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On the sensitivity of rotational CARS N2 thermometry to the Herman–Wallis factor


  • This article is part of the Journal of Raman Spectroscopy special issue entitled “Proceedings of the 9th European Conference on Nonlinear Optical Spectroscopy (ECONOS), Bremen, Germany, June 21–23, 2010” edited by Peter Radi, PSI, Villigen, Switzerland, and Arnulf Materny, Jacobs University, Bremen, Germany.


Purely rotational spectral signals of coherent anti-Stokes Raman scattering (CARS) from nitrogen molecules are studied as a function of the vibration–rotation interaction that weakens the rigid rotor approximation under which the dominant terms of the Raman cross section are calculated. The effect of the vibration–rotation interaction is quantified by means of the Herman–Wallis (HW) factor, and different approaches to its determination are evaluated in terms of their relative contribution to the CARS intensity and thermometric measurements made in a fuel-rich hydrocarbon flame. Known HW factors are contrasted with more complete expressions of recent derivation, and it is found that relative line strength adjustments amount to about a few percent. Such differences result in temperature corrections of less than 1%. This value should be considered for the definition of the ideal thermometric accuracy of the technique but it is of minor importance in comparison with other sources of uncertainty (e.g. Raman line widths) that emerge from the complexity typical of reactive gas mixtures. Copyright © 2011 John Wiley & Sons, Ltd.