  We study the inverse problem of localization (imaging) of a laser beam from
measurements of the intensity of light scattered off-axis by a Poisson cloud of
small particles. Starting from the wave equation, we analyze the microscopic
coherence of the scattered intensity and show that it is possible to determine
the laser beam from the speckle pattern captured by a group of CCD cameras. Two
groups of cameras are sufficient when the particles are either small or large
with respect to the wavelength. For general particle sizes the accuracy of the
laser localization with two groups of cameras is subject to knowing the
scattering properties of the cloud. However, three or more groups of cameras
allow accurate localization that is robust to uncertainty of the type, size,
shape and concentration of the particles in the cloud. We introduce a novel
laser beam localization algorithm and give some numerical illustrations in a
regime relevant to the application of imaging high energy lasers in a maritime
atmosphere.
