Statistical description of the free-space propagation of highly aberrated optical beams

The free-space propagation of initially aberrated optical beams is considered with an emphasis on aero-optical applications. An exact statistical solution of the paraxial wave equation is derived that can be used to obtain statistics of the beam such as beam center, spread, and higher-order statistics as algebraic functions of propagation distance, wavelength, and statistics of the initial wavefront. Correlations between the proposed description and intensity-based statistics, such as the Strehl ratio, are investigated. It is found that the root-mean-square (rms) of the gradient of the wavefront plays an important role in causing coherence degradation and that the rms of the wavefront error is not always an appropriate measure of the degradation. To illustrate the use of this statistical tool, index of refraction data from a numerical simulation of compressible flow over a cylinder are employed to perform an aero-optical analysis.