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Abstract
Dual-frequency comb spectroscopy has emerged as a disruptive technique for measuring wide-spanning spectra with high resolution, yielding a particularly powerful technique for sensitive multi-component gas analysis. We present a spectrometer based on two electro-optical combs with subsequent conversion to the mid-infrared via tunable difference frequency generation, operating in the range from 3 to 4.7 µm. The repetition rate of the combs can be tuned from 250 to 500 MHz. For 500 MHz, the number of detected comb modes is 440 with a signal-to-noise ratio exceeding 105 in 1 s. The conversion preserves the coherence of the combs within 3 s measurement time. Concentration measurements of 5 ppm methane at 3.3 µm, 100 ppm nitrous oxide at 3.9 µm and a mixture of 15 ppm carbon monoxide and 5% carbon dioxide at 4.5 µm are demonstrated with a noise-equivalent absorption coefficient of 6.4(3) x 10−6 cm−1 Hz−1/2.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Established methods for mid-infrared (MIR) gas analysis are tunable laser absorption spectroscopy and Fourier-Transform infrared spectroscopy (FTIR). Approaches based on tunable lasers offer high spectral resolution and sensitivity but are often limited by their covered spectral width. FTIR systems excel in spectral coverage but struggle to provide spectral resolution below few GHz, especially in combination with high acquisition rates.
Frequency combs are likely to play an important role in bridging this gap. They typically cover a broad spectral span with evenly-spaced laser modes and are employed for various applications as distance measurements [1,2], hyperspectral imaging [3,4] and spectroscopy [5].
Especially the technique of dual-comb spectroscopy (DCS) [6] is a promising candidate for a novel generation of highly sensitive and fast spectrometers. There, two frequency combs with slightly different mode spacing are combined such that one comb acts as an optical clockwork [7] for the other. This results in an intensity modulation labeled as interferogram, which itself is represented by a comb in the radio-frequency (RF) domain. The spectrum can be recovered from a fast intensity measurement of the interferogram with a single photodetector and subsequent Fourier-transformation, rendering an additional spectrometer unnecessary.
Many gases of profound interest, e.g. the greenhouse gases carbon dioxide, methane, nitrous oxide, sulfur hexafluoride, as well as toxic gases like carbon monoxide, ammonia or hydrogen sulfide - not only toxic to humans but also poisonous for fuel cells or catalysts in power-to-gas reactors [8] - exhibit strong and characteristic absorption features in the MIR. The full width at half maximum (FWHM) of the corresponding rotational vibrational absorption lines at atmospheric pressures (1 atm) is typically few GHz or less. It requires frequency combs with sufficiently small mode spacing to sample their spectral signature, if no additional methods like frequency-sweeping are implemented [9].
Different approaches have been followed to provide dual frequency combs, further referred to as dual combs, in the MIR. Optical-parametric oscillators (OPO), for which an overview is given in [10], have been used for direct generation of high resolution dual combs [11,12]. Alternatively, frequency combs from mode-locked Ti:Sa or fiber lasers [13,14] generated in the near-infrared (NIR) with subsequent nonlinear-optical frequency conversion to the MIR can be employed [15] and allow for gas sensing to analyze combustion [16] . In these realizations, the two frequency combs forming the DCS systems are generated separately. To provide the coherence between those two frequency combs, which is required for stable and coherent long-term DCS measurements, different approaches based on additional hardware and hence higher system complexity are pursued [17,18]. In contrast, DCS systems based on two frequency combs generated by electro-optical modulation of light from a single common continuous-wave (cw) laser are mutually coherent, leading to a reduced complexity [19,20]. Switching the mode spacing fast combined with an optical delay in one branch of an interferometer allows to even further simplify the setup [21]. The conversion of electro-optic combs into the MIR was demonstrated via intra-pulse difference frequency generation (DFG) of a single 10 GHz-comb [22], which requires multiple stages of spectral broadening, and with superimposed combs in a single DFG [23].
In this work, we follow the approach of Millot et al. [24] for the electro-optic dual comb generation, which combines comb initialization via fast intensity modulation and spectral broadening in a dispersion compensating fiber. It allows for direct control of the mode spacing in the range of hundreds of MHz and spectral bandwidth of hundreds of GHz [25]. Employing a fixed-frequency pump laser for the DFG conversion yields a usable spectral range from 3.15 µm to 3.5 µm [26]. With this approach, the MIR-tunability is provided by the wavelength agility of the NIR-comb itself. Limitation arises from the fact that most optical components for comb generation at 1550 nm do not provide a broad spectrum. In order to increase the tuning range of the DCS system, we combine a fixed-frequency laser source for comb generation in the NIR with a tunable optical-parametric oscillator (OPO) as pump light for the DFG to reach the MIR. Additionally, both combs are superimposed already in the NIR and converted simultaneously, allowing to maintain the intrinsic coherence and simplifying the setup.
For characterization of the spectrometer, we investigate the tunability of the system and dual comb related quantities, including the signal-to-noise ratio (SNR), linewidth of the RF-comb modes, and spectral coverage. Using acquisition times of few seconds, the spectrometer is utilized for transmission measurements of methane, nitrous oxide and a mixture of carbon dioxide and carbon monoxide for which we determine the respective concentrations.
2. Experimental realization
2.1 Near-infrared comb-source
The DCS spectrometer is based on the generation of two frequency combs from a cw fiber laser in the telecommunications band at 1550 nm. This is achieved by fast electro-optical intensity modulators and further spectral broadening within a dispersion compensating fiber. This approach has been demonstrated by Millot et al. [24], where the setup included both combs propagating in opposite directions through the same dispersion compensating fiber.
In our realization, two fully separate branches are used for comb generation to avoid any counter-propagation of optical signals before the combs fully evolve. This suppresses mixing of undesired reflections into the signals and offers flexibilities useful for system investigation. The dual comb is generated as shown in Fig. 1. A single frequency cw laser (ADJUSTIK E15 HP / NKT Photonics) centered at 1550 nm is split into two branches with equal power. The initial combs are generated by intensity modulation with benchtop modules (Modbox-PG-CBand-50 / iXBlue), delivering pulse trains with pulse duration of roughly 50 ps and an extinction ratio larger than 40 dB. The repetition rate (frep) of the internal electrical pulse generator driving the intensity modulators equals the input clock signals. The frequencies ranging from 250 to 500 MHz are set via an additional multi-clockboard. The difference in repetition rates (Δfrep) is typically chosen in the range from 2 kHz to 20 kHz. For spectral broadening of the initial combs, spanning roughly 40 GHz, the pulse trains are amplified to average powers of 100 to 400 mW with standard cw erbium-doped fiber amplifiers (EDFA). In the second step, the combs are launched into dispersion compensating fibers (SMFDK-S-010 / OFS) where they undergo spectral broadening, and optical wave-breaking occurs [27]. To optimize polarization with respect to both orientation and linearity we employ fiber-loop based polarization controllers (FPC025 / Thorlabs). Polarizing beam splitters (PFC1550A / Thorlabs) filter the desired polarization, see Fig. 1. The polarization controllers are adjusted for maximum transmission (i.e. minimizing the power of the undesired orthogonal polarization guided to the powermeter) through the polarizers once after the warm-up of the EDFAs. The comb from one branch is attenuated by 3 dB where in the other branch an acousto-optic modulator (I-FS040-2S2J-3-GH53 / Gooch and Housego) shifts the second comb by 40 MHz (Δ$f$). The electrical power driving the acousto-optic modulator (AOM) is set such that both combs have the same average optical power. The combs are then superimposed by using a polarization-maintaining fiber-coupler, which blocks the fast axis guiding the undesired polarization. This effectively acts as an additional polarizer, further suppressing imperfections during polarization control. For driving the AOM, we use a signal generator (SMA100B / R&S), which by the same time provides a reference clock. This reference clock is connected to the multi-clock board, which provides all other frequencies needed to generate the combs and to synchronize the personal computer hosted digitizer with 16-bit analog-to-digital-converters running at 250 MSPS for data acquisition.
Fig. 1. Schematic of the fiber-based electro-optic dual comb generation. Boxes indicate benchtop modules or fiber components. Solid lines stand for polarization maintaining fibers (PMF), dashed lines for PMF guiding the orthogonal polarization. All couplers have 1:1 split ratio. Legend: (IM) intensity modulator, (EDFA) erbium-doped fiber amplifier, (DCF) dispersion compensating fiber (not maintaining polarization), (PBS) polarizing beam splitter, (AOM) acousto-optic modulator, (DFG) difference frequency generation, (PD) photodetector.
2.2 Conversion to the mid-infrared
In order to maintain the mutual coherence of the two frequency combs upon conversion, they are superimposed and then simultaneously frequency-converted from NIR to MIR by a single DFG stage. In contrast to similar realizations based on a fixed-frequency pump laser for the DFG [23,26], we use a tunable pump extending the tuning range of the converted MIR combs. The conversion setup is depicted in Fig. 2. A continuous-wave OPO in a four mirror bow-tie configuration acts as the pump source for the DFG. To pump the OPO, we use a cw laser with an output power of 7 W at 775 nm (Koheras HARMONIK / NKT Photonics). This laser is focused to a beam radius of 40 µm in the center of a 30 mm long periodically-poled lithium niobate crystal (PPLN) in a thermally controlled housing mounted on a linear stage. The PPLN comprises ten different channels with poling periods between 19.5 and 21.1 µm. By temperature tuning and switching between the different poling periods, the OPO emission can be tuned in a wavelength range of 1.0 to 1.3 µm, providing up to 1.0 W of output power [28]. For frequency stabilization, the OPO is side-of-fringe-locked [29] to a temperature-stabilized low-finesse external cavity. As a result, drifts of the OPO frequency are limited to 1 MHz/s. For difference frequency generation with the dual-comb, the OPO output is coupled into a second bow-tie cavity with a finesse of 270, resonantly enhancing the power up to 70 W. This second cavity is stabilized with a Pound-Drever-Hall scheme [30]. A 10 mm long PPLN, which has 10 different poling channels with poling periods between 27.58 and 31.59 µm, is placed in one focus of the cavity with a beam waist of 65 µm. The NIR dual frequency comb is coupled out of the fiber and focused into the center of the DFG PPLN to guarantee for optimal overlap with the cavity mode. The DFG transfers the NIR dual-comb to the MIR in the range between 3.0 µm and 4.7 µm for an OPO-wavelength of 1.02 µm and 1.17 µm respectively. Phase-matching is ensured by choosing the appropriate poling period and fine tuning the temperature in a second step. Switching between two arbitrary regions of interest is determined by the time required for the tuning of the OPO. In the current setup, this requires manual adjustments and takes several minutes. The average power of the MIR dual comb is about 1.0 mW, which is typically attenuated to few hundreds of µW to avoid saturation of the photodetectors. After the conversion, the MIR dual comb is collimated using a CaF2 lens and split into a reference and a sample branch with a pellicle beam splitter. The reference branch is guided directly to a HgCdTe-detector. In the sample branch, the dual comb propagates through a Herriott-type multi-reflection cell with an optical path length of 720 cm and is detected with a second HgCdTe-detector. Both detectors (PVI-4TE / Vigo) exhibit a high detection bandwidth (> 100 MHz).
Fig. 2. Sketch of the dual frequency-comb converter. The near-infrared (NIR) combs are converted to the mid-infrared (MIR) by difference frequency generation (DFG) in a bowtie-cavity. The continuous-wave pump light for the DFG is generated by an optical-parametric oscillator (OPO) in a first bow-tie cavity, which is stabilized to an external cavity (RC). For that, a small fraction of the OPO light reflected from a surface of the air-spaced etalon (AE) is used. In addition, a part of this reflected light is fed to a wavelength meter. The OPO itself is pumped with a continuous-wave laser at 775 nm. For gas analysis, the MIR dual comb is split into two branches where one branch is detected with a fast photodiode (PDMIR1) while the other propagates through a multi-reflection flow cell with 720 cm absorption path before detection by PDMIR2. The pressure (p) and temperature (T) of the gas sample are measured downstream of the cell. For clarity the locking electronics, for which PDOPO and PDDFG provide the signals, are not depicted. Legend: (BS) beam splitter, (EOM) electro-optical modulator, (PZT) piezo-mounted mirror, (PPLN) periodically poled lithium niobate, (BS) beam splitter.
3. Mid-infrared dual-frequency comb performance
As the spectrometer performance is predominantly determined by the quality of the frequency comb, we first focus on basic comb characteristics like the signal-to-noise ratio of the rf-comb modes (comb mode SNR) and the detectable number of modes M, which yields the spectral span when multiplied with the repetition rate. In addition, we determine the linewidth of the radio-frequency beat notes, which gives insights on the coherence of the MIR combs.
For that, we define two configurations making use of the flexibilities in repetition rates and spectral bandwidth of the comb-source. The first configuration is conducted with frep = 250 MHz, where Δfrep is set to 5 kHz and the average output power for both EDFAs is 400 mW. The other configuration is using frep = 500 MHz, Δfrep = 20 kHz, and 100 mW EDFA output power. The higher EDFA power for the 250 MHz configuration leads to higher pulse peak powers for increased spectral broadening of the combs in the DCF. The parameters of both configurations were chosen such that all comb modes reside within a 10 MHz detection band centered at Δf = 40 MHz to take effects, which might be caused by the rf-comb-mode density into account. Linear detection is ensured by carefully reducing the power levels on the photodetector until out-of-band signals in the radio-frequency spectrum are eliminated [31]. In general, we record time series $\vec{x}$ of the time-domain interferograms with a sampling rate of 250 MSPS (125 MHz bandwidth), 16-bit resolution and 1 s total measurement time. From this time series the power spectral densities (PSD) are computed via
with the Fast-Fourier-Transform (FFT). In this picture, the powers of the recovered dual comb beat notes represent the multiplied intensities of the respective optical comb modes. It should be noted that the comb mode SNR derived in this section not only depends on the optical comb properties, but also on the detector, amplifier and digitizer performances. With this analysis we investigate the capability to detect the combs, although it is not given that those performance parameters directly translate to e.g. a spectroscopic SNR, which will also depend on point-to-point noise across the comb mode spectrum.We calculate the comb mode SNR as average over all powers of all radio-frequency comb modes higher than 10 dB with respect to the noise floor in between the modes. With this threshold, the comb modes consistently exceed the standard deviation of the surrounding noise. The noise level at the frequencies of comb modes is estimated by interpolating the average powers of the noise floor closest to the respective comb modes where no sidebands are present as highlighted by black areas shown in Fig. 3 (left) – here only shown exemplary for the 37.98, 38.0 and 38.02 MHz modes.. This evaluation also yields the effective number of comb modes M. The comb mode sidebands visible in the RF spectrum are proportional to the powers of their adjacent comb mode. The dominating sidebands are located at a 1 kHz offset with approx. −30 dB with respect to the comb mode. They originate from the active modulation used to stabilize the intensity modulators for comb generation. Other sidebands are attributed to mechanical noise, e.g. from a compressor for water cooling of our EDFAs. Those can couple into the DCF, leading to polarization state modulations and, in conjunction with the polarizers, to intensity modulations. To retrieve the dual comb spectra, only the maxima of the comb modes are selected, which effectively filters out the sidebands. Consequently, operating at Δfrep > 4 kHz avoids any interference by parasitic sidebands. Nevertheless, it is desirable to suppress those sidebands, as any power, which would originally reside in the comb modes, is distributed over them.
Fig. 3. (left) Zoom-in on the power spectral density of the Fourier-transformed time-domain interferogram signals, showing the resolved comb modes at 38 MHz ± 20 kHz. Sidebands originating from imperfections in electronics and vibrations are visible in the 6 kHz band – grey – centered around each mode. To derive the noise floor level for the comb modes, we average the noise floor powers between the comb modes – black – and interpolate them – red line. (right) Dual comb envelopes, which are the selected maxima of the comb modes, retrieved from the power spectral density of a single trace of interferograms acquired over 1 s for 250 MHz repetition rate. The power level of noise floor is set to zero for convenience. For higher wavelengths, the peak conversion efficiency of the DFG as well as the FWHM of the conversion gain bandwidth decrease, which is clearly visible in the 4700 nm spectrum.
Four dual comb spectra with wavelengths of 1550 nm, 3000 nm, 3900 nm and 4700 nm are plotted in Fig. 3 (right) for the 250 MHz configuration. To reach those spectral regions, the OPO was tuned to 1022 nm, 1107 nm and 1168 nm. The poling-periods for the DFG are 29.98 µm, 29.98 µm and 27.91 µm with crystal temperatures of 80° C, 63° C and 86° C respectively. The dual comb characteristics in the MIR evaluated at the central wavelength of 3000, 3900 and 4700 nm for both repetition rate configurations are listed in Tab. 1. The comb mode SNR in 1 s consistently exceeds 104 and a maximum value of 5.7(4) x 105 is reached for 500 MHz repetition rate at 3900 nm. The comb spectra are impacted by the DFG towards longer MIR wavelengths via two major mechanisms. First, the conversion window given by the phase-matching condition decreases towards longer target wavelengths due to dispersion in the PPLN. Second, the onset of absorption in the PPLN above 4.5 µm decreases the overall power of the generated DFG combs, thus reducing the number of lines above the 10 dB threshold criterion. Both effects constrain the spectral coverage of the combs towards the long-wavelength end. The impact of the DFG conversion becomes apparent in the spectrum at 4700 nm, where it leads to a reduced average SNR of the comb amplitudes – especially for the 250 MHz configuration. This is also visible in the comb mode spectrum plotted in Fig. 3 (right). The full bandwidth at −20 dB of the DFG conversion gain is roughly 440 GHz for the conversion to 4700 nm according to simulation [32] using absorption data from [33] and refractive indices from [34]. For a conversion to 3900 nm, the full bandwidth at −20 dB exceeds the maximum span of the dual combs by far, and thus imposes no narrowing effect on the comb span. Broader simultaneous conversion can be achieved by using shorter length of the PPLN or employing a chirped PPLN. The tradeoff is lower conversion efficiency, which could be counteracted using waveguides as in [15].
Table 1. Dual frequency comb characteristics
The evolution of the comb mode SNR in dependence of the integration time, which equals the length of $\vec{x}$, see Eq. (1), is of particular interest when aiming for high spectra acquisition rates – an additional advantage of dual comb-based spectrometers. For the analysis, the power spectra with integrations times up to 4 s at 3 µm wavelength are computed, and the comb mode SNR is determined with the procedure outlined above. The mode threshold is set to 0 dB instead of 10 dB to account for lower mode powers occurring for short integration times. The resulting SNR is plotted in Fig. 4 (left) for the average over all comb modes for the 500 MHz configurations (all). In addition, the evolution of a weak mode at 35.5 MHz in the RF-domain, which is situated at the edge of the comb spectrum, and a high power comb mode at 39.5 MHz (strong) close to the center frequency are plotted.
Fig. 4. (left) Evolution of the signal-to-noise ratio of the comb modes (comb mode SNR) calculated from a continuously digitized interferogram series with a comb repetition rate of 500 MHz. “All” represents the average over all comb modes. In addition, the evolution of a mode residing at the edge of the comb spectrum (weak) and one in the center (strong) are plotted. The interferogram series is cropped to the respective integration time. (right) Zoom-in on a single comb mode resulting from a 3 s time series, which yields a frequency resolution of 0.33 Hz of a Fourier transform. Fitting a Cauchy distribution results in a FWHM of 0.14 Hz.
The evolution of the comb mode SNR scales linearly with integration time up to 3 s. The increasing integration time simultaneously increases statistics as well as increases the resolution of the power spectra. Hence, the contrast of the actual comb mode with respect to the surrounding noise floor is increased. It is important to consider this, especially when aiming for fast acquisition rates. More explicitly, Δfrep defines the maximum possible spectra acquisition rate. Fourier-transforming a time series with duration 1/Δfrep results in a resolution, for which each comb mode resides in one frequency bin. In that case, all noise contributions, e.g. from the detector and amplifier within a frequency band of Δfrep, centered at the respective comb mode, are added to this signal as well. However, those contributions do not reflect the light-sample interaction and should be kept as low as possible. As can be seen in Fig. 4 (left) a comb mode SNR of 30 dB in average is reached in already 1 ms, which can be instrumentalized for fast spectra acquisition rates.
To quantify the coherence of the combs, we evaluate the comb mode linewidth. In Fig. 4 (right) the normalized spectrum zoomed in one comb mode is shown for an integration time of 3 s, which results in a resolution of 0.33 Hz. Fitting a Cauchy distribution results in a FWHM of 0.14 Hz, which is even below this resolution limit. For integration times larger than 3 s, the averaged comb mode SNR saturates or even drops as can be seen in Fig. 4 (left). This is mainly attributed to instabilities of the resonant enhancement cavity for the DFG process. Nevertheless, it can be concluded, that coherence of the combs can be ensured up to 3 s with the current setup.
It should be noted that the optical linewidth of the comb modes cannot be determined with this procedure, since every contribution common to both combs - like the linewidth of the pump laser and the OPO – does not express itself in the beat signals. We estimate, that the OPO linewidth with typical values of < 500 kHz, is the dominating contribution [28]. The contribution from the cw laser can be neglected, as it is below 1 kHz according to the manufacturer. According to the presented linewidth analysis, Fig. 4 (right), we conclude that other contributions caused by phase noise from the modulators and fibers in both comb branches – especially the 1 km long DCF for comb generation - have a negligible effect as well.
4. Retrieval of transmission spectra
The basic data for the determination of the species concentrations in a gas sample are transmission spectra. In the following, the steps to retrieve normalized transmission spectra from the recorded dual comb spectra are described.
From the amplitude spectral density of the FFT of recorded time series with 1s length, we select the comb mode amplitudes, resulting in the dual comb spectra S (see Fig. 3 (left)). As we aim for high sensitivity, we use the 500 MHz configuration to utilize the highest comb mode SNR available. The signals of the reference and sample detectors are recorded simultaneously, and the respective dual comb spectra are labeled as ${S_{\textrm{ref}}}$ and ${S_{gas}}$. Their ratio spectrum $R{S_{gas}}$ accounts for the comb envelope structure, as visible in Fig. 3 (right), and is given by
From these ratio spectra, the transmission spectra T are calculated as the quotient of two subsequent measurements from both a sample gas and nitrogen (N2) filled cell according to
which accounts for the cell’s transmission properties.An exemplary “100-%” transmission spectrum is shown in Fig. 5, where the N2-filled cell is taken for both, sample and the N2 spectra. Both spectra are taken 3 minutes apart. When repeating this type of measurement, we typically find systematic deviations from the expected 100-% transmission. These deviations originate from instabilities in the comb envelopes, which are caused by drifts in optical powers in between the acquisitions of the spectra (RS). We treat these deviations, in the following referred to as baseline, by fitting a 2nd-order polynomial function ($\textrm{pol}{\textrm{y}^{(2 )}}$). This baseline function with parameters obtained by the fit is then used to normalize the derived transmission spectra, yielding the normalized transmission shown in Fig. 5 (bottom). The noise equivalent absorption coefficient (NNEA) is calculated from the standard deviation of the normalized transmission spectrum, taking the total absorption path of 720 cm into account. The accumulated integration time is 2 s for both, sample and reference spectra. For six measurements, an average NNEA of 6.4(3) x 10−6 cm−1 Hz−1/2 is found. The use of higher order polynomials does not further improve the NEA. Hence it is chosen as hypothesis for the baseline underlying the transmission of a sample. This low polynomial order of the baseline is beneficial as it will be more easily discriminated from more complex structures, e.g. line profiles of gas absorptions, during fitting later.
Fig. 5. Baseline estimation to normalize the measured transmission spectra. The recorded data represent the ratio of two nitrogen spectra at 3.3 µm, which are derived from 1 s acquisition time and are taken 3 minutes apart. A 2nd-order polynomial function is fitted to the recorded spectrum and used for normalization. The standard deviation of the normalized spectrum for this measurement is 3.2 × 10−3 as indicated by the grey shaded area.
The x-axis is calculated for each NIR comb separately, where the optical mode spacing is ${f_{\textrm{rep}}}$ (+$\Delta {f_{\textrm{rep}}}$ likewise) and one comb is shifted by Δ$f$. The repetition rate ${f_{\textrm{rep}}}$ is derived from the master clock (internal reference clock of R&S SMA100B) with an accuracy better than 10−7. The axes are averaged and shifted to the central spectral frequency in the MIR, where the central frequency is estimated by the difference frequency between the OPO light and the NIR cw laser used for comb generation. The frequency of the free-running NIR cw laser is known with a precision of 5 GHz, while short-term drifts are 0.01 MHz/s in the worst case known from an a-priori calibration, for which a wavelength meter (WS7 / High Finesse) was used. The frequency of the OPO is measured continuously during the operation of the spectrometer and drifts of up to 1 MHz/s are observed. This motivates limiting the data acquisition to few seconds to avoid smearing out of the absorption profiles later. Drifts of the NIR cw laser do not contribute significantly. The remaining uncertainty in the absolute x-axis offset is accounted for by allowing a global frequency shift ${x_0}$ during fitting of the spectra.
As a side effect of the system layout with superimposed MIR combs, both combs interact with the sample, but at slightly different optical frequencies - on average $\Delta f = 40\; \textrm{MHz}$ apart. While the resulting beat note represents a single spectral element, it contains the attenuation information from two slightly different spectral positions, leading to systematic deviations of the retrieved data from the true spectrum. The magnitude of the deviation caused by the 40 MHz split depends on the widths of the absorption lines. As an example, the resulting absorption deviations for nitrous oxide at 3.9 µm with 100 ppm concentration under atmospheric pressure are calculated to be less than 2 ‰. Compared with the NNEA obtainable within 2 s acquisition time (see Fig. 5), these effects remain too small to be observed.
5. Analysis of trace gases
In order to give a first demonstration of the capabilities for trace gas detection we choose 3 sample mixtures and tune the spectrometer to the spectral regions of interest, where the respective molecular signatures are expected.
To gain first insights on the capabilities to retrieve gas concentrations, we define a simple model function $\; {f_{\textrm{fit}}}$, which will be fitted to the respective transmission spectra (T). It is composed of the baseline hypotheses derived in section 4, and a simulated transmission spectrum using the HITRAN database [35]. The simulated spectrum is composed of all absorption lines, assuming Voigt-profiles. For compatibility with HITRAN, the values of the x-axis are converted to wavenumbers [cm−1] before fitting:
Free parameters are a global wavenumber offset ${x_0}$, the volume mixing ratios ($\overrightarrow {VMR} $) of the gas species used to calculate the absorption coefficient α and the baseline coefficients $\vec{c}$. The total absorption path length L is 720(14) cm. Pressure and temperature of the gas cell are held constant at their respective measured values.
In three separate measurements, labeled as I, II and III, the spectrometer is tuned to 3.3 µm to detect CH4 (I), to 3.9 µm for N2O (II) and to 4.5 µm for a mixture of CO and CO2 (III). The OPO was tuned to 1056 nm, 1107 nm and 1154 nm with poling-periods for the DFG of 30.49 µm, 29.98 µm and 28.28 µm and crystal temperatures of 58° C, 90° C and 143° C. The different line shapes and overlaps of the gas absorptions provide a variety of scenarios to test if the respective molecular signatures can be recovered with the recorded transmission spectra. The time delay between the nitrogen spectra $R{S_{\textrm{N}2}}$ and sample spectra $R{S_{sample}}$ was 60 s, and transmission spectra are derived according to Eq. (3). The measured transmission spectra as well as the simulated spectra are shown in Fig. 6. For convenience, the plotted spectra are already normalized with respect to the baseline determined by the respective fits according to Eq. (4).
Fig. 6. A) Transmission spectra of methane (CH4) (I), nitrous oxide (N2O) (II) and a mixture of carbon monoxide (CO) with carbon dioxide (CO2) (III) at atmospheric pressures and room temperature. For the individual measurements I to III, the central wavelength of the dual frequency comb was set to 3.3, 3.9 and 4.5 µm, respectively. B) Simulated spectra based on HITRAN providing the best fit to the experimental spectra. c) Residues between measured spectra and model fit. The residues exhibit standard deviations below 3.2 × 10−3. Systematic deviations are expected as the used HITRAN parameters, e.g. pressure broadening coefficients are stated to be correct only within 2% to 5% for N2O at 3.9 µm and contribute to the residues as well.
For I, a mixture of 103.3 ppm ± 2% CH4 in synthetic air is further diluted with nitrogen to reach a target concentration of 5 ppm. For, II the supplied mixture of 99.8 ppm ± 2% N2O in nitrogen was used without further dilution. For measurement III, we mixed two supplied dilutions of 59.5 ppm ± 2% CO in synthetic air and 19.9% ± 2% CO2 in synthetic air with 50:50 ratio. This mixture was further diluted with N2 to further reduce the concentrations to approximately 15 ppm CO and 5% CO2. For mixing of the gases, three mass flow controllers (EL-FLOWprestige / Bronkhorst) were used. The gas mixtures, their respective target gas concentrations with uncertainties derived from gas mixtures and mixing procedure and the concentrations obtained by the fit, see Eq. (4), are listed in Tab. 2. For the calculation of the line shapes, only the air-broadening coefficients from the HITRAN database were used.
Table 2. Target and measured gas concentrations for measurements I, II and III
The uncertainties on the derived concentrations represent the uncertainties of the fit results σ. For CH4, N2O and CO, the derived concentrations deviate by 3.3% from expected concentration, for CO2 the deviation is 6.6%. The noise-equivalent-absorption coefficient is calculated from the standard deviation of the residues, see Fig. 6, and is below 6.2 × 10−6 cm−1 Hz−1/2. It matches with the findings for the nitrogen spectra comparison presented before and is in the same order of magnitude as in [36].
The precision of the determined concentrations considering the uncertainties σ is consistently in the permille range. Given this precision, the imperfection in accuracy becomes apparent. Various aspects, which are not included in the error budget in Tab. 2, are contributing to this concentration determination as well. Line intensities listed in HITRAN are precise to roughly 1% to 5%, and the length of the total absorption path has an uncertainty of 2%. In addition, the fit model, see Eq. (4), suffers from uncertainties of the simulation parameters. The air pressure broadening coefficients exhibit an uncertainty of 1% up to 10%. Due to the imperfect approximation of air as a dilutant, further deviations in the resulting line shapes are to be expected. The investigated gas mixtures have nitrogen concentrations that deviate by more than 10% from air. As the pressure broadening coefficients of air are typically few percent larger than of nitrogen, this also contributes to the uncertainty budget. As a result, an incorrect broadening of the Voigt profiles differs from the line shape simulated by the fit function. During regression, this may be compensated by an increasing contribution of the simultaneously fitted baseline and introduces an error in the determined concentration.
For CO2, most absorption lines investigated originate from exited states. A mismatch in temperature of 1 K leads to a relative change on the line intensity of 1.7% or more – depending on the respective lower states. With the temperature and pressure sensor being placed downstream of the gas outlet and housing covering the resonators and cell this might lead to the increased deviation found for CO2. To conclude on accuracy, improvements in the experimental approach and spectroscopic data are needed.
Using calibrated gas mixtures and synthetic air as dilutant as well as conducting systematic measurements including pressure series to retrieve the required spectroscopic data with higher precision will allow to better quantify the contributions to the uncertainty budget. In addition, the temperature and pressure sensors could be directly installed inside the transmission cell. Improvements in system stability might allow to improve the photometric accuracy to a level, where the baseline impact cannot be resolved and hence can be excluded from the fit. Alternatively, gases can be measured at lower pressures, which leads to a narrowing of the absorption profiles. In combination with the possibility to tune the dual comb to a spectral region, where parts of the recovered transmission spectra show no absorption, the fit will be able to better discriminate between the baseline and the molecular signatures. Probing narrower absorption profiles is supported by the system due to the flexibility in the repetition rates of the EO-combs. Repetition rates even below the presented 250 MHz are in principle accessible [26]. Adjusting the repetition rates allows for optimization of the spectral sampling with the smallest number of comb mode required and hence leverage the comb modes SNR.
6. Conclusion
We present a mutually coherent dual comb spectrometer for gas sensing, freely tunable over the mid-infrared range of 3 to 4.7 µm. For this purpose, an EOM-based dual comb is converted from the NIR via DFG to the MIR. Using a tunable OPO as pump allows to position the dual comb across the full range of 3 to 4.7 µm. The system allows to choose repetition rates from 250 MHz to 500 MHz. The number of comb modes can be adjusted from 400 to 1800 and be detected with a signal-to-noise ratio exceeding 105 to 104 respectively. A single spectrum spans 450 GHz (15 cm−1) for 250 MHz repetition rate and 240 GHz (8 cm−1) for 500 MHz. The coherence time of the combs derived from the FWHM of the rf-comb modes is 3 s. Transmission spectra of CH4 at 3.3 µm, N2O at 3.9 µm and a mixture of CO and CO2 at 4.5 µm are taken in 3 different measurements and show good agreement with simulations using the HITRAN database while the normalized NNEA is 6.4(3) x 10−6 cm−1 Hz−1/2. The concentrations of the gases are determined with relative uncertainty in the per-mile range in 2 s of total integration time. This validates the potential of the technique of dual comb spectroscopy – the parallel sensing of multiple spectral elements to cover multiple absorptions features while maintaining high sensitivity and acquisition speed.
Future challenges are to improve the robustness, especially for the NIR-to-MIR conversion, in order to further improve in photometric accuracy and to enable gas analysis in complex gas matrices with high accuracy. In addition, converting to longer wavelengths around 10 µm would allow to address a different set of gas species.
Funding
Fraunhofer-Gesellschaft.
Acknowledgements
This work was supported by the Fraunhofer and Max Planck cooperation program.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available but may be obtained from the authors upon reasonable request.
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