Orthogonal spectra and cross sections: Application to optimization of multi-spectral absorption and fluorescence lidar

摘要

This report addresses the problem of selection of lidar parameters, namely wavelengths for absorption lidar and excitation fluorescence pairs for fluorescence lidar, for optimal detection of species. Orthogonal spectra and cross sections are used as mathematical representations which provide a quantitative measure of species distinguishability in mixtures. Using these quantities, a simple expression for the absolute error in calculated species concentration is derived and optimization is accomplished by variation of lidar parameters to minimize this error. It is shown that the optimum number of wavelengths for detection of a species using absorption lidar (excitation fluorescence pairs for fluorescence lidar) is the same as the number of species in the mixture. Each species present in the mixture has its own set of optimum wavelengths. There is usually some overlap in these sets. The optimization method is applied to two examples, one using absorption and the other using fluorescence lidar, for analyzing mixtures of four organic compounds. The effect of atmospheric attenuation is included in the optimization process. Although the number of optimum wavelengths might be small, it is essential to do large numbers of measurements at these wavelengths in order to maximize canceling of statistical errors.