Statistics of a Geometric Representation of Wavefront Distortion

A precise statistical definition is established for the geometric “shape” of a randomly distorted wavefront. Relationships between the phase-structure function and the statistics governing the shape are derived. The most significant portion of wavefront distortion caused by atmospheric turbulence is a random tilting of the plane-wave front. A procedure is outlined for calculating the influence of wavefront distortion on optical systems. Estimates are formed of the effect of wave-front distortion on photographic resolution and optical heterodyne efficiency.