1. Introduction

Laser absorption spectroscopy (LAS) is a powerful technique that can measure quantitative species concentration, temperature, and pressure. Although standard laser absorption is typically a straightforward experimental setup, often accomplished using a simple pitch-and-catch approach, it is hindered by the need to detect—particularly for minor species—small absorption features within a large, nonuniform background. This renders single-shot measurements difficult because of dynamic-range limitations of many detectors and shot-to-shot laser intensity fluctuations (i.e., background fluctuations). For this reason, several LAS variations have been developed to reduce noise induced by large background signal (e.g., wavelength modulation) [1,2], utilize strong line-strength transitions (e.g., electronic or fundamental vibrational transitions) [3,4], or increase the effective path length to increase the absorption rate (e.g., cavity ring-down spectroscopy) [5,6]. LAS using fundamental vibrational transitions in the mid-infrared (∼2.5–25 μm) is of particular interest for single-shot measurements, given the relatively high absorption rates of fundamental transitions as compared to those of vibrational overtones, which can be accessed using more readily available near-infrared tunable-diode laser technology. In addition, all molecules except homonuclear diatomic species have infrared-active fundamental vibrational transitions that are unique to the molecule, allowing species selectivity.

In order to use absorption features to measure gas temperature, at least two transitions must be probed simultaneously to obtain the relative populations in multiple quantum states. Although some techniques, such as tunable-diode LAS (TDLAS), often limit the measurement to two transitions, additional transitions provide higher accuracy considering relative populations can be compared across several transitions. This multi-transition approach is exploited in dual-frequency-comb spectroscopy, in which the broad spectral envelope spanned by the frequency comb is used to excite multiple absorption features simultaneously, and the dual-comb approach allows rapid acquisition of the time-domain response of these spectral features [7]. Outside of the context of frequency-comb absorption measurements, the broadband aspect of ultrashort [typically femtosecond (fs) duration] pulses has been less frequently exploited for direct single-laser-shot absorption measurements, often limited by spectral instabilities associated with supercontinuum sources [8]. However, recent demonstration of fs-duration mid-IR pulses used directly as LAS sources has emphasized the capabilities of such sources to provide multi-line direct absorption measurements— spanning 30 nm near a central wavelength of 3.3 μm—of fundamental molecular vibrational transitions under single-shot conditions [9].

One particularly intriguing aspect of the use of ultra-short, fs-duration pulses as an absorption light source is that absorption features entrained in the broadband excitation pulse following interaction with gas-phase species exhibit narrow linewidths—indicative of long-duration [greater than picosecond (ps)] responses in the temporal domain. Fourier transform absorption spectroscopy techniques that use fs-duration pulses exploit this temporal behavior by interfering a series of replica fs-duration pulses with the molecular free-induction-decay (FID) response in the time domain; the resultant Fourier transform produces the frequency-domain absorption spectrum [7,10–16]. These techniques, however, are restricted by the need for multiple pulses to sweep through a time series to produce a single Fourier-transformed spectrum. Moreover, the measured spectra still retain the background characteristics of the light source, similar to standard absorption methods. However, several approaches have been implemented to remove this background, either via data processing [17] or inherent interferometric approaches to remove the impulsive component from dual-comb spectroscopy signals [18,19]. Recently, time-resolved optically gated absorption (TOGA) has been demonstrated to capture essentially background-free, broadband resonant absorption features under single-laser-shot conditions. TOGA exploits the timescale difference between a fs-duration laser pulse used as a LAS light source and the long-lived [ps to nanosecond (ns)] features of the molecular FID response by using a time-delayed ps-duration gate pulse to capture exclusively a portion of the molecular response while dramatically suppressing the fs-duration impulse [20]. This first demonstration of TOGA probed electronic absorption features of both atomic rubidium and hydroxyl (OH) radicals using a time-asymmetric gate pulse that induced frequency upconversion and downconversion, respectively, in a nonlinear medium to capture the resonant absorption features. The work presented here extends the capabilities of this TOGA technique into the mid-infrared (mid-IR) spectral regime, allowing direct multiplexed excitation and well-resolved single-laser-shot detection of rovibrational structure associated with fundamental vibrational transitions of gas-phase species. This mid-IR TOGA detection scheme has the important added benefit that the frequency-upconversion process inherent to the gating step of TOGA shifts the measured spectral features from the mid-IR region into the visible range, allowing detection using standard visible CCD cameras, which provide significant advantages as compared to mid-IR detectors [21], including significantly reduced dark counts and operation without the need for cryogenic cooling.

Methane (CH₄) is used as a target species in this work based on its common role in combustion environments as well as its spectral isolation from other combustion-relevant species. The TOGA approach employs two laser beams (Fig.  1), referred to as the absorption and gating beams; the absorption beam is tuned to span absorption resonances of the species of interest, whereas the time-asymmetric gating beam is used for time-gated isolation—via frequency mixing—of the long-lived molecular-response component present in the absorption beam following interaction with the sample of interest. Only the broadband absorption beam is directed through the sample of interest in TOGA; gating of the molecular response is facilitated via sum-frequency generation (SFG) or difference-frequency mixing in a nonlinear mixing crystal [20] outside of the absorbing medium. The narrowband gating beam is delayed by adjusting its optical path length such that it arrives at the nonlinear mixing crystal at a delay (order of picoseconds) that allows temporal overlap of the gating beam with the long-lived molecular-response component of the absorption beam while suppressing or rejecting the impulsive, fs-duration component of the absorption beam that produces the broadband background.

 

Fig. 1. Mid-infrared TOGA experimental setup showing the absorption beam (3.3 μm) and gating beam (800 nm). OSC: oscillator; AMP: amplifier; OPA: optical parametric oscillator; NDFG: non-collinear difference frequency generation; DL: delay line, BS: beamsplitter; E: étalon; SFG: sum-frequency-generation crystal; M: mirror; DM: dichroic mirror; BD: beam dump; CCD: charge-coupled device. Simulated spectra depicting the broadband absorption pulse and the CH₄ absorption spectrum at 300 K and 1 atm are also shown (inset).

Download Full Size | PDF

2. Experimental details

In the work described here, an amplified Ti:sapphire ultrafast system (Coherent Astrella; 5 mJ/pulse near 800 nm at 1 kHz; 60–100 fs pulse duration; 270 cm⁻¹ bandwidth) was used as the initial source for both beams (Fig.  1). To produce the mid-IR absorption source, an optical parametric amplifier (OPA) (Coherent, TOPAS-Prime) was pumped by approximately 4 mJ/pulse of this amplifier output to produce signal and idler beams (1 mJ/pulse combined); these signal and idler beams were subsequently directed into a difference-frequency generator (Coherent, NDFG) to produce tunable mid-IR output. As indicated in the inset of Fig.  1, the absorption beam was tuned to ∼3.3 μm (∼10 μJ/pulse), assuring maximum overlap with the R-branch rotational manifold of the fundamental (Δn = +1) υ₃ vibrational mode of CH₄, thereby ensuring that high-J rotational states could be observed at high temperatures. The direct output of this mid-IR beam was used as the absorption beam in these experiments; no additional pulse shaping has been conducted to ensure transform-limited pulses. The remaining 1 mJ/pulse from the amplifier was directed into a Fabry–Pérot étalon [TecOptics; free spectral range (FSR) = 288 cm⁻¹; finesse ∼109] to produce the time-asymmetric gating beam via spectral narrowing, increasing the pulse duration while maintaining a sharp rising edge (∼200 fs) [22].

The temporal gating in this work was facilitated via sum-frequency generation (SFG) in a nonlinear crystal (LiIO₃, United Crystals; type I, θ = 20°). The gating pulse was delayed ∼6 ps after the peak of the impulsive component of the absorption beam via a retroreflecting delay line such that it provided upconversion exclusively of the long-lived molecular response contained within the absorption beam while rejecting the broadband, fs-duration component. For mid-IR absorption demonstrated here, this process has the additional benefit of shifting the observed signal into the visible spectral regime (∼640 nm) for ease of broadband, high-resolution detection. The upconverted TOGA signal was separated from the absorption (3.3 μm) and gating (800 nm) beams with dichroic mirrors and subsequently directed into a 1 m spectrometer (grating: 1200 grooves/mm) equipped a CCD camera (Andor, iDus) to detect the spectrally resolved TOGA signal at the laser repetition rate.

Two sample setups were used to facilitate adjustment of temperature and CH₄ concentration; these include a temperature-controlled gas cell containing dilute CH₄ in nitrogen and a near-adiabatic, laminar methane–air diffusion flame operated at fuel-rich conditions. The heat-tape-wrapped cell allows adjustment of pressure, species concentrations, and temperature, which was monitored for calibration purposes by three thermocouples inserted along the length of the cell. This 25.4 cm long cell was filled—following several purge/fill cycles—with an N₂/CH₄ mixture containing a CH₄ mole fraction ($x_{{\rm C}{\rm H}_4}$) of 0.01 at 100 mbar. For high-temperature measurements at flame-relevant conditions, a Hencken burner [23] with a 25.4 mm square cross section was used to stabilize a laminar flame at varying fuel:oxygen equivalence ratios, ϕ. Because CH₄/air mixtures above ϕ ∼ 2 exceed the flammability limit (observed by flame blow-out at higher ϕ), a gas mixture with the N₂:O₂ ratio reduced to 3—below that of air (3.76)—was used, thereby allowing stable flame operation up to ϕ = 6.

3. Results and discussion

Initial measurements were performed in the heated gas cell to provide temperature and CH₄ concentration calibration. In addition, the well-controlled conditions provide an opportunity to optimize the fitting routine that is used to determine the temperature. Representative single-shot spectra at three select temperatures—determined from the average of the three thermocouple measurements—are shown in Fig.  2 following subtraction of the weak residual broadband upconverted background signal that remains at this gating-pulse delay (6 ps), the spectrum of which is shown in Fig.  2(d). This weak residual background signal likely arises as a result of temporal overlap between the decaying, time-asymmetric ps-duration gating pulse and weak secondary reflections of the absorption beam by transmissive optics along the absorption beam path, similar to those observed in previous TOGA measurements of electronic transitions [20]. The linewidth of the gating beam (2.6 cm⁻¹; approximately 10× the spectrometer resolution) is the limiting factor that dictates the spectral resolution of the measurement; however, this resolution is sufficient to resolve multiple rotational transitions within the observed spectra, which span ∼150 cm⁻¹ (∼160 nm near the central wavelength of 3.3 μm). The Q-branch of the absorption spectrum is visible near 3018 cm⁻¹ but is much weaker than the R-branch transitions, since the absorption beam spectrum was tuned to be centered over the R-branch for greater temperature sensitivity. As the temperature increases, relative initial state populations in higher rotational states (located at higher frequencies) are clearly observed to increase.

 

Fig. 2. Example single-laser-shot mid-IR TOGA spectra in a static cell at three temperatures, measured at a gating-pulse delay of 6 ps following the impulsive peak of the absorption beam. (a)-(c) Data and simulated fits for three nominal temperatures described by the mean temperature from thermocouples in gas cell (T_thermo). T_fit corresponds to the extracted temperature of the depicted laser shot from least-squares fit of the simulated spectrum. Residuals, calculated as the difference between the experimental spectrum and the best-fit simulated spectrum, are included in each panel. (d) Residual background signal spectrum obtained at the same gating-pulse delay (6 ps) under evacuated-cell conditions.

Download Full Size | PDF

The measured TOGA data were compared to simulated spectra via least-squares fitting to determine the temperature. The simulated data were computed by modeling the effects of both the absorption and gating beams on the temperature-dependent resonant absorption spectra of methane, which were extracted from the high-resolution transmission molecular absorption database (HITRAN) database [24] over the 2700–3500 nm spectral range. The mid-IR absorption beam spectrum was not measured directly; instead, it was modeled using a Gaussian frequency domain profile to match the measured experimental central frequency—centered over the R-branch of the CH₄ absorption spectrum near 3100 cm^-1—and bandwidth of this beam as determined by the sum-frequency spectrum produced upon mixing with a temporally overlapped gating pulse. Laser absorption was modeled as resolved frequency domain depletion within the broadband absorption-beam spectrum using the temperature-dependent database of spectra acquired from HITRAN. The gating beam was modeled to match its measured spectral profile; this spectrum consists of a series of Lorentzian profiles equally spaced by the 288 cm^-1 FSR of the etalon and weighted by the spectral profile of the input broadband beam used to produce the gating pulse. Frequency mixing was modeled as a convolution of the Beer’s law–modified absorption pulse and a temporally delayed gating pulse, thereby producing the simulated TOGA spectra for fitting to experimental results. The best-fit simulated data exhibit good matches to the experimental spectra. At most frequencies, the absolute difference in signal is less than 0.1, as indicated by the residuals. Moreover, the simulated temperatures are in close agreement with experimental temperatures averaged across thermocouple measurements.

Statistical analysis of the fidelity of the best-fit temperatures was conducted on single-laser/single-detection spectra from 300 to 575 K. The mean temperature extracted from 100 single shot spectra and from the three thermocouples are shown in Fig.  3. Error bars are included, which indicate the range of temperatures extracted from the thermocouples (horizontal axis) and the standard deviations of the temperatures calculated from the single shot TOGA measurements (vertical axis). Overall, the mean temperatures acquired from TOGA were, on average, 2% different than the mean temperatures acquired from the three thermocouples. Moreover, the average standard deviations (or precision) of 9–17 K over this temperature range are, on average, 4% of the mean temperatures.

 

Fig. 3. Simulated best-fit temperature (T_fit) plotted against the temperature acquired from the thermocouples that were placed inside the gas cell (T_thermo). Vertical axis error bars indicate the range of temperatures acquired from the thermocouples; horizontal axis error bars indicate standard deviations of 100 single-shot measurements from TOGA.

Download Full Size | PDF

Further measurements of CH₄ TOGA were carried out under fuel-rich flame conditions approximately 10 mm above the surface of a Hencken burner. The best-fit temperatures obtained from these measurements are shown in Fig.  4, with error bars indicating one standard deviation. Figure  4 also includes the calculated equilibrium flame temperature and $x_{{\rm C}{\rm H}_4}$ under adiabatic conditions. Note that the adiabatic calculated $x_{{\rm C}{\rm H}_4}$ increases exponentially from 1 ppm at ϕ ∼ 2.5 to ∼10000 ppm at ϕ ∼ 3.25 before leveling off to a more linear relationship at higher ϕ values. The standard deviation for these measurements is less than 2% different than the mean, indicating 2% precision. The temperatures calculated from CH₄ TOGA measurements are slightly lower than those predicted from the adiabatic flame calculation. This is expected, considering the flame likely has heat loss to the burner surface. Although the measured temperatures are slightly lower than those from the adiabatic flame simulations, the trends between the simulations and experiment are similar. Overall, this approach demonstrates the capability to extract single-shot temperatures using CH₄ TOGA in flame conditions down to at about 1000 ppm over a 25 mm length.

 

Fig. 4. Best-fit temperature (T_fit) measurements in a Hencken flame and calculated equilibrium adiabatic temperature (T_equil) and methane mole fraction ($x_{{\rm C}{\rm H}_4}$) plotted with respect to equivalence ratio, ϕ.

Download Full Size | PDF

From Figs.  3 and 4, it was shown that the measurement precision was 4% in low temperature conditions (300–575 K) and 2% in high temperature conditions (700–900 K). In addition, the detection sensitivity in flame conditions was ∼1000 ppm over a 25 mm length. In general, these 2 factors can be dramatically improved by the removal (i.e., background subtraction) and stability (shot-to-shot fluctuations) of a small degree of residual broadband background signal that remains without the presence of CH₄. This residual background is present predominantly because of secondary reflections within the probe beam path; as a result, weak secondary pulses, typically an order of magnitude weaker than the main gating pulse, have a small degree of temporal overlap with the impulse, broadband excitation pulse within the mixing crystal, contributing some residual background signal. To better understand the impact of fluctuations in this background signal as well as random shot-to-shot noise fluctuations, the temperature errors produced by both of these contributions were separately characterized by simulating a CH₄ TOGA spectra at 1000 K, adding background interference, and inputting the new spectra into the least-squares algorithm to determine the temperature with the addition of background interference.

To understand the uncertainty introduced by the remaining background signal, replicas of measured residual background signal [shown in Fig.  2(d)] were added to the simulated 1000 K TOGA spectrum at different levels, determined by the maximum TOGA to background signal ratio. The percent error for different signal-to-background ratios is shown in Fig.  5; an expanded spectrum of the remaining background is shown in the inset. At relatively low ratios, the error is as high as 10% near a ratio of 1. As the signal ratio becomes larger, the error decreases. Above a signal ratio of approximately 25, the error from the stable background is less than 1%. Measurements in the gas cell always had signal ratios above 100, and hence had little error contribution from the fluctuating background signal. Temperature measurements in the Hencken flame, however, had signal ratios of 20 and 80 at ϕ = 3 and 6, respectively. Thus, a maximum of approximately 1% error was accumulated at ϕ = 3 from the fluctuations in the background signal.

 

Fig. 5. Simulated error at 1000 K when the broadband, residual background signal (shown in the frequency domain within the inset) or random noise are added to the TOGA signal. The shaded area represents one standard deviation of the error for a given signal ratio.

Download Full Size | PDF

In a similar way, error from the random background noise—associated with random shot-to-shot fluctuations in the spectral profile of the absorption beam—was characterized by adding a random noise distribution to the TOGA signal such that the signal-to-noise ratio (SNR) varied from 1–100. Here, the SNR is defined as the ratio of the maximum TOGA signal to 1σ standard deviation of the noise. Since the noise was simulated as a random distribution, 100 samples were calculated to determine the mean and 1σ standard deviation of errors, indicated by the solid line and shaded area in Fig.  5. At relatively low SNRs, the error was 13%–15% and with little deviation (i.e., the temperature converged to similar incorrect temperatures). As the SNR approached 15, the percent error dramatically reduced to 1%, on average. However, the percent error deviation was very high (i.e., the average temperature was approaching 1000 K, but there was a much larger range of temperatures). The average error is less than 1% and the deviation is significantly reduced above a signal ratio of 25. The SNR in the gas cell was always greater than 100, which led to less than 1% error from random noise. In the flame, the SNR was approximately 33 and 133 at ϕ = 3 and 6, respectively. Hence, the error from random noise was at or below 1% in flame conditions.

4. Conclusions

Time-resolved optically gated absorption (TOGA) has been demonstrated in the mid-infrared spectral region to measure single-laser-shot, background-free multi-transition absorption by methane in both a temperature-controlled gas cell and in a Hencken flame. This was accomplished by tuning the broadband absorption beam to ∼3.3 μm to directly probe the rotational structure of the fundamental asymmetric CH stretch vibrational transition of CH₄ while using a temporal gate for exclusive upconversion of the molecular response into the visible spectral regime. Mean temperature measurements acquired with TOGA were approximately 2% different than thermocouple embedded in the gas cell. Moreover, the temperature standard deviation using TOGA was, on average, 4% between 300–575 K. In flame conditions, the precision was better than 2%. These measurements demonstrate the ability to measure mid-infrared absorption features while using detectors that are only sensitive in the visible spectrum. Moreover, this work demonstrates the ability for TOGA to be extended beyond electronic transitions to fundamental vibrational transitions. Measurements were achievable down to 1000 ppm in flame condition, and the universality of this approach suggest feasibility for extension to detection of fundamental vibrational transitions of other combustion-relevant species, including CO and CO₂.