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Approximation to beam propagation in ocean water

Using a modified form of the anomalous diffraction approximation we first derived in closed form an analytic expression for the phase function of Mie scatterers integrated over an inverse power law (Junge) size distribution. A simple analysis explained the apparent singularity seen experimentally at the forward scattering angle. Relationships were derived that related the inverse power law as a function of scattering angle in the near forward direction to the power law of the size distribution. The parameters of the formula are the relative index of refraction and the inverse power of the size distribution. Using the formula and path integrals, we have derived approximate analytic expressions that model laser beam propagation in ocean waters. The effect of strong absorption on beam shape and temporal spreading is accounted for. The results are currently being integrated into a comprehensive model of underwater active imaging systems.