Modeling of Fluorescence Lidar ROC Curves

In this paper, an analytical model of a receiver operating characteristic (ROC) curve for digital fluorescence lidar sensing of an aerosol biowarfare agent (BWA) simulant in the presence of a single aerosol interferent is presented. The BWA simulant and interferent are characterized by their concentrations, particle size distributions, fluorescence cross sections, and complex refractive indexes. The ROC curve calculation is performed for simulant and interferent lidar signals that are plotted in a biodiscrimination plane defined by normalized particle size ratio $X$ and particle fluorescence ratio $Y$ . Probability density functions (PDFs) of BWA simulant and interferent in the biodiscrimination plane are due to finite signal-to-noise lidar measurements. These functions are modeled with a joint distribution density function of $X$ and $Y$ as correlated variables. The $X$ and $Y$ variables are calculated from the corresponding lidar equations that compute signal and noise from elastic backscatter and fluorescence cross sections, the concentration of aerosol particles, and lidar optical system parameters. Elastic backscatter is calculated from Mie scattering theory using a particle size distribution approximated by a log-normal distribution. Fluorescence cross sections of BWA simulant or interferent aerosols given in the literature are approximated as being independent/dependent from particle size distribution in the model. Each point of the ROC curve of BWA simulant in the presence of an interferent is defined as the integral of the interferent PDF over the elliptical contour projection of BWA simulant PDF in the biodiscrimination plane for a fixed threshold of aerosol cloud detection, and thus, a fixed probability of aerosol cloud detection. Presented ROC curve method can be generalized to the case of the simultaneous presence of several interferents to the discrimination of one BWA simulant. Calculated elliptical contour projections of the bioaerosol PDF in the biodiscrimination plane, and corresponding ROC curves are computed and presented for the parameters of an experimental lidar that was tested during BWA simulant and interferent aerosol cloud releases, where aerosol cloud particle concentrations and size distributions were also measured. When the number and identity of interferents and their corresponding concentrations are unknown, the ROC curve can be estimated by assuming a constant bioaerosol PDF in the biodiscrimination plane.