Sparse Zernike Fitting for Dynamic LAS Tomographic Images of Temperature and Water Vapor Concentration

Laser absorption spectroscopy (LAS) tomography yields cross-sectional images of flame temperature and gas molar concentration in combustions. The total laser absorbance of a specific gas, such as water vapor at each point in the region of interest, was obtained from local normalized second harmonics on limited detectors. These detectors restrict the spatial resolution during image reconstructions through typical iterative methods. A sparse Zernike fitting method was introduced for LAS tomography, as the temperature in real physical reality is smoothly distributed. The distributions of total absorbance were sparsely fit as finite Zernike polynomials, and the coefficients were mostly zero or about zero. The number of coefficients was much smaller than that of pixels, i.e., unknowns in iterative methods. The underdetermined inverse problem was effectively alleviated, and a higher spatial resolution was achieved. A fast convergence and effective method for optimal step selection was also introduced for the iterative solution of the sparse model. The effectiveness of the proposed method was validated by both simulated and experimental data for temperature and concentration imaging. Performance comparisons were made with the typical iterative methods, such as SART and Landweber methods; temporal variations of reconstructed distributions for dynamical flames were captured with higher signal-to-noise ratios. Both the fundamental frequencies of 8.797 Hz without acoustic excitation and 12.7 Hz in the case of 150-Hz excitation were successfully captured, and tomographic images agreed well with the dynamical flame evolutions.