Optimum truncation of a Gaussian beam for propagation through atmospheric turbulence.

The mean on-axis far-field (or focal-plane) irradiance of a Gaussian beam that is truncated by a circular aperture in the presence of atmospheric turbulence is considered. In the absence of turbulence, an accurate analytic approximation for the irradiance distribution that is valid within the main central lobe of the beam is presented. Based on this approximation, the mean on-axis far-field irradiance and the corresponding turbulence Strehl ratio for the truncated Gaussian beam are then obtained. By maximization of the on-axis irradiance, the optimum ratio of the beam diameter to the aperture diameter in the presence of turbulence is obtained, and the results for the corresponding maximum on-axis irradiance as a function of the strength of turbulence are presented. In particular, for D/r(0) > 1, where D is the aperture diameter and r(0) is Fried's coherence length, optimum truncation of a Gaussian beam and uniform illumination of a circular aperture (where the same total power isuniformly distributed over the aperture) result in the same on-axis irradiance in the presence of uncompensated turbulence.