CARS spectral fitting with multiple resonant species using sparse libraries

The dual pump CARS technique is often used in the study of turbulent flames. Fast and accurate algorithms are needed for fitting dual-pump CARS spectra for temperature and multiple chemical species. This paper describes the development of such an algorithm. The algorithm employs sparse libraries, whose size grows more slowly with number of species than a conventional library. The method was demonstrated by fitting synthetic "experimental" spectra containing 4 resonant species (N₂, O₂, H₂ and CO₂), both with noise and without it, and by fitting experimental spectra from a H₂-air flame produced by a Hencken burner. In both studies, weighted least squares fitting of signal, as opposed to least squares fitting signal or square-root signal, was shown to produce the least random error and minimize bias error in the fitted parameters.