Prediction and Measurement of the Unwrapped Phase for Speckle Propagating in Turbulence.

Intensity and wrapped phase characteristics of a signal from speckle propagating in a vacuum and from a point source propagating in air turbulence have been studied extensively. The intensity characteristics of a speckle signal propagating in turbulence have also been studied. Wrapped phase is phase data that is limited to the principal values of phase defined for a circle. Additional information about the speckle and turbulence is contained in the unwrapped phase which is obtained by extending the wrapped phase beyond the principal values by mapping them onto an infinite line or by integrating the signal frequency. Statistical models for the unwrapped phase of speckle produced by a laser illuminating a diffuse target and propagating through the atmosphere are proposed. It is shown that the unwrapped phase can be used to measure properties of a remote target or the atmosphere. Targets of different roughness can be distinguished at a distance of 1000 meters and target movement and wind activity are easily observable from the unwrapped phase data. Measurements of unwrapped phase are also shown to be capable of sensing atmospheric turbulence levels from a remote location.