We present a practical implementation of calibration-free wavelength-modulation spectroscopy with second harmonic detection (WMS-2f) for measurements of gas temperature and concentration in harsh environments. The method is applicable to measurements using lasers with synchronous wavelength and intensity modulation (such as injection current-tuned diode lasers). The key factors that enable measurements without the on-site calibration normally associated with WMS are (1) normalization of the WMS-2f signal by the first harmonic (1f) signal to account for laser intensity, and (2) the inclusion of laser-specific tuning characteristics in the spectral-absorption model that is used to compare with measured 1f-normalized, WMS-2f signals to infer gas properties. The uncertainties associated with the calibration-free WMS method are discussed, with particular emphasis on the influence of pressure and optical depth on the WMS signals. Many of these uncertainties are also applicable to calibrated WMS measurements. An example experimental setup that combines six tunable diode laser sources between 1.3 and 2.0 mum into one probe beam for measurements of temperature, H(2)O, and CO(2) is shown. A hybrid combination of wavelength and frequency demultiplexing is used to distinguish among the laser signals, and the optimal set of laser-modulation waveforms is presented. The system is demonstrated in the harsh environment of a ground-test scramjet combustor. A comparison of direct absorption and 1f-normalized, WMS-2f shows a factor of 4 increase in signal-to-noise ratio with the WMS technique for measurements of CO(2) in the supersonic flow. Multidimensional computational fluid-dynamics (CFD) calculations are compared with measurements of temperature and H(2)O using a simple method that accounts for the influence of line-of-sight (LOS) nonuniformity on the absorption measurements. The comparisons show the ability of the LOS calibration-free technique to gain useful information about multidimensional CFD models.

Wavelength-modulation spectroscopy for measurements of gas temperature and concentration in harsh environments

A tunable diode laser (TDL) is used to measure the absorption spectra of the R46 through R54 transitions of the 20012←00001 band of CO2 near 2.0 μm (5000 cm−1) at room temperature and pressures to 10 atm (densities to 9.2 amagat). Spectra are recorded using direct absorption spectroscopy and wavelength modulation spectroscopy with second-harmonic detection (WMS-2f) in a mixture containing 11% CO2 in air. The direct absorption spectra are influenced by non-Lorentzian effects including finite-duration collisions which perturb far-wing absorption, and an empirical χ-function correction to the Voigt line shape is shown to greatly reduce error in the spectral model. WMS-2f spectra are shown to be at least a factor of four less-influenced by non-Lorentzian effects in this region, making this approach more resistant to errors in the far-wing line shape model and allowing a comparison between the spectral parameters of HITRAN and a new database which includes pressure-induced shift coefficients. The implications of these measurements on practical, high-pressure CO2 sensor design are discussed.

Measurements of high-pressure CO2 absorption near 2.0 μm and implications on tunable diode laser sensor design

A far-wing line shape theory which satisfies the detailed balance principle is applied to the H2O-H2O system Within this formalism, two line shapes are introduced, corresponding to band-averages over the positive and negative resonance lines, respectively Using the coordinate representation, the two line shapes can be obtained by evaluating 11-dimensional integrations whose integrands are a product of two factors One depends on the interaction between the two molecules and is easy to evaluate The other contains the density matrix of the system and is expressed as a product of two 3-dimensional distributions associated with the density matrices of the absorber and the perturber molecule, respectively If most of the populated states are included in the averaging process, to obtain these distributions requires extensive computer CPU time, but only have to be computed once for a given temperature The 11-dimensional integrations are evaluated using the Monte Carlo method, and in order to reduce the variance, the integration variables are chosen such that the sensitivity of the integrands on them is clearly distinguished

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The frequency detuning correction and the asymmetry of line shapes: The far wings of H2O–H2O

Within the formalism developed previously for the calculation of the far-wing line shape for molecular systems, most of the computer resources were used to diagonalize anisotropic potential-energy matrices whose sizes are determined by the number of states included. As this number is increased, one expects the results to converge. However, for some systems of atmospheric interest, e.g., CO2, the convergence is so slow that one is unable to obtain converged results within reasonable computer limitations. In the present paper, a new formalism is presented in which the eigenfunctions of the orientations of the system, not the states themselves, are chosen as the complete set of basis functions in Hilbert space. In this case, the diagonalization procedure is unnecessary and one can include as many states as desired. The main computational task is transformed from a diagonalization procedure to the carrying out of multidimensional integrations over the continuous orientational variables. In practice, the integ...

The distribution of density matrices over potential-energy surfaces: Application to the calculation of the far-wing line shapes for CO2

A kinetic theory of spectral band shapes is developed which accounts for the effects of line mixing and finite duration of collisions. The theory is based on a projection operator technique with a nonorthogonal metric. The roles and hierarchy of various approximations commonly employed are analyzed. It is shown that the relaxation operator must be defined before the initial correlations are suppressed so that the double sum rule for the matrix elements of this operator is conserved. This conservation is important for the calculations of the wings of band shapes. Rotovibrational band shapes for some specific cases of Raman and infrared absorption spectra of gases are considered. The expressions obtained relate the band wing profiles with the spectral density of molecular torque arising from binary collisions.

Kinetic theory of band shapes in molecular spectra of gases: Application to band wings

We develop the basic formalism of a far‐wing line shape theory that satisfies the detailed balance principle. For molecular systems of interest, e.g., CO2–Ar at room temperature or higher, there are many individual vibration–rotational lines in a given band and many bands in the spectrum. In such cases, one must make additional approximations in order to carry out accurate calculations of the absorption coefficient using a reasonable amount of computer time. In the present paper, we discuss two such simplifications: the frequency detuning approximation of the line‐coupling functions and the band‐average approximation. We then apply the theory to a calculation of the far‐wing absorption of the ν3 band of CO2 perturbed by Ar, successively including the effects of more lines in the calculations by increasing Jmax from 40 to 108. From the results of this work, we find that the frequency detuning approximation is good only for frequencies of interest far from the band center. In addition, we find that contrary...

The frequency detuning and band‐average approximations in a far‐wing line shape theory satisfying detailed balance

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The frequency detuning and band‐average approximations in a far‐wing line shape theory satisfying detailed balance