Adaptive Modeling Powers Fast Multi-parameter Fitting of CARS Spectra

Coherent anti-Stokes Raman Spectroscopy (CARS) is a laser-based measurement technique widely applied across many science and engineering disciplines to perform non-intrusive gas diagnostics. CARS is often used to study combustion, where the measured spectra can be used to simultaneously recover multiple flow parameters from the reacting gas such as temperature and relative species mole fractions. This is typically done by using numerical optimization to find the flow parameters for which a theoretical model of the CARS spectra best matches the actual measurements. The most commonly used theoretical model is the CARSFT spectrum calculator. Unfortunately, this CARSFT spectrum generator is computationally expensive and using it to recover multiple flow parameters can be prohibitively time-consuming, especially when experiments have hundreds or thousands of measurements distributed over time or space. To overcome these issues, several methods have been developed to approximate CARSFT using a library of pre-computed theoretical spectra. In this work we present a new approach that leverages ideas from the machine learning literature to build an adaptively smoothed kernel-based approximator. In application on a simulated dual-pump CARS experiment probing a $H_2/$air flame, we show that the approach can use a small number library spectra to quickly and accurately recover temperature and four gas species' mole fractions. The method's flexibility allows fine-tuned navigation of the trade-off between speed and accuracy, and makes the approach suitable for a wide range of problems and flow regimes.