse in time. To ensure all the comb teeth are in constructive interference, the cavity dispersion must be well controlled by the mirror coating, assuring also a high reflectivity, which provides high finesse. With a couple of lenses for the transverse mode matching, the incident frequency comb can have a strong resonance with the high-finesse Fabry–Pérot cavity, which greatly enhances the effective interaction length. When the resonance is established, the incident pulse can be turned off and the ringdown trace of the comb mode can be analyzed by a dispersion spectrometer with an array of photodiodes.127 Alternatively, the Fabry–Pérot cavity can be locked on resonance to the stable frequency comb, and the transmitted light can be analyzed by a Fourier transform, grating based Czerny–Turner or VIPA spectrometer.128–131 

The demonstrated broad spectrum ranges of the available frequency combs from the UV to the mid-IR have already covered the majority of spectroscopic gas sensing target molecules. As a result, direct absorption FCS has already found numerous applications, in particular, relevant to environmental monitoring and breath analysis.120,129,131

In 2002, Schiller proposed a novel type of spectrometer utilizing the properties of heterodyning of two frequency combs with a small difference (δ) in the repetition rate.132 In 2004, Keilmann et al. demonstrated DFCS in the mid-infrared range.133 In 2008, Coddington et al. achieved the comb teeth resolution of the DFCS by absolutely locking the dual combs to two stabilized continuous-wave lasers and maintaining the mutual coherence between dual combs.134 Several adaptive sampling schemes were proposed to eliminate the requirements of the ultra-stable continuous-wave lasers.135–137 Moreover, multi-dimensional dual comb methods were demonstrated to study the coupling of the transition resonance.138,139 By using the direction, polarization, or wavelength multiplexing, one femtosecond laser could be used to convert to a dual comb source.140–142 Further, with the development of the electro-optic comb and micro-resonator comb, the DFCS was demonstrated with these two types of comb sources in the gas sensing and ranging applications.143–146 

There is a notable analogy between DFCS and Fourier transform spectroscopy. For Fourier transform spectroscopy, the light beam (either incoherent or coherent) is divided into two beams after passing through the 50:50 beam splitter: one beam is reflected by a fixed mirror and has a constant path length and the other beam is reflected by a moving mirror and goes over a changing path length. The two light beams finally overlap in space at a photodetector. The photodetector records the interferogram, which is the two beams superposition intensity vs the changing path length and can be Fourier transferred to the spectral domain. The spectral resolution of the traditional Fourier transform spectroscopy is usually determined by the total of the changing path length, and the spectral range depends on the actual sampling rate of the interferogram. Thus, the velocity and total displacement of the moving mirror are critical for the quality of the spectroscopic measurement. For the usual implementation of the DFCS, two frequency combs with slightly different repetition rates are utilized and no moving parts are involved. The basic working principle is illustrated in Fig. 12.

FIG. 12.

Principle of the dual frequency comb spectroscopy. For two frequency combs, f1n = nfr1 + fo1 (blue) and f2n = nfr2 + fo2 (red), the slight difference of the repetition rates of the dual comb is δ = fr2 − fr1. In the time domain, the S(t) is the repeated interferogram with an update rate δ. In the frequency domain, beat notes in the RF range between the optical comb teeth with the nearby order can be filtered by a lowpass filter, which is usually from DC to fr/2.

FIG. 12.

Principle of the dual frequency comb spectroscopy. For two frequency combs, f1n = nfr1 + fo1 (blue) and f2n = nfr2 + fo2 (red), the slight difference of the repetition rates of the dual comb is δ = fr2 − fr1. In the time domain, the S(t) is the repeated interferogram with an update rate δ. In the frequency domain, beat notes in the RF range between the optical comb teeth with the nearby order can be filtered by a lowpass filter, which is usually from DC to fr/2.

Close modal

In the time domain, the pulses emitted by two frequency comb sources form pulse pairs. Because of the slightly different repetition rates of the pulse trains, each pulse pair impinges on the fast photodetector with a linearly incremental time delay. When the pulses in a pair are exactly coincident on the photodetector, just like the zero-path difference in the traditional Fourier transform spectroscopy, the constructive interference gives the center burst of an interferogram. Subsequent pulse pairs arrive on the photodetector with a linearly increasing time delay, analogous to the delay introduced by the moving mirror with constant velocity in Fourier transform spectroscopy. Because pulse pairs constantly move through each other, a new interferogram begins to form after the previous one is finished with a rate equal to the repetition rate difference δ. In the frequency domain, the pulse trains of the two sources form two sets of comb lines with slightly different comb spacing. Comb lines beat with each other. A lowpass filter from DC to fr/2 rejects the beat frequencies of the higher orders other than the adjacent comb modes. Hence, the absorption information carried in optical frequency is downconverted to the radio frequency range, which is just the Fourier transform of the interferogram series. To obtain the spectrum in the optical domain, the radio frequency needs to be upconverted by the fr/δ factor.

We set up the mid-IR DFCS with a multipass cell to detect acetone, one of the volatile organic compounds considered as a biomarker of diabetes.82,83 The experimental setup and the measured spectrum are presented in Fig. 13. The difference frequency generated mid-IR combs are carrier-envelop offset-free.126 We designed the electronics to lock the repetition rates of dual combs with a small difference δ. With the fast Fourier transform performed by a digital oscilloscope, the spectrum can be viewed almost in real time.

FIG. 13.

The experimental setup and the spectroscopic results of mid-IR DFCS for acetone detection. In (a), a screen image of the oscilloscope is presented. The yellow trace is the interferogram averaged over 80 ms. The gray traces are the FFT spectra of the reference and air. The red trace is the FFT spectrum of the acetone mixture. The top panel of (b) shows the normalized absorption spectrum (black) of mixture of 15.0 ± 0.8 ppm acetone in air and PNNL simulation (purple) of 15 ppm acetone. The methane (red) and water vapor (blue) HITRAN76 simulations are inverted in the bottom panel of (b) for viewing clarity. The CH4 and H2O mole fractions retrieved from the fittings are 1.9 ± 0.1 and 3500 ± 200 ppm, respectively. The detection limit of acetone is estimated to be about 0.8 ppm in 80 ms measurement time with a resolution of 0.3 nm.

FIG. 13.

The experimental setup and the spectroscopic results of mid-IR DFCS for acetone detection. In (a), a screen image of the oscilloscope is presented. The yellow trace is the interferogram averaged over 80 ms. The gray traces are the FFT spectra of the reference and air. The red trace is the FFT spectrum of the acetone mixture. The top panel of (b) shows the normalized absorption spectrum (black) of mixture of 15.0 ± 0.8 ppm acetone in air and PNNL simulation (purple) of 15 ppm acetone. The methane (red) and water vapor (blue) HITRAN76 simulations are inverted in the bottom panel of (b) for viewing clarity. The CH4 and H2O mole fractions retrieved from the fittings are 1.9 ± 0.1 and 3500 ± 200 ppm, respectively. The detection limit of acetone is estimated to be about 0.8 ppm in 80 ms measurement time with a resolution of 0.3 nm.

Close modal

It is worth noting that since the measurement principle of the dual frequency comb is that the pulse pairs emitted from the two frequency comb sources are interfering with each other and are asynchronously sampled, this means that essentially the cross correlation measurement of the pulse pairs is performed.

Thus, if the coherence between the two optical combs is degraded over time, it would cause serious distortion of the interferogram and the FFT spectrum. Indeed, in this case, the average of distorted interferograms would lead to a degraded signal-to-noise ratio and reduced sensitivity of the measurement. Although the frequency comb-locked to radio frequency reference has demonstrated excellent performance in many applications, its short-term stability is limited by that of the RF reference itself, which usually is about 10−11–10−12 in 1 s. Under these circumstances, the comb teeth of a visible comb source would have a linewidth of ∼5 × 103–5 × 102 Hz in 1 s, which is comparable to the usual repetition rate difference δ. Hence, any noise in combs (fr or fo noise) would cause the interferogram distortion within a few tens of milliseconds, and, consequently, the DFCS referenced to a commercial RF reference cannot reach the single comb line resolution.

To overcome this difficulty of maintaining the coherence of the two frequency combs, several schemes are demonstrated. One scheme is that the high degree mutual coherence in seconds can be maintained by locking the frequency comb to ultra-stable continuous-wave lasers. Thus, the distortion of the interferogram is eliminated, and the coherent averaging over seconds can be implemented.144,147 The second scheme is to track and record the timing jitter and phase fluctuations of the frequency combs and use them through mixing and redefining the interferogram acquisition time grid to eliminate interferogram distortion and achieve effective coherent averaging.135–137,148 The third way is to generate two frequency combs from the same laser resonator, in which case they have an intrinsic coherence. By using multiplexing technology in direction, polarization, wavelength, and transmission path, two mutually coherent pulse trains with a small repetition rate difference can be produced in one resonator, and demonstration experiments have been carried out.140–142,149–151

As a new type of spectral detection method under active development, DFCS is used to identify the species, their structure, and concentration by detecting the spectral response and analyzing it with already known spectral information. Based on the mode-locked lasers, such as solid-state lasers and fiber lasers, the comb spectrum can cover the spectral range from UV to mid-IR. The overtone and the fundamental vibrational bands of many important atmospheric constituents, such as CO2, CH4, C2H6, CH3COCH3, etc., have been investigated with the DFCS. The cavity-enhanced technique has been used to improve the detection sensitivity.152,153 Sensitive and reliable field detections of greenhouse gases have been demonstrated.122–125 However, for remote detection, the range of the existing dual comb spectrometers is relatively short, and also only the averaged values through the whole optical path can be measured. Therefore, high power frequency comb sources need to be developed in the future to increase the detection range, especially in the mid- to far-IR regions to increase the sensitivity and expand the detection to a multitude of the molecular species. Improvements in the detection techniques in combination with the comb ranging and LIDAR approaches possibly will lead to the development of distance-resolved atmospheric trace gas analyses that will have a great impact on the development of trace gas monitoring.154,155

Successful implementation of dual frequency comb spectroscopy for atmospheric sensing has promoted its rapid application to many other fields, such as materials science, biochemistry, combustion, food safety, and drug research and development.156–160 The samples to be investigated also vary considerably from gas phase to liquid or solid phase with more complicated transmission spectra and various refractive indexes.158,160 In addition, on the basis of non-linear interaction between light and matter, dual frequency comb spectroscopies were also developed to measure the two-photon absorption spectra and analyze multi-component species of biochemical materials and organic substances with a coherent Raman scheme.157,159,161,162 Moreover, with the development of the electro-optic and micro-resonator combs, more novel applications with on-chip integration potential are emerging.110–113,118,144–146 In short, the DFCS technology is rapidly developing, and it can be foreseen that with the increase of the pulse intensity in the combs and employment of nonlinear optical interactions, the applications of dual frequency comb spectroscopy will be further extended.

Vernier spectroscopy exploits the optical mode structure of a high-finesse cavity to provide both extended optical path length as well as high spectral resolution detection. Just as with CW cavity ringdown spectroscopy, a resonant optical cavity provides a multiplication of the interaction length between the laser light and the gas sample, and in addition, the mode structure of the cavity is used for spectral filtering. This filtering action is advantageous as it yields a higher effective comb repetition rate, which can easily be resolved with a simple diffraction grating, while still retaining the ability to resolve spectral features at the lower repetition rate.

The coupling of a frequency comb into an optical cavity is more complex than for a CW laser, which, apart from the transverse intensity profile matching, only requires that the laser light matches one of the resonant frequencies of the cavity. Coupling of frequency comb modes into a cavity requires that the cavity-free spectral range matches the repetition rate of the comb, a task which is further complicated by the fact that the cavity modes are not evenly spaced in the presence of dispersion, a result of both the cavity mirror coatings and the presence of an absorber in the cavity. This dispersion imposes additional constraints on the carrier-envelope offset frequency of the comb. Vernier filtering163 is the result of intentionally mismatching the comb repetition rate to the free spectral range of the cavity to form a moiré pattern of transmissions that are much more widely spaced than either the comb modes or the cavity free spectral range.

A high-finesse optical resonator has resonances that are spaced by the free spectral range FSR = 2 π c / ( n r L ), where n r is the effective refractive index, and L is the round trip length of the optical cavity. Vernier filtering takes place when every m th frequency comb mode is resonant with every n th cavity resonance by appropriate choice of the cavity length.163 It is standard to choose the cavity length in analogy with the scales on a Vernier caliper such that n = m 1 (n   1 and integer). This choice yields a resonator length that is nearly the same as a perfectly matched resonator, where the free spectral range of the cavity is equal to the repetition rate of the comb, which is advantageous to account for the induced mismatch, because a cavity mirror can then be displaced a known distance from this length using a small translation stage.

We define the Vernier ratio as the ratio between the cavity-free spectral range and the comb repetition rate FSR / f rep. We can choose this ratio to be of the form
(13)
The transmission for an optical cavity can be written as
(14)
Here, F = π R / ( 1 R ) is the finesse of the cavity, defined by the mirror reflectivity R. H max = T 2 / ( 1 R ) 2 is the maximum transmission, accounting for the product of all input and output couplers; T is the mirror transmission. The phase accumulated for a round trip in the cavity in the absence of absorption or dispersion is ϕ ( ν ) = 2 π ν L n r / c ϕ 0, where ϕ 0 is a constant phase shift of the cavity. The function H ( ν ) has maxima where ϕ ( ν ) = n 2 π. In order to perfectly couple a comb to the resonance of the cavity, we have the condition
(15)

For a comb of a particular repetition rate, we need to set the cavity length to be Lrep = c/(nrfrep), and the laser carrier-envelope offset frequency to be fceo = (φ0/2π) ⋅ frep. This corresponds to the case where the frequencies of the comb teeth are landing on the maxima of the cavity transmission function of Eq. (14).

When the matching condition of Eq. (13) is fulfilled, every m th comb mode coincides with a maximum of the cavity transmission given by Eq. (14). This yields an output from the cavity, which is similar to that of a comb having a repetition rate of m times the original repetition rate, as can be seen in Fig. 14. For a large cavity finesse, we can assume that only one comb mode is transmitted on each cavity resonance, and the condition of Eq. (13) holds. The transmission function for a comb coupled to a cavity having a lower finesse has been explored elsewhere.164 

FIG. 14.

Vernier filtering scheme for FSR / f rep = 10 / 9. Red dashed lines are frequency comb modes and black solid lines are cavity resonant modes. Large blue dots mark the transmitted comb modes, forming regularly spaced intervals, which are larger than both the cavity free spectral range and the comb repetition rate.

FIG. 14.

Vernier filtering scheme for FSR / f rep = 10 / 9. Red dashed lines are frequency comb modes and black solid lines are cavity resonant modes. Large blue dots mark the transmitted comb modes, forming regularly spaced intervals, which are larger than both the cavity free spectral range and the comb repetition rate.

Close modal

1. Highly parallelized data acquisition

The Vernier matching condition of Eq. (13) gives a cavity transmission, such that every m th comb mode is transmitted. As the cavity round trip length is continuously increased or decreased (by about one wavelength) compared to the length satisfying exactly this condition, then the next set of every m th modes will be transmitted. This cavity length scanning allows all modes to be transmitted in groups that can be easily resolved by a diffraction grating.

Detection of the transmitted comb modes is performed using a spectrometer of sufficient resolving power to detect the cavity filtered comb modes. For larger Vernier orders, this is easily done using a dispersive type spectrometer which gives spatial separation of the different wavelengths output from the optical cavity. This approach lends itself to parallel acquisition using 2D detectors such as a camera or focal plane array detector. The light transmitted from the cavity can be dispersed in one spatial direction across a 2D sensor and then swept across the perpendicular direction using a movable mirror. This can yield rapid measurement times of less than 1 s.167 

The Vernier filtered output from the cavity can be detected serially using a single photodetector164–166 or in parallel using a focal plane array detector.163,167 In Ref. 168, a Fourier transform spectrometer was used to measure the output of an enhancement cavity locked to the output of a frequency comb laser. Even higher sensitivity of the Vernier spectroscopy approach can be expected when using a mid-IR frequency comb.126 

2. Experimental setup

A femtosecond erbium fiber laser (Menlo Systems GmbH, M-Fiber) was used as a frequency comb source with a repetition rate stabilized to 250 MHz and consisted of a separate oscillator and amplifier (see the setup schematic in Fig. 15). The output of the amplifier was broadened using a highly nonlinear fiber to generate a comb spectrum ranging from 1500 nm to 1700 nm. The light from the comb was mode-matched to a scanning high-finesse Fabry–Pérot cavity consisting of two high reflectivity mirrors (Layertec GmbH), one being flat and the other concave with a 2 m radius of curvature. The high mirror reflectivity yields a cavity finesse of ∼30 000, which was confirmed with a cavity ringdown measurement. In order to precisely control cavity length and impose different Vernier ratios, the flat mirror was mounted on a high precision motorized translational stage (Newport, GTS150). The concave mirror was mounted on a piezoelectric transducer (PZT) in order to provide fast cavity length changes of larger than one wavelength.

FIG. 15.

Setup for Vernier spectroscopy. Light from the comb is mode-matched to the optical cavity, which is displaced from perfect repetition rate matching using a high-resolution translational stage (not shown). A piezoelectric transducer and a galvo mounted tilt mirror (both shown in green) move synchronously to map the different groups of comb modes onto different positions on the detector image.

FIG. 15.

Setup for Vernier spectroscopy. Light from the comb is mode-matched to the optical cavity, which is displaced from perfect repetition rate matching using a high-resolution translational stage (not shown). A piezoelectric transducer and a galvo mounted tilt mirror (both shown in green) move synchronously to map the different groups of comb modes onto different positions on the detector image.

Close modal

The detector used was a 512 × 640 InGaAs focal plane array (Princeton Instruments, PIoNIR 640) with a pixel size of 20 × 20 μm2. The detector was cooled thermoelectrically to −80 °C to reduce the dark current. Light was dispersed in the horizontal image direction of this detector using a homebuilt Czerny–Turner spectrometer incorporating a 5 × 5 cm2, 300 grooves per millimeter gold coated grating (McPherson). Using a tilt mirror mounted to a galvanometer, dispersed light was streaked across the detector in the vertical image direction (Fig. 16). This was done synchronously with the changing cavity length provided by the piezoelectric transducer such that the different groups of filtered comb modes from the cavity were mapped in the vertical image direction. Additionally, the exposure time of the InGaAs camera was synchronized with the cavity scan and galvo mirror tilt to yield scans recorded in a single image.

FIG. 16.

Formation of 2D image. The grating is oriented to disperse the light in the horizontal direction of the image, yielding the horizontal rows of spots. As the cavity length is changed, the cavity transmission has many overlaps with the comb structure of the laser, which is mapped onto the image by the tilting mirror (shown in vertical direction). This produces the vertical columns of spots on the image, which allows counting of individual comb modes. Scanning the cavity length far enough causes the cavity-comb transmission to repeat, yielding repeating absorption features. These repeating features can be used as a guide to unwrap the image into a spectrum in the manner shown by the black arrows.

FIG. 16.

Formation of 2D image. The grating is oriented to disperse the light in the horizontal direction of the image, yielding the horizontal rows of spots. As the cavity length is changed, the cavity transmission has many overlaps with the comb structure of the laser, which is mapped onto the image by the tilting mirror (shown in vertical direction). This produces the vertical columns of spots on the image, which allows counting of individual comb modes. Scanning the cavity length far enough causes the cavity-comb transmission to repeat, yielding repeating absorption features. These repeating features can be used as a guide to unwrap the image into a spectrum in the manner shown by the black arrows.

Close modal

3. Results

Shown in Fig. 17 are images that we obtained on the focal plane array detector for a cavity filled with 5 ppm acetylene and the empty cavity. The vertical image direction is the sweep direction of the tilt mirror mounted on a galvo. The horizontal direction is the grating dispersion direction. Acetylene spectrum obtained from the images of Fig. 17 is shown in Fig. 18 together with the calculated HITRAN fit. The observed absorption spectrum shown in Fig. 18 is in good agreement with previously published;167 however, it is slightly reduced in amplitude compared to the HITRAN simulation of 5 ppmv acetylene. The probable reason is that the absorption that results from the application of Eq. (16) is dependent on any wavelength variation of the cavity mirror reflectivity, as this term determines the effective interaction length with the sample. The wavelength dependent reflectivity of the mirrors in our cavity was not fully characterized for the entire wavelength region shown and as a result, the amplitudes of the peaks in the long wavelength region are somewhat reduced compared to the shorter wavelength peaks. The achieved absorption sensitivity is about 8 × 10−8 cm−1 Hz−1/2, corresponding to a detection limit of about 70 ppbv for acetylene. The spectral resolution is about 1.1 GHz in single images taken in 0.5 s, and the wavelength range is between 1510 to 1550 nm.

FIG. 17.

Images recorded using InGaAs camera for a Vernier ratio of 500/499. The image on the left is the reference image, taken in ambient air. The right image shows absorptions from the ν1 + ν3 band of acetylene at 5 ppm concentration.

FIG. 17.

Images recorded using InGaAs camera for a Vernier ratio of 500/499. The image on the left is the reference image, taken in ambient air. The right image shows absorptions from the ν1 + ν3 band of acetylene at 5 ppm concentration.

Close modal
FIG. 18.

Acetylene spectrum obtained from the images of Fig. 17 for a Vernier ratio of 500/499 (top). This is compared to line shapes simulated from the HITRAN database for 5 ppm of acetylene at 1 atm pressure and 296 K and shown in red with the inverted axis (bottom).

FIG. 18.

Acetylene spectrum obtained from the images of Fig. 17 for a Vernier ratio of 500/499 (top). This is compared to line shapes simulated from the HITRAN database for 5 ppm of acetylene at 1 atm pressure and 296 K and shown in red with the inverted axis (bottom).

Close modal
The density of spectral information is high in these images. The spots depicted in Fig. 17 have been smeared into vertical bands, as the individual spots do not occupy enough pixels on the image to be resolvable. However, using repeating absorption features, we were able to successfully recover the spectrum of acetylene by dividing each vertical band into a number of banks corresponding to the Vernier number m. The pixels in each of these banks were summed to yield a measure of the integrated intensity, which was performed both when the cavity contained ambient air and acetylene. Equivalent image positions were used to evaluate the fractional change in intensity between the cavity containing an absorber and the cavity containing ambient air. This fractional intensity change can be related to the absorption coefficient by169 
(16)

Here, L is the round trip cavity length, R is the mirror reflectivity, and Δ I / I 0 is the fractional change in intensity.

In order to calibrate the wavelength of the resulting spectrum, it is required that a known absorption feature be present in the image, as the frequency spacing can be found by counting the resolved spots in the image. In our case, since the individual comb modes were not resolved, two absorption features were used to calibrate the wavelength scale. However, when the spots can be resolved with enough image pixels, phase information can be retrieved from fits to the spot shapes.163 

For every spectrometer, the most important specifications are the resolution, sensitivity, bandwidth, and acquisition time. Compared to other spectroscopic techniques, the biggest advantage of the FCS is that these four specifications can achieve high performance simultaneously owing to the remarkable properties of the comb source. However, for each of these specifications, there is no obvious advantage. Therefore, the primary task of the future development for frequency comb spectroscopy is to find the appropriate application and to improve the specifications that are needed for this particular application.

In principle, the spectral sampling of the frequency comb spectroscopy is limited by the repetition rate, which can usually be regarded as the spectral resolution. Therefore, the most direct method to increase the sampling of the frequency comb spectroscopy is to reduce the repetition rate of the comb source. However, the low repetition rate optical comb has a long cavity and is severely affected by environmental disturbances, presenting a significant challenge. There exist two ways to circumvent this difficulty. One approach is implemented by Hébert et al.170 to use the phase-modulated pulse technique of picking one pulse out of many coherent pulses to reduce the repetition rate. Though it increases the spectral resolution, in the time domain, the sampling rate is also decreasing. Hence, the overall bandwidth is limited by the Nyquist law. The other approach is the spectral interleaving by changing the repetition rate in very small steps and stitching spectra with slightly different comb teeth.171,172 In theory, the resolution in the interleaving method can break through the comb repetition rate restriction and is only limited by the linewidth of the comb teeth, i.e., the reciprocal of the coherence time of the pulse train. But this method requires a significant increase in the acquisition time to collect multiple sets of spectra, which cannot meet the real-time or onsite requirements of many applications.

The detection sensitivity of a spectrometer can usually be concluded from the signal-to-noise ratio of the spectrum of a gas standard. The major factors affecting the signal-to-noise ratio in the FCS can be categorized as noise and experimental conditions. Noise includes the additive and multiplicative noise introduced in the measurement process. Additive noise is mainly shot noise, relative intensity noise of the comb sources, and the measurement noise caused by the limited dynamic range of the detector. Multiplicative noise is the relative time jitter and phase noise between two pulse trains in the DFCS. The experimental conditions refer to the acquisition time of the spectrum, the number of spectral elements, the measurement bandwidth, the interaction distance with the sample, and others. To evaluate the experimental results in the DFCS, Newbury et al.173 proposed the quality factor, which is the product of the signal-to-noise ratio and the number of resolved spectral elements normalized by the square root of the total acquisition time. The quality factors of most demonstrated dual frequency comb spectrometers were around 106–107 Hz1/2.173,174 The exception was the measurement with the quality factor of 2 × 108 Hz1/2 that was achieved with the continuous coherent averaging of the interferogram for 24 h.136 To compare to the traditional spectrometer, the noise-equivalent absorption (NEA) coefficient per spectral element is defined as the absorption sensitivity normalized by the square root of the ratio between the number of resolved spectral elements and the acquisition time. The fractional detection limit of the target molecule normalized by 1 s acquisition time can be estimated as NEA/(σmax ⋅ n), where σmax is the maximum absorption cross section of the target molecular transitions in the detection range for the single resolved spectral element, and n is the number density of the gas mixture. In Table II, the achieved detection characteristics of the frequency comb spectrometers with cavity-enhanced128,131,153 or open path122,125 configurations for environmental122,125 or breath analysis131 are summarized.

TABLE II.

Performance characteristics of the frequency comb spectrometers.

SpeciesFractional detection limitNEA per spectral element (cm–1 Hz–1/2)SNR@ acquisition timeResolution (GHz)Spectral coverage bandwith@center
CO2 CO153  12 ppm, 11 ppm 1.5 × 10−8 189@320 s 0.203 0.35 nm@1570 nm 
CO2
CH4122  
1 ppm
3 ppb 
7.3 × 10−10 588@300 s 0.10 70 nm@1635 nm 
C2H2167  70 ppb 1.2 × 10−9 70@1 s 1.1 40 nm@1530 nm 
C2H2128  2 ppb 3.4 × 10−11 1000@6s 0.380 30 nm@1530 nm 
CH3COCH3 C3H8O C2H6125  5.7 ppm m, 2.4 ppm m, 0.4 ppb 2 × 10−9 10@60s 2.0 400 nm@3400 nm 
H2CO
C2H6
CH4
CH3OH
OCS
HDO
C2H4
CS2
NH3
H2O131  
126 ppt
378 ppt
644 ppt
722 ppt
900 ppt
1.4 ppb
19 ppb
17 ppb
103 ppb
813 ppb 
5 × 10−11 ∼500@6 s 0.272 160 nm@3480 nm 
SpeciesFractional detection limitNEA per spectral element (cm–1 Hz–1/2)SNR@ acquisition timeResolution (GHz)Spectral coverage bandwith@center
CO2 CO153  12 ppm, 11 ppm 1.5 × 10−8 189@320 s 0.203 0.35 nm@1570 nm 
CO2
CH4122  
1 ppm
3 ppb 
7.3 × 10−10 588@300 s 0.10 70 nm@1635 nm 
C2H2167  70 ppb 1.2 × 10−9 70@1 s 1.1 40 nm@1530 nm 
C2H2128  2 ppb 3.4 × 10−11 1000@6s 0.380 30 nm@1530 nm 
CH3COCH3 C3H8O C2H6125  5.7 ppm m, 2.4 ppm m, 0.4 ppb 2 × 10−9 10@60s 2.0 400 nm@3400 nm 
H2CO
C2H6
CH4
CH3OH
OCS
HDO
C2H4
CS2
NH3
H2O131  
126 ppt
378 ppt
644 ppt
722 ppt
900 ppt
1.4 ppb
19 ppb
17 ppb
103 ppb
813 ppb 
5 × 10−11 ∼500@6 s 0.272 160 nm@3480 nm 

The spectral detection bandwidth is usually limited by the frequency comb source. The development of frequency comb sources from the deep ultraviolet to THz range was progressing at a fast pace.175,176 Together with the electro-optic and micro-resonator frequency combs, reliable coherent sources have been adopted for large bandwidth detections. Moreover, the high-performance detectors for different spectral ranges are showing fast improvements,177 which allow us to expand the variety of target molecules and improve the sensitivity of their detection.

The acquisition time of the FCS is generally short compared to the methods with tunable continuous-wave laser sources. For the direct FCS, the acquisition time is often limited by the spectrometer. While for the DFCS, the single interferogram trace acquisition time is limited by the update rate, which is the repetition rate difference. The spectral detection bandwidth is at most as wide as the pulse bandwidth and is also limited by Δ ν = f r 2 / ( 2 δ ) in dual comb setup. Hence, if the desired spectral range is narrower than that provided by the source, the repetition rate difference ( δ ) can be increased to reduce the acquisition time.178 

With the broadband coherent frequency comb source, the FCS is a natural fit to the multicomponent analysis. There have already been successful applications of the greenhouse gases monitoring, the breath analysis, and so on in different wavelength intervals.112,116,120,129,131,122–125 If the target molecular species have sharp absorption features that are not overlapping, the multicomponent analysis is straightforward. However, in many cases, the molecules have broad spectral features, and these features overlap. It remains quite challenging to accurately decompose the complicated spectrum to get the correct concentrations of the multispecies. The usual way to tackle this issue starts with the collection of spectra of various separate species in a database. After acquiring the spectrum from a multicomponent sample, many characteristic data points can be determined from the pre-examination of the sample spectrum and used as the input of the analysis model, which calculates the concentration of each component with multivariate data analysis by appropriate algorithms. The popular models include the classic least square method, inverse least square method, principal component regression, partial least squares method, neural network, etc.179 The first three are mainly for the low gas concentration of each component, so that the absorbance of each component is in the linear regime. The partial least squares method and neural network can achieve the approximation of nonlinear functions, which is suitable also for the retrieval of the high concentrations of the components.

FCS has been successfully used in high-resolution, high-sensitivity, and multi-component real-time atmospheric and breath analysis. In the direction of transferring the laboratory prototype to the field deployable instruments, the microcavity combs together with the nanophotonics will take the instrumentation to the chip scale. With the rapid development of the FCS spectrometers, spectroscopy of single events, kinetics, and microscopy will find applications in many fields such as atmospheric chemistry and respiratory diagnosis.116 

In this paper, we considered several spectroscopic techniques for sensitive detection of trace gases in the atmospheric air and in exhaled breath. Wavelength modulation spectroscopy and its application to the detection of acetone and methane were described. Both types of methane measurements point-like with a multipass cell as well as long open-path were described. In view of the relative simplicity, low cost, and robustness, this technique finds numerous applications, including those in the field conditions. WMS sensors for the detection of methane, carbon monoxide, ammonia, acetylene, carbon dioxide, nitrogen oxide, and formaldehyde were reviewed and compared. Overall, the WMS technique shows high potential for the real time, high resolution, and sensitive detection of trace gases.

Cavity ringdown spectroscopy can provide high sensitivity with the detection limit down to ppb and even ppt levels and can directly provide concentration values for target gases. At the same time, this technique does not possess high noise and vibration immunity and requires a very thorough alignment of the system.

A lot of progress in recent years in the field of spectroscopy is related to the development of optical frequency combs. Frequency comb spectroscopy has been successfully used in high-resolution, high-sensitivity, and multi-component real-time atmospheric and breath analysis. Remarkably, such measurements can be performed fast with a broadband wavelength coverage. We presented the results obtained with direct, dual comb, and Vernier frequency comb techniques. Different realizations of the approach were compared by their fractional detection limits, noise-equivalent absorption, spectral resolution, and coverage. Currently, efforts are being made to improve the key performance indicators of spectrometers based on frequency comb sources to meet different application requirements. These include breaking through the resolution limit imposed by the repetition rate, achieving high sensitivity, which is restricted by the comb and environmental noise, developing frequency comb sources in different electromagnetic wave bands, using parallel detection and other techniques to analyze multicomponent samples, reducing the data acquisition time, etc. At the same time, the development of portable, sensitive, and onsite detection equipment is the primary task for the field applications of frequency comb spectroscopy in the future.

This work was supported by the Robert A. Welch Foundation (Grant No. A1546), the Open Fund of State Key Laboratory of Applied Optics (No. SKLA02020001A12), the Shandong Provincial Key Research and Development Project (No. 2020CXGC010104), and the National Natural Science Foundation of China (Grant No. 12074439).

The authors have no conflict of interest to disclose.

The data that support the findings of this study are available within the article.

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