OCR Text |
Show 8 the overlapped beams gave a measure of the interaction length. The non-resonant signal produced in the glass indicates that 90 percent of the CARS signal would be generated in a distance of 5.3 mm in an isothermal environment. The beam waists were measured by translating a razor blade into the focal region while noting the attenuation. Diameters of 0.18 and 0.33 mm were found for the pump and Stokes beams, respectively. B. Analysis For a given stoichiometry, fly ash-seed loading, and longitudinal location, five or more spectra were recorded at each transverse position in the gas stream-three with active and two with inactive purge. Additionally, a background spectrum was recorded for every five data spectra by blocking the Stokes beam and operating the OMA for the same number of scans and channel read times used to record the corresponding data. After subtracting the background spectrum, the data were normalized to an instrument response function to eliminate spectral distortions from the optics train and channel-to-channel variations in the OMA sensitivity. This normalization spectrum was obtained by recording the output from a hot tungsten ribbon placed at the focal point of the collection lens. The tungsten emission was calculated using an optical pyrometer measurement of the filament temperature and known values for the emissivity.20 After processing, the data were compared to model spectra. Because recent work21 indicates that CARS spectra produced by multimode lasers are more accurately modeled using a convolution expression introduced by Kataoka et al.11 and Teets12 (K-T), this formalism was employed to generate the synthetic spectra rather than the commonly used expression given by Yuratich22 and Hall.23 Gaussian spectral profiles for both the pump and Stokes radiation were used in the convolution. A value of 0.65 ± 0.1 cm was measured for the bandwidth of the pump beam. The nitrogen spectrum was calculated using molecular constants consistent with those given by Gilson et al.21f The N2 Raman linewidths were given the temperature and rotational quantum number dependence deduced by Hall25 from the data by Owyoung and Rahn.26 The calculated anti-Stokes spectra were convoluted with a Voight function (FWHM ^ 0.7 cm ) that was fit to the response of the spectrograph-OMA system to the Neon line at 473.4 nm. The unconvoluted spectra were precalculated for temperatures between 300 and 2700 K in increments of 25 K. Each spectrum was stored as three |