Two-tone frequency-modulation spectroscopy for quantitative measurements of gaseous species: theoretical, numerical, and experimental investigation of line shapes.

The capability of retrieving spectral information from line shapes recorded by two-tone frequency-modulation spectroscopy (TTFMS) is investigated. A TTFMS theory accounting for dispersion and nonlinear distortion of diode laser frequency modulation response is presented. The adequacy of the theory for a detailed modeling of line shapes recorded with high resolution is examined. An extensive error analysis of line parameters (i.e., width, intensity, and line center) retrieved by a nonlinear least-squares fitting procedure is made. Plots of residual errors with characteristic signatures that are due to incorrectly assigned modulation parameters and choice of line profile are presented. In least-squares fits to experimental oxygen data with a Voigt profile influence from collisional(Dicke) narrowing is clearly exhibited, and when we used a collisionally narrowed line profile deviations of the model were reduced to less than 0.2%. We demonstrate that accurate quantitative measurements by TTFMS over a wide range of concentrations, temperatures, and pressures are possible.