EXACT SPREAD FUNCTION FOR A PULSED COLLIMATED BEAM IN A MEDIUM WITH SMALL-ANGLE SCATTERING

A solution has been obtained for the spatial and temporal distribution function for a pulsed fully collimated beam propagating through a hom ogeneous medium with Gaussian small-angle scattering. The solution was obtained first by separation of the general problem into two plane pr oblems, which results in a partial differential equation in three vari ables. A Fourier transform on two projected variables (one angular and one spatial) and a Laplace transform on the projected temporal variab le yielded a set of nonlinear differential equations, which were solve d. A recursion relation for the moments of the distribution function w as also obtained, and the software MATHEMATICA was used to evaluate th ese moments to high orders. The contractions on certain variables are also presented; they correspond to the solutions of less-general probl ems contained in the main problem. A change in the definition of the t ime-delay produces a remarkable change in the structure of the equatio ns. These solutions should be quite useful for lidar studies in atmosp heric and oceanic optics, x-ray and radio-wave scattering in the atmos phere and interstellar medium, and in medical physics.