CARS.jl: Efficient fitting of dual-pump multi-species CARS spectra using compressed libraries

In this publication, we demonstrate the extension of our loss-less library approach previously limited to fitting ro-vibrational N₂ CARS spectra for thermometry purposes to accurate and efficient fitting of dual-pump CARS spectra with multiple species. The fundamental reasoning behind the compression approach is to make use of finite resolution effects arising from the laser linewidths, which are typically larger than the transitional linewidths. For accurate reconstruction at runtime of the fit, in addition to the squared modulus and real component, also the imaginary component as well as intra-region species cross terms have to be compressed and tabulated for dual-pump multi-species spectra. The resulting libraries do not require to tabulate combinations of mole fractions, leading to a near linear growth of the library with respect to the number of species. The accuracy and computational efficiency of the method is benchmarked using a reference implementation provided alongside this publication. Library generation times, mainly depending on the underlying spectral model, are typically in the order of seconds to a few minutes. The simulation of a single dual-pump spectrum containing three species is sped up by a factor of >5000 without significantly affecting the accuracy of reconstruction. In a simulated experiment with Stokes-noise imposed data, the time required to it temperature, mole fraction of three resonant species and wavenumber shift on a single spectrum required $\approx$90 ms.