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West Desert Test Center (WDTC) at Dugway Proving Ground uses measurement, modeling and simulation capabilities to characterize and referee customer standoff biological and, to a lesser extent, chemical detection systems. The WDTC LIDAR model of aerosol clouds uses a Mie scattering model and associated joint aerosol cloud distribution function N(a, r), where a is the particle radius and r is the position vector of the particle. We make the key simplifying assumption that the two parameters a and r axe statistically independent. Justification for this well-mixed assumption is that aerosol particles with dimensions of less than a few microns remain in the atmosphere for a long time, typically days. Large particles are removed by gravity segregation. For the associated inverse problem, the LIDAR elastic scattering equation is formally inverted to yield an estimate of the aerosol particle concentration (p) over cap (r). Inversion requires knowledge of boundary conditions along an arc of constant range R = R-f. Given a seed value on the arc from a point detector, a two-frequency algorithm is shown to correctly populate all values on the arc R = Rf, leading to near-real-time accurate inversions over the entire LIDAR sweep. Numerical results in a noise background and a representative choice of numerical parameters are given.