  This paper concerns the reconstruction of properties of narrow laser beams
propagating in turbulent atmospheres. We consider the setting of off-axis
measurements, based on light detection away from the main path of the beam. We
first model light propagation in the beam itself by macroscopic approximations
of radiative transfer equations that take the form of Fermi pencil beam or
fractional Fermi pencil beam equations. Such models are effective in the small
mean-free-path, large transport-mean-free path regime. The reconstruction of
their constitutive parameters is also greatly simplified compared to the more
accurate radiative transfer equations or (fractional) Fokker-Planck models.
From off-axis measurements based on wide-angle single scattering off the beam,
we propose a framework allowing us to reconstruct the main features of the
beam, and in particular its direction of propagation and the location of the
emitting source.
