The application of non-linear coherent optical processes to the measurement of number density and temperature

The theoretical power functions for CARS and SRS as a function of laser difference frequency are convolved with representative Gaussian laser linewidths. Spectral profiles are generated for N₂ Q-branch CARS and O₂ Q-branch SRS and are compared to experimental data. The effects of different number density and temperature regimes as well as laser linewidths are considered and illustrated.

The utility of CARS and SRS in the measurement of number density and temperature is determined within representative experimental regimes for two possible techniques: (1) fitting observed spectral profiles by the method of minimizing a weighted least squares functions or (2) ratioing the peak height intensity of two selected resonances including a linewidth normalization scheme.

For the method of profile fitting, the functional linewidth derivatives of the convolved power expressions and an assumed (N, T) linewidth dependence are used within the framework of multivariate non-linear regression analysis to predict realistic measurement errors from Gaussiat) shot noise, a finite signal-to-noise ratio, and linewidth uncertainties, The resonance linewidth masking due to a comparable order-of-magnitude laser linewidth is demonstrated as beneficial in regards to the error influence of detection noise as well as resonance linewidth uncertainties.