Temperature estimation of coherent anti-stokes Raman scattering spectra using Levenberg-Marquarat algorithm

In order to solve the defects of CARSFT program found in parameter estimation of coherent anti-Stokes Raman scattering (CARS) spectra, Levenberg-Marquarat (L-M) algorithm was used. Due to the complexity of CARS spectrum theoretical formulas. The Jacobian matrix was obtained by numerical differentiation. On the basis of analyzing the effects of lateral deviation, longitudinal deviation, and temperature on the fitting residual error, the initial value of the longitudinal deviation is considered to be more important on the rate of convergence. L-M algorithm was applied to fit a standard CARS spectrum in 2000 K. The more deviant the initial values of parameters are, the better result is obtained. After running 167 iterations, the temperature is stabilized to 2 005.6 K, and its residual error is 0.027 463. Another example with low signal-to-noise ratio data was followed, and the result converges. The results show that Levenberg-Marquarat algorithm has little dependence on initial values, and could be applied to temperature estimation of CARS spectra in harsh environments.