We report the first application of cavity-enhanced absorption spectroscopy (CEAS) using a coherent light source for sensitive and rapid gaseous species time-history measurements in a shock tube. Off-axis alignment and fast scanning of the laser wavelength were used to minimize coupling noise in a low-finesse cavity. An absorption gain factor of 83 with a measurement time resolution of 20 µs was demonstrated for C2H2 detection using a near-infrared transition near 1537 nm, corresponding to a noise-equivalent detection limit of 20 ppm at 296 K and 76 ppm at 906 K at 50 kHz. This substantial gain in signal, relative to conventional single-pass absorption, will enable ultra-sensitive species detection in shock tube kinetics studies, particularly useful for measurements of minor species and for studies of dilute reactive systems.
© 2014 Optical Society of America
Shock tubes have served for decades as one of the most effective experimental systems for chemical kinetics studies, thanks to their capability of almost instantaneously creating a uniform, well-controlled test environment of high-temperature gases at a user-specified pressure . Due to the rapid transient characteristics of such an environment, continuous wave (cw) laser absorption spectroscopy is an often-used diagnostic tool that can provide in situ species time-history measurements with microsecond time resolution [2,3]. Such data are critical for validating and improving chemical kinetics models, especially for high-temperature environments. Here we report the use of cavity-enhanced absorption spectroscopy (CEAS) [4–7] (also called integrated cavity output spectroscopy (ICOS) [8–10]) to improve detection sensitivity for cw laser absorption in shock tubes.
Laser absorption is described by the Beer-Lambert law for the fractional transmission of monochromatic light at frequency ν, (It/Io)ν. The frequency-integrated form of this relation in Eq. (1) shows that the integrated absorbance is proportional to the absorption line strength S, the absorption path length L, and the partial pressure of the absorbing gas Pi = XiP where Xi is the mole fraction of the target species i and P the total static pressure.Eq. (1) offers the choice of using a stronger transition (larger S) or a longer path length L. Thus there is a long history of laser absorption measurements of open shell radical intermediates such as OH  or CH3  using strong electronic transitions in the ultraviolet (UV). However, ro-vibrational transitions in the infrared provide access to many more chemical species, and indeed lead-salt diode lasers were used to access strong transitions in fundamental vibrational bands for shock tube chemistry studies nearly forty years ago (e.g., CO ). Recently, the emergence of commercial quantum-cascade lasers in the mid-infrared has improved access to strong fundamental vibrational bands for applications in shock tube experiments . Here we focus on improving sensitivity for shock tube species measurements by increasing the effective absorption path length using an optical cavity.
Shock tubes have several barriers to increasing the absorption path length. First, the shock-heated gases are confined in a relatively small diameter tube (typically 0.05-0.15 m) with modest optical access (typically ≤ 0.025 m diameter windows) that must be vacuum/pressure sealed against the pressure change behind the shock wave. Second, the reaction times behind the shock wave may require tens of microsecond time resolution or better. Third, the gas dynamics of the shock structure can produce significant steering of the laser beam. Standard multi-pass detection schemes have been used successfully to increase sensitivity via increased path length for absorption measurements in static or slow-flow cells; e.g., White  and Herriot cells  have been used more than 50 years. However, due to the challenges listed above these approaches have proven quite difficult to implement in shock tubes, and only modest increases in sensitivity have been reported, e.g., a factor of 5 from a 12-pass White cell . This same group has also built a Fabry-Perot cavity around the shock tube and detected OH absorption using a UV lamp with a factor of 12 increase in the effective path length; however, the loss from the anti-reflection coated shock tube windows inside the cavity dominated the single-pass intensity loss .
Here we report a major improvement in absorption sensitivity behind incident and reflected shock waves in a shock tube using off-axis CEAS, applied as an example to detection of C2H2 using combination band transitions in the near infrared (NIR). The off-axis injection of light into the cavity is known to be insensitive to optical alignment [9,19] and thus is robust to the beam steering due to strong gradients in density of the shock-heated gases and from mechanical vibrations in the shock tube. Many previous CEAS workers [e.g., 4–10] have obtained large increases in the effective path length by using a high-finesse cavity (mirror reflectivity > 99.9%); however, such cavities preclude the time resolution needed for fast shock tube chemistry experiments. Here we exploit a low-finesse cavity (mirror reflectivity: 98.8%) to obtain measurements at 50 kHz (20 μs time resolution). The advantages of a low-finesse cavity for shock tube measurements will be discussed in the context of CEAS fundamentals and optical system design in section 2. Then in section 3, demonstration measurements of C2H2 using a NIR transition (near 1537 nm) report an enhancement factor of ~83, corresponding to an effective path length of 12.5 m in a shock tube of 0.15 m inner diameter.
These first-ever, time-resolved laser absorption measurements in a shock tube using off-axis CEAS illustrate the advantages of this scheme to realize fast, sensitive species detection of interest in shock tube studies of gas-phase reaction kinetics.
2. Experimental design specific to off-axis CEAS in a low-finesse cavity
The theory of off-axis CEAS is well documented in [19–21]. Here we will briefly review enough CEAS fundamentals to put in context the design principles specific to our shock tube application for time-resolved absorption in a low-finesse cavity.
The CEAS cavity is formed by a pair of concave mirrors (Fig. 1) of reflectivity R. The laser light is injected through the back of one mirror and travels back and forth between the two mirrors, with intensity reduced on each round trip by a factor of R2 from mirror reflection plus losses due to absorption and scattering from gases in the cavity. Some of the light leaks through the mirrors and exits the cavity, where it is collected and monitored on a photodiode as shown in Fig. 1.
Like a Fabry-Perot cavity, the cavity acts as a spectral filter, with transmission peaks spaced by the free-spectral-range (FSR) defined as10,19] and is a consequence of spurious-coupling to stable cavity modes. This phenomena is predictable and not noise in the sense of random fluctuations. However, the spurious coupling to stable cavity modes can dominate the uncertainty in scanned-wavelength-transmission measurements, and this phenomena is called “optical noise” in Ref. 19; here we call this transmission fluctuation with wavelength spurious-coupling noise to distinguish this from other noise sources in the absorption measurement. To suppress such spurious-coupling noise, one can rapidly scan the laser wavelength  and/or the cavity length , employ an off-axis alignment [9,20], or reduce the cavity finesse. For our current experiments we use all these ideas except cavity-length modulation to manage the spurious-coupling noise.
When the spurious-coupling noise is fully suppressed and the light transmission is uniform with wavelength, the expression for the total transmitted light intensity reduces to a simple form :
The measured absorption signal transmitted through a CEAS cavity can be derived from Eq. (3) as:
In this work, the cavity was formed with a pair of coated dielectric mirrors (RMI, with R~98.8%, radius of curvature (ROC) = −1 m, 0.025 m diameter); the mirrors were backside polished and antireflection coated (loss < 0.2%) to aid coupling light into (out of) the cavity. These mirrors were used as windows on the shock tube (see Fig. 1) and were epoxied to plugs mounted nearly flush on the shock tube wall for the vacuum/pressure seal.
Compared with previous work [8–10,20] that employed extractive sampling, this in situ shock tube cavity design has three major differences: (1) A relatively small mirror reflectivity was used (most CEAS applications use > 99.9% reflectivity). From Eq. (3) we note a higher reflectivity R leads to a larger gain in absorption signal, but unfortunately this gain comes at a cost of lower transmitted intensity, longer cavity residence time, and increased spurious-coupling noise. By using a relatively low-finesse cavity, there is sufficient transmitted light from a standard telecommunications diode laser (NEL) that a fast photodiode detector could be used (Throlabs, model number: PDA 20CS, diameter = 2 mm, 1.9 MHz bandwidth at 20 dB gain). (2) A ROC much larger than confocal was chosen to make the measurement less sensitive to the alignment  so that beam steering by the shock front was minimized. (3) An off-axis alignment was chosen to fill only a small fraction of the cavity volume (see Fig. 1). The shock tube has a diameter of 0.15 m, and after the shock wave is launched it travels down the tube at a velocity ~1000 m/s. If the cavity is filled, the time resolution will be determined by the transit time of the shock wave across the full width of the cavity. Thus, an off-axis alignment was selected as indicated in Fig. 1 where the light in the cavity is confined to a narrow elliptical region perpendicular to the shock tube axis. Reducing the width of this region (i.e., reducing the fraction of the cavity volume filled) reduces the degree of off-axis alignment, increases the overlap of the circulating laser light in the cavity and increases the cavity-coupling noise. For the experiment below, the width of this region was less than 0.005 m, or roughly a 5 μs limit to the time resolution for a shock velocity ~1000 m/s.
Because of the short cavity length (0.15 m) and the small fraction of the cavity filled, the off-axis alignment does not completely suppress the spurious-coupling noise. However, wavelength scanning was also employed with the output wavelength of the DFB diode laser scanned over 1 cm−1 range with a linear sawtooth waveform at 50 kHz. The combination of wavelength scanning, off-axis alignment, and relatively low finesse successfully suppressed the cavity-coupling noise as will be apparent in the results of single-scan absorption data shown below. A faster data acquisition system (in this study, limited to 10MS/s) and detector would have allowed the 20 μs data rate demonstrated below to be improved and approach the 5 μs resolution limit of the cavity alignment.
3. Shock tube measurement results and discussions
A detailed description of the shock tube operation for chemical kinetics experiments is documented in , and here only the fundamental principles needed to understand the off-axis CEAS application are presented. A gas-driven shock tube consists of a long tube with driver and driven sections separated by a diaphragm (typically a plastic film, e.g. Lexan) as seen in the left panel of Fig. 2.A pressure difference between the sections causes the diaphragm to burst, and a shock wave is launched into the lower pressure gas in the driven section, with a nearly instantaneous increase in the gas temperature and pressure behind it. When the shock wave reaches the endwall, it is reflected back toward the driver section, stagnating the gas and further raising its temperature and pressure. The temperature increases are well-known from standard gas dynamics relations and the measured shock speed [2,3]. Kinetics measurements are usually done in the stagnated high-temperature and pressure region behind the reflected shock wave. The off-axis CEAS cavity of Fig. 1 is located 0.02 m from the endwall. The right panel of Fig. 2 shows the pressure trace (blue) measured by a transducer (at nearly the cavity location) for a helium-driven shock wave into a test gas of 2000 ppm C2H2 dilute in argon. The two rapid increases of the pressure indicate the arrival of the incident and reflected shock waves at the laser test location, respectively; time zero is defined as the arrival of the reflected shock wave at the measurement location. The red trace shows the transmitted intensity of the laser driven by a 50kHz linear sawtooth function. Each of the individual wavelength scans of the laser provide a direct absorption measurement of C2H2, and the 50 kHz scan rate (20 μs time resolution) provides sufficient time resolution for this demonstration. Note that the cavity alignment is well-maintained throughout the arrival of both incident and reflected shock waves as indicated by the small (< 2%) scan-to-scan variation in the transmitted laser intensity.
Examples of single-sweep wavelength-scanned direct absorption are shown in Fig. 3; the upper panels are for the pre-incident-shock data and the lower panels for the post-reflected-shock data. A solid etalon (FSR = 0.067 cm−1) was used to convert the time scale to laser wavelength, and the scan-to-scan wavelength reproducibility for the telecommunications laser used was significantly better than the 0.007 cm−1 spacing between measurement points. No averaging has been performed for this data, so the smooth variation in laser intensity illustrates the effective suppression of spurious-coupling noise from the combination of off-axis alignment, fast wavelength scanning, and low-finesse cavity. Each reduced single-scan absorption spectrum was best-fit to a Voigt profile to yield the effective absorbance , as shown in the two panels on the right side of Fig. 3. The small residuals in the Voigt fits illustrate the suppression of the spurious-coupling noise. Note the linewidth of the data behind the reflected shock is larger than behind the incident shock due to the rise in pressure, and the shift in peak absorbance reflects the pressure shift of this transition.
To accurately determine the C2H2 mole fraction, the gain factor G must be known. In the present case, we infer G from the measured integrated absorbance, using the known pre-shock gas conditions and the spectroscopic parameters ((1 0 1 0 0 0 + u - 0 0 0 0 0 0 + g) P(19e) line at 6507.398 cm−1, line strength = 0.121 cm−2atm−1 at 296 K, lower state energy = 446.89 cm−1) from HITRAN 2012 . At the low (906 K) temperature behind this reflected shock, there is no thermal decomposition of C2H2 during the measurement time. Figure 4 shows the time-resolved C2H2 absorption measurements from the same experiment used for Fig. 3. The constant C2H2 mole fraction determined before and after the shock heating show that the gain factor G remained unchanged throughout the measurement, demonstrating the validity of the calibration strategy and the consistent performance of the CEAS absorption system. The standard deviation (1σ) of the time-resolved mole fraction showed a noise-limited uncertainty of 20 ppm at 296 K and 76 ppm at 906 K (note the single-pass peak absorption of the targeted transition is more than two times larger before the incident shock at 296 K than after the reflected shock at 906 K due to the temperature dependence of the line strength and the increase in pressure broadening). Single-pass wavelength-scanned direct absorption of C2H2 with this NIR transition was not possible at the low 2000 ppm mole fraction, but the CEAS measurement has excellent signal-to-noise. These measurements thus clearly illustrate the benefits of off-axis CEAS for shock tube chemistry measurements with lower reactant concentrations.
An example shock tube chemistry experiment is shown in Fig. 5 for the ignition and combustion of C2H2 with oxygen at a fuel-lean equivalence ratio of 0.2 at a temperature of 1090 K (determined by the measured shock speed) and pressure of 1.50 atm immediately behind the reflected shock wave. Such measurements can be used to refine detailed chemical mechanisms used for combustion modeling. To compare model and experiment, the measured time-history of C2H2 is compared against that of the model. Because of the heat release from the combustion of 2000 ppm of C2H2, the temperature of the gas rises and the temperature dependence of the absorption line strength must be considered. The time- resolved temperature rise can be measured (in our shock tubes we use laser absorption of twotransitions from the same species ). Alternatively the time-dependent temperature can be calculated from the chemistry model being tested, and the model determines the time-dependent gas composition and the heat release (and thus the time dependent gas temperature). To compare measurement with model, the time-resolved integrated C2H2 absorbance measured in the experiment is compared to the absorbance predicted by the model in Fig. 5 (thus the data points in Fig. 5 are independent of the model predicted temperature rise). Recall the integrated absorbance (the exponent in Beer’s law) is given by αCEAS = ln(1 + GαSP(ν)) = ln(1 + GS(T)PXC2H2D). The measurement shows the C2H2 and oxygen ignite after a delay time of 578 μs and the C2H2 is completely consumed by oxidation chemistry after ~1200 μs. The improved sensitivity of the CEAS absorption scheme enables detection of time-resolved C2H2 concentration with an initial concentration of only 2000 ppm using robust telecommunications lasers. A simulation of the C2H2 absorbance time-history using the reaction mechanism of Hidaka  shows remarkable agreement with the measured C2H2 time-history.
The increase in absorption sensitivity achieved with this fast, in situ CEAS diagnostic strategy enables the use of low reactant concentrations for chemical kinetics studies in a shock tube. Low reactant concentrations offer distinct benefits in unraveling and evaluating the chemistry by reducing the temperature rise from chemical heat release when studying exothermic chemistry and reducing the influence of secondary chemistry .
The mirror reflectivity (cavity finesse) can be selected to tune the CEAS gain and adjust the species detection limit (at a potential cost of smaller transmitted laser intensity, increased cavity-coupling noise and reduced time resolution. For example, Fig. 6 illustrates the detection limit for the C2H2 NIR transition used in this experiment (near 1.537 μm) as a function of mirror reflectivity; three gas temperatures (300 K, 900 K and 1500 K) illustrate the temperature dependence of the absorption transition. Note, however, that as the reflectivity increases to 0.999, the time resolution of CEAS absorption also increases to several microseconds, limited by the characteristic cavity frequency fc = 1/(2πτ) [10,19,20] (τ is the photon residence time in the cavity or cavity ring-down time given by: τ = L/[(1-R) × c]) ). Thus 1 μs time resolution in our 0.15 m diameter shock tube requires the use of mirrors with R < 0.997. Although this limits the effective path length L / (1 – R) to about 47 m or an effective path length gain of ~300, this is still a major improvement in potential detection sensitivity over current single-pass absorption approaches. Further gains in species detection limits may be achieved by combining this sensitivity gain for low-finesse, off-axis CEAS with stronger transitions, e.g., using mid-IR light sources for the fundamental vibrational bands of most molecules or UV sources for electronic transitions in the important open shell radicals such as OH, CH, and CH3. Detector noise also limits the use of high-reflectivity mirrors because the transmitted laser intensity by the cavity is proportional to (1-R). Thus, as the mirror reflectivity increases either a more powerful laser or a lower noise detector is needed to avoid reduced absorption sensitivity .
4. Concluding remarks
An alignment-robust, off-axis cavity-enhanced absorption spectroscopy (CEAS) diagnostic is demonstrated for the first time in a shock tube. In situ, time-resolved species history measurements of C2H2 using a robust telecommunications NIR laser were achieved with an absorption gain of 83 using a low-finesse cavity for robust alignment and rapid time resolution. Additional sensitivity improvements are possible using mirrors with R > 0.99 and/or using light sources that access stronger transitions; however, for the desired 1 μs time resolution, R < 0.997.
The low-finesse, off-axis CEAS strategy shows potential for enhancing absorption signals up to a gain of 300 with one microsecond time resolution. This new method offers important advantages for studying high-temperature chemistry in shock tubes: (1) it allows sensitive species detection with the weaker near-infrared transitions accessible by cheap and readily available lasers, and (2) it will enable ultra-sensitive detection of species with strong absorption transitions. Thus, CEAS offers prospects for detecting reaction products and reaction intermediates not previously monitored in shock tube experiments as well as the ability to reduce secondary chemistry by reducing the concentrations of reactants.
Future work will focus on extending the method to other light sources (e.g., mid-IR and UV), optimizing the system design (e.g., mirror reflectivity, laser scan rate and wavelength multiplexing), and on applying the method in the study of high-temperature reaction kinetics.
This work was sponsored by the AFOSR with Dr. Chiping Li as technical monitor. We thank Dr. Joshua Paul of Aeris Technology for useful discussions on the use of cavity-enhanced absorption schemes with rapid time resolution.
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