This paper concerns the analytic reconstruction of properties for narrow laser beams propagating in turbulent atmospheres. We consider the setting of off-axis measurements based on wide-angle single scattering of light detected away from the main path of the beam. Light propagation in the beam itself is modeled by macroscopic approximations of radiative transfer equations that take the form of Fermi pencil beam or fractional Fermi pencil beam equations. This allows for a simplified reconstruction procedure of the beam's constitutive parameters, in particular, its direction of propagation and the location of the emitting source.