Theory of branch-point detection and its implementation

It is shown that branch points present in a turbulence-distorted optical fi eld can be visualized as peaks and valleys of a certain potential function. Peaks correspond to positive branch points and valleys correspond to negat ive ones, thus allowing one to study the formation, movements, and merging of branch points. A closed-form formula is given for the potential in terms of wave-front-sensor measurements; branch points appear as logarithmic sin gularities that are easy to detect visually through computer-generated imag es. In fact, the branch-point potential is obtained by means of a single ma trix multiplication. An electrostatic analogy is given, as well as a proof that the continuous part of the wave front does not change the location of the potential singularities. Applications can be found in adaptive optics, in the airborne laser system, in speckle or coherent imaging, and in high-b andwidth laser communication. (C) 1999 Optical Society of America [S0740-32 32(99)00707-3].