Propagation of the mutual coherence function

This dissertation deals with the propagation of the Mutual Coherence Function (MCF) of a point source through homogeneous and inhomogeneous turbulence. The MCF contains complete information to reconstruct the image of the point source. The analysis of this MCF propagation was originally formulated in the context of an aero-optics problem. However, our results are applicable in the very general situation of propagation through any turbulent medium, whose statistics locally obey second stationarity conditions. Our most important result is the following: the MCF of a point source propagating in a turbulent medium needs to be split into two components. One component of the MCF is a delta component which represents a point image. The other component is a blurring function which is a consequence of scattering and diffraction introduced by the turbulent medium. This component causes the blur in the image of the point source. As the MCF propagates deeper into the turbulence, the delta component loses energy to the blur component. The intensity of the point image decreases while the image blur increases. We also derive differential equations and integrated solutions governing the propagation through turbulence of the delta component and the blur component of the MCF. Finally, we compare results obtained from the integrated and iterative solutions for the blur component.