Four-color fiber-coupled mid-infrared laser-absorption sensor for temperature, CO, CO2, and NO at 5 kHz in internal combustion engine vehicle exhaust.

A mid-infrared (MIR) laser absorption spectroscopy (LAS) sensor was developed for temperature, CO, NO, and C O 2 measurements at 5 kHz in engine-out exhaust. It used fiber-coupled quantum cascade lasers (QCLs) for measuring CO and NO, and an interband cascade laser (ICL) for measuring C O 2. Validation tests in a heated gas cell confirmed that the LAS measurements of CO, C O 2, NO, and temperature are accurate to within 4.8%, 5.1%, 4.6%, and 3.1%, respectively, at 1-2 atm and 300-1000 K. The LAS sensor was applied to characterize the engine-out exhaust gas of an 8-cylinder gasoline engine in a light-duty truck at operating conditions where commercial instruments lack sufficient time response to quantify important emission dynamics.

Broadband ultrafast-laser-absorption spectroscopy for multi-hydrocarbon measurements near 3.3 µm in flames.

This paper presents the development and application of a broadband ultrafast-laser-absorption-spectroscopy (ULAS) technique operating in the mid-infrared for simultaneous measurements of temperature, methane (C H 4), and propane (C 3 H 8) mole fractions. Single-shot measurements targeting the C-H stretch fundamental vibration bands of C H 4 and C 3 H 8 near 3.3 µm were acquired in both a heated gas cell up to ≈650K and laminar diffusion flames at 5 kHz. The average temperature error is 0.6%. The average species mole fraction errors are 5.4% for C H 4 and 9.9% for C 3 H 8. This demonstrates that ULAS is capable of providing high-fidelity hydrocarbon-based thermometry and simultaneous measurements of both large and small hydrocarbons in combustion gases.

Characterization of non-Boltzmann CN X2Σ+ behind shock waves in CH4-N2 via broadband ultraviolet femtosecond absorption spectroscopy.

This article describes the temporal evolution of rotationally and vibrationally non-Boltzmann CN X2Σ+ formed behind reflected shock waves in N2-CH4 mixtures at conditions relevant to atmospheric entry into Titan. A novel ultrafast (i.e., femtosecond) laser absorption spectroscopy diagnostic was developed to provide broadband (≈400 cm-1) spectrally resolved (0.02 nm resolution) measurements of CN absorbance spectra belonging to its B2Σ+ ← X2Σ+ electronic system and its first four Δv = 0 vibrational bands (v″ = 0, 1, 2, 3). Measurements were acquired behind reflected shock waves in a mixture with 5.65% CH4 and 94.35% N2 at initial chemically and vibrationally frozen temperatures and pressures of 4400-5900 K and 0.55-0.75 bar, respectively. A six-temperature line-by-line absorption spectroscopy model for CN was developed to determine the rotational temperature of CN in v″ = 0, 1, 2, and 3, as well as two vibrational temperatures via least-squares fitting. The measured CN spectra revealed rotationally and vibrationally non-Boltzmann population distributions that strengthened with increasing shock speed and persisted for over 100 µs. The measured vibrational temperatures of CN initially increase in time with the increasing CN mole fraction and eventually exceed the expected post-shock rotational temperature of N2. The results suggest that strong chemical pumping is ultimately responsible for these trends and that, at the conditions studied, CN is primarily formed in high vibrational states within the A2Π or B2Σ+ state at characteristic rates, which are comparable to or exceed those of key vibrational equilibration processes.

Quantum-cascade-laser-absorption-spectroscopy diagnostic for temperature, pressure, and NO X 2 Π 1/2 at 500 kHz in shock-heated air at elevated pressures.

The design, validation, and application of a quantum-cascade-laser-absorption-spectroscopy diagnostic for measuring gas temperature, pressure, and nitric oxide (NO) in high-temperature air are presented. A distributed-feedback quantum-cascade laser (QCL) centered near 1976c m -1 was used to scan across two transitions of NO in its ground electronic state (X 2 Π 1/2). A measurement rate of 500 kHz was achieved using a single QCL by: (1) performing current modulation through a bias-tee, and (2) targeting closely spaced transitions with a large difference in lower-state energy. The diagnostic was validated in a mixture of 95% argon and 5% NO, which was shock-heated to ≈2000 to 3700 K. The average mean percent differences between laser-absorption-spectroscopy (LAS) measurements and predictions from shock-jump relations for temperature, pressure, and NO mole fraction were 3.1%, 4.1%, and 6.5%, respectively. The diagnostic was then applied to characterize shock-heated air at high temperatures (up to ≈5500K) and high pressures (up to 12 atm) behind either incident or reflected shocks. The LAS measurements were compared to theoretical predictions from shock-jump relations, pressure sensors mounted in the wall of the shock tube, and equilibrium values of the NO mole fraction. The average mean percent differences between LAS measurements and their aforementioned reference values were 3.2%, 10.8%, and 10.4% for temperature, pressure, and NO mole fraction, respectively. Last, a comparison between a measured NO mole fraction time history and a time-stepped homogeneous reactor simulation performed using two different chemical kinetics mechanisms is presented.

Near-MHz temperature and H2O measurements in post-detonation fireballs of 25 g hemispherical explosives using scanned-wavelength-modulation spectroscopy.

A laser absorption spectroscopy diagnostic integrated within a hardened optical probe was used to measure temperature and water mole fraction at 500 kHz in post-detonation fireballs of explosives. In the experiments, an exploding-bridgewire detonator initiated a 25 g hemisphere of explosive (N5 or PETN). This produced a hemispherical fireball that traveled radially towards a hardened measurement probe. The probe contained a pressure transducer and optical equipment to pitch fiber-coupled laser light across a 12.6 cm gap onto a detector. Tunable diode lasers emitting near 7185.6 and 6806c m -1 were used to measure the absorbance spectrum of H 2 O utilizing peak-picking scanned-wavelength-modulation spectroscopy with a scan frequency of 500 kHz and modulation frequencies of 35 and 45.5 MHz, respectively. This enabled measurements of temperature and X H 2 O in the shock-heated air and trailing fireball at 500 kHz. Time histories of pressure, temperature, and H 2 O mole fraction were acquired at different standoff distances to quantify how the fireball evolved in space and time as well as to compare measured quantities between PETN and N5 fireballs. The standard deviation of temperature and X H 2 O during one representative test were found to be 17 K (1.3%) and 0.011 (5%), respectively. These measurements demonstrate this diagnostic's ability to provide rapid and reliable measurements in harsh, highly transient post-detonation environments produced by solid explosives.

Ultrafast-laser-absorption spectroscopy in the mid-infrared for single-shot, calibration-free temperature and species measurements in low- and high-pressure combustion gases.

This manuscript presents an ultrafast-laser-absorption-spectroscopy (ULAS) diagnostic capable of providing calibration-free, single-shot measurements of temperature and CO at 5 kHz in combustion gases at low and high pressures. Additionally, this diagnostic was extended to provide 1D, single-shot measurements of temperature and CO in a propellant flame. A detailed description of the spectral-fitting routine, data-processing procedures, and determination of the instrument response function are also presented. The accuracy of the diagnostic was validated at 1000 K and pressures up to 40 bar in a heated-gas cell before being applied to characterize the spatiotemporal evolution of temperature and CO in AP-HTPB and AP-HTPB-aluminum propellant flames at pressures between 1 and 40 bar. The results presented here demonstrate that ULAS in the mid-IR can provide high-fidelity, calibration-free measurements of gas properties with sub-nanosecond time resolution in harsh, high-pressure combustion environments representative of rocket motors.

Spectrally resolved, 1D, mid-infrared imaging of temperature, CO2, and HCl in propellant flames.

This work presents a high-speed, spectrally resolved, mid-infrared imaging diagnostic for providing 1D measurements of gas temperature and relative mole fraction of ${{\rm{CO}}_2}$ and HCl in flames. An imaging spectrometer and a high-speed mid-infrared camera were used to provide 1D measurements of ${{\rm{CO}}_2}$ and HCl emission spectra from 2386 to ${{2402}}\;{{\rm{cm}}^{- 1}}$ with a spectral resolution of ${0.46}\;{{\rm{cm}}^{- 1}}$, and simulated emission spectra were least-squares fit to the data to determine the aforementioned gas properties. Measurements were acquired in HMX and AP-HTPB flames burning in air at 1 atm. This diagnostic was applied to characterize how the path-integrated gas temperature of HMX flames varies in time and with distance above the burning surface. Additionally, Abel inversion with Tikhonov regularization was applied to determine the radial distribution of temperature and relative concentration of ${{\rm{CO}}_2}$ and HCl within the core of AP-HTPB flames. The results demonstrate that this diagnostic has potential to further our understanding of propellant combustion physics by quantifying thermochemical flame structure at rates up to 2 kHz.

Cepstral analysis for baseline-insensitive absorption spectroscopy using light sources with pronounced intensity variations.

This paper presents a data-processing technique that improves the accuracy and precision of absorption-spectroscopy measurements by isolating the molecular absorbance signal from errors in the baseline light intensity (Io) using cepstral analysis. Recently, cepstral analysis has been used with traditional absorption spectrometers to create a modified form of the time-domain molecular free-induction decay (m-FID) signal, which can be analyzed independently from Io. However, independent analysis of the molecular signature is not possible when the baseline intensity and molecular response do not separate well in the time domain, which is typical when using injection-current-tuned lasers [e.g., tunable diode and quantum cascade lasers (QCLs)] and other light sources with pronounced intensity tuning. In contrast, the method presented here is applicable to virtually all light sources since it determines gas properties by least-squares fitting a simulated m-FID signal (comprising an estimated Io and simulated absorbance spectrum) to the measured m-FID signal in the time domain. This method is insensitive to errors in the estimated Io, which vary slowly with optical frequency and, therefore, decay rapidly in the time domain. The benefits provided by this method are demonstrated via scanned-wavelength direct-absorption-spectroscopy measurements acquired with a distributed-feedback (DFB) QCL. The wavelength of a DFB QCL was scanned across the CO P(0,20) and P(1,14) absorption transitions at 1 kHz to measure the gas temperature and concentration of CO. Measurements were acquired in a gas cell and in a laminar ethylene-air diffusion flame at 1 atm. The measured spectra were processed using the new m-FID-based method and two traditional methods, which rely on inferring (instead of rejecting) the baseline error within the spectral-fitting routine. The m-FID-based method demonstrated superior accuracy in all cases and a measurement precision that was ≈1.5 to 10 times smaller than that provided using traditional methods.

Simulation technique enabling calibration-free frequency-modulation spectroscopy measurements of gas conditions and lineshapes with modulation frequencies spanning kHz to GHz.

A simulation technique enabling calibration-free measurements of gas properties (e.g., temperature, mole fraction) and lineshapes via wavelength- or frequency-modulation spectroscopy (WMS or FMS) is presented. Unlike previously developed models, this simulation technique accurately accounts for (1) absorption and dispersion physics and (2) variations in the WMS/FMS harmonic signals, which can result from intensity tuning induced by scanning the laser's carrier frequency [e.g., via injection-current tuning of tunable diode lasers (TDLs)]. As a result, this approach is applicable to both WMS and FMS experiments employing a wide variety of light sources and any modulation frequency [typically kilohertz (kHz) to gigahertz (GHz)]. The accuracy of the simulation technique is validated via comparison with (1) simulated signals produced by established WMS and FMS models under conditions where they are accurate and (2) experimental data acquired under conditions where existing models are inaccurate. Under conditions where existing WMS and FMS models are accurate, this simulation technique yields nearly identical (within 0.1%) results. For experimental validation, the wavelength of a TDL emitting near 1392 nm was scanned across a single absorption line of H2O with a half-width at half-maximum of 350 MHz while frequency modulation was performed at 100 MHz. The best-fit first-harmonic (1f) signal produced by this simulation technique agrees within 1.6% of the measured 1f signal, and the H2O mole fraction and transition collisional width corresponding to the best-fit 1f spectrum agree within 1% of expected values.

2D mid-infrared laser-absorption imaging for tomographic reconstruction of temperature and carbon monoxide in laminar flames.

This manuscript presents the design and initial application of a mid-infrared laser-absorption-imaging (LAI) technique for two-dimensional (2D) measurements and tomographic reconstruction of gas temperature and CO in laminar flames. In this technique, the output beam from a quantum-cascade laser (QCL) is expanded, passed through the test gas, and imaged in 2D using a high-speed mid-infrared camera. The wavelength of the QCL is scanned across the P(0,20) and P(1,14) transitions of CO near 4.8 µm at 50 Hz to provide 2D measurements of path-integrated gas temperature and CO column density across over 3,300 lines-of-sight simultaneously. This enabled the first sub-second (0.1 s), high-resolution (140 µm), 2D laser-absorption measurements and tomographic reconstruction of flame temperature and CO mole fraction using mid-infrared wavelengths. Prior to entering the test gas, the beam was reflected off two diffusers spinning at 90,000 RPM (≈9400 rad/s) to break the laser coherence and prevent diffraction-induced image artifacts. This technique was validated with measurements of CO in an isothermal jet and then demonstrated in laminar, partially premixed, oxygen-ethylene flames despite large background emission from soot and combustion products.

Design and application of a high-pressure combustion chamber for studying propellant flames with laser diagnostics.

This manuscript presents the design and initial application of a high-pressure combustion chamber (HPCC). The HPCC exhibits several unique design attributes to enable high-fidelity studies of propellant-combustion physics at high pressures. The HPCC employs a flangeless and weldless design to provide a compact, easy to access, and relatively light weight (for its size and pressure capability) test chamber. It has a cylindrical test volume of 13.1 L and is capable of operating at pressures from approximately 0.4 mbar to 200 bar. The vessel is equipped with a ZnSe window to enable the laser ignition of propellants and energetic materials and 4 sapphire windows (2″ diameter and 4″ × 2″ slots) to enable the use of multiple optical diagnostics spanning the ultraviolet to mid-infrared. The sapphire windows are mounted in plugs with adjustable length to bring the windows inside of the test volume and facilitate line-of-sight optical measurements. The vessel can be accessed from the top and bottom via removable 5″ diameter plugs, and the bottom plug can be modified to enable studies of gaseous jets and flames. Some of the HPCC's testing capabilities are demonstrated via high-speed IR imaging and laser-absorption-spectroscopy measurements of temperature and CO in laser-ignited HMX (i.e., 1,3,5,7-tetranitro-1,3,5,7-tetrazoctane) flames at pressures from 2 to 25 bar.

Compact, fiber-coupled, single-ended laser-absorption-spectroscopy sensors for high-temperature environments.

The design and demonstration of a compact single-ended laser-absorption-spectroscopy sensor for measuring temperature and H2O in high-temperature combustion gases is presented. The primary novelty of this work lies in the design, demonstration, and evaluation of a sensor architecture that uses a single lens to provide single-ended, alignment-free (after initial assembly) measurements of gas properties in a combustor without windows. We demonstrate that the sensor is capable of sustaining operation at temperatures up to at least 625 K and is capable of withstanding direct exposure to high-temperature (≈1000 K) flame gases for long durations (at least 30 min) without compromising measurement quality. The sensor employs a fiber bundle and a 6 mm diameter antireflection-coated lens mounted in a 1/8'' NPT-threaded stainless-steel body to collect laser light that is backscattered off native surfaces. Distributed-feedback tunable diode lasers (TDLs) with a wavelength near 1392 nm and 1343 nm were used to interrogate well-characterized H2O absorption transitions using wavelength-modulation-spectroscopy techniques. The sensor was demonstrated with measurements of gas temperature and H2O mole fraction in a propane-air burner with a measurement bandwidth up to 25 kHz. In addition, this work presents an improved wavelength-modulation spectroscopy spectral-fitting technique that reduces computational time by a factor of 100 compared to previously developed techniques.

Tomographic laser absorption imaging of combustion species and temperature in the mid-wave infrared.

In this work, laser absorption spectroscopy techniques are expanded in spatial resolution capability by utilizing a high-speed infrared camera to image flow fields backlit with tunable mid-wave infrared laser radiation. The laser absorption imaging (LAI) method yields spectrally-resolved and spatially-rich datasets from which quantitative species and temperature profiles can be generated using tomographic reconstruction. Access to the mid-wave infrared (3-5 µm) enables imaging of fuels, intermediates, and products of combustion in canonical small-diameter flames (< 1 cm). Example 1D measurements and 2D reconstructions of ethane (3.34 µm), carbon monoxide (4.97 µm), and carbon dioxide (4.19 µm) in an axisymmetric laminar flame are presented and discussed. LAI is shown to significantly enhance spatio-temporal data bandwidth (∼400 simultaneously sampled lines-of-sight) and resolution (∼50 µm) compared to other tomographic absorption spectroscopy techniques, and with a simplified optical arrangement.

Wavelength-modulated planar laser-induced fluorescence for imaging gases.

This work presents the development of wavelength-modulated planar laser-induced fluorescence (WM-PLIF) and its initial application to infrared imaging of carbon monoxide in a laminar flame. A continuous-wave quantum-cascade laser producing 50 mW near 4.8 µm was injection-current modulated at 1 kHz and scanned across the P(20) transition of CO at 20 Hz. The corresponding infrared-laser-induced fluorescence from 2065 cm-1 to 2155 cm-1 was imaged orthogonal to the laser sheet using a high-speed IR camera, and digital lock-in detection of the WM-PLIF first-harmonic signal (SF,1f) was performed to provide high-fidelity, background-free imaging of CO. Images of the peak-SF,1f signal are presented for a laminar CO-H2 diffusion flame in air at atmospheric pressure. We demonstrate that this technique is sensitive enough to image nascent CO in flames and present a strategy for simulating the WM-PLIF harmonic signals.

Single-ended mid-infrared laser-absorption sensor for simultaneous in situ measurements of H2O, CO2, CO, and temperature in combustion flows.

The development and demonstration of a four-color single-ended mid-infrared tunable laser-absorption sensor for simultaneous measurements of H2O, CO2, CO, and temperature in combustion flows is described. This sensor operates by transmitting laser light through a single optical port and measuring the backscattered radiation from within the combustion device. Scanned-wavelength-modulation spectroscopy with second-harmonic detection and first-harmonic normalization (scanned-WMS-2f/1f) was used to account for variable signal collection and nonabsorption losses in the harsh environment. Two tunable diode lasers operating near 2551 and 2482 nm were utilized to measure H2O concentration and temperature, while an interband cascade laser near 4176 nm and a quantum cascade laser near 4865 nm were used for measuring CO2 and CO, respectively. The lasers were modulated at either 90 or 112 kHz and scanned across the peaks of their respective absorption features at 1 kHz, leading to a measurement rate of 2 kHz. A hybrid demultiplexing strategy involving both spectral filtering and frequency-domain demodulation was used to decouple the backscattered radiation into its constituent signals. Demonstration measurements were made in the exhaust of a laboratory-scale laminar methane-air flat-flame burner at atmospheric pressure and equivalence ratios ranging from 0.7 to 1.2. A stainless steel reflective plate was placed 0.78 cm away from the sensor head within the combustion exhaust, leading to a total absorption path length of 1.56 cm. Detection limits of 1.4% H2O, 0.6% CO2, and 0.4% CO by mole were reported. To the best of the authors' knowledge, this work represents the first demonstration of a mid-infrared laser-absorption sensor using a single-ended architecture in combustion flows.

Kinetics of Excited Oxygen Formation in Shock-Heated O2-Ar Mixtures.

The formation of electronically excited atomic oxygen was studied behind reflected shock waves using cavity-enhanced absorption spectroscopy. Mixtures of 1% O2-Ar were shock-heated to 5400-7500 K, and two distributed-feedback diode lasers near 777.2 and 844.6 nm were used to measure time-resolved populations of atomic oxygen's 5S° and 3S° electronic states, respectively. Measurements were compared with simulated population time histories obtained using two different kinetic models that accounted for thermal nonequilibrium effects: (1) a multitemperature model and (2) a reduced collisional-radiative model. The former assumed a Boltzmann distribution of electronic energy, whereas the latter allowed for non-Boltzmann populations by treating the probed electronic states as pseudospecies and accounting for dominant electronic excitation/de-excitation processes. The effects of heavy-particle collisions were investigated and found to play a major role in the kinetics of O atom electronic excitation at the conditions studied. For the first time, rate constants (kM) for O atom electronic excitation from the ground state (3P) due to collisions with argon atoms were directly inferred using the reduced collisional-radiative model, kM(3P → 5S°) = 7.8 × 10-17T0.5 exp(-1.061 × 105K/T) ± 25% cm3 s-1 and kM(3P → 3S°) = 2.5 × 10-17T0.5 exp(-1.105 × 105K/T) ± 25% cm3 s-1.

Fiber-coupled diode-laser sensors for calibration-free stand-off measurements of gas temperature, pressure, and composition.

A fiber-coupled near-infrared diode-laser sensor for stand-off measurements of gas temperature, pressure, and composition is presented. This sensor utilizes a fiber bundle with six multimode catch fibers surrounding one single-mode pitch fiber to transmit and receive backscattered laser light in a handheld transmitter/receiver. Scanned-wavelength-modulation spectroscopy with 1f-normalized 2f-detection and fast (80-200 kHz) wavelength modulation were used to provide calibration-free measurements and reduce the influence of spurious cavity noise formed by the overlapping transmitted and reflected laser light. Demonstrations include two-color measurements of temperature, pressure, and H(2)O near 1.4 µm in a propane flame at 2 kHz (SNR=200) and measurements of CH(4) near 1.65 µm (SNR=20 to 1500) at stand-off distances of 15 cm and 10 m, respectively. The fraction of photons collected ranged from 10(4) to 1 parts per million at stand-off distances from 10 cm to 10 m, respectively, and is similar for aluminum and paper reflectors.

Shock-tube measurements of excited oxygen atoms using cavity-enhanced absorption spectroscopy.

We report the use of cavity-enhanced absorption spectroscopy (CEAS) using two distributed feedback diode lasers near 777.2 and 844.6 nm for sensitive, time-resolved, in situ measurements of excited-state populations of atomic oxygen in a shock tube. Here, a 1% O2/Ar mixture was shock-heated to 5400-8000 K behind reflected shock waves. The combined use of a low-finesse cavity, fast wavelength scanning of the lasers, and an off-axis alignment enabled measurements with 10 µs time response and low cavity noise. The CEAS absorption gain factors of 104 and 142 for the P35←S520 (777.2 nm) and P0,1,23←S310 (844.6 nm) atomic oxygen transitions, respectively, significantly improved the detection sensitivity over conventional single-pass measurements. This work demonstrates the potential of using CEAS to improve shock-tube studies of nonequilibrium electronic-excitation processes at high temperatures.

Fitting of calibration-free scanned-wavelength-modulation spectroscopy spectra for determination of gas properties and absorption lineshapes.

The development and initial demonstration of a scanned-wavelength, first-harmonic-normalized, wavelength-modulation spectroscopy with nf detection (scanned-WMS-nf/1f) strategy for calibration-free measurements of gas conditions are presented. In this technique, the nominal wavelength of a modulated tunable diode laser (TDL) is scanned over an absorption transition to measure the corresponding scanned-WMS-nf/1f spectrum. Gas conditions are then inferred from least-squares fitting the simulated scanned-WMS-nf/1f spectrum to the measured scanned-WMS-nf/1f spectrum, in a manner that is analogous to widely used scanned-wavelength direct-absorption techniques. This scanned-WMS-nf/1f technique does not require prior knowledge of the transition linewidth for determination of gas properties. Furthermore, this technique can be used with any higher harmonic (i.e., n>1), modulation depth, and optical depth. Selection of the laser modulation index to maximize both signal strength and sensitivity to spectroscopic parameters (i.e., gas conditions), while mitigating distortion, is described. Last, this technique is demonstrated with two-color measurements in a well-characterized supersonic flow within the Stanford Expansion Tube. In this demonstration, two frequency-multiplexed telecommunication-grade TDLs near 1.4 µm were scanned at 12.5 kHz (i.e., measurement repetition rate of 25 kHz) and modulated at 637.5 and 825 kHz to determine the gas temperature, pressure, H2O mole fraction, velocity, and absorption transition lineshape. Measurements are shown to agree within uncertainty (1%-5%) of expected values.

Two-color absorption spectroscopy strategy for measuring the column density and path average temperature of the absorbing species in nonuniform gases.

A two-color absorption spectroscopy strategy has been developed for measuring the column density and density-weighted path-average temperature of the absorbing species in nonuniform gases. This strategy uses two transitions with strengths that scale nearly linearly with temperature. In addition, measured lineshapes are used to accurately model absorbance spectra. As a result, the column density and density-weighted path-average temperature of the absorbing species can be inferred from a comparison of signals measured across a nonuniform line of sight (LOS) with simulated signals calculated using a uniform LOS. This strategy is demonstrated with simulations of water-vapor absorption across a nonuniform LOS with temperature and composition gradients comparable to those in hydrogen-air diffusion flames. In this demonstration, both the column density and density-weighted path-average temperature of water vapor are recovered to within 0.5%.