On Processing Optical Images Propagated Through the Atmosphere

The problem of how to process optical images that have propagated through a turbulent atmosphere is considered. It is assumed that either the object or its (free-space) scattered field at the receiving aperture is known, except for unknown parameters that are to be estimated. Isotropic and homogeneous turbulence as discussed by Tatarski and Chernov is assumed. It is assumed that a very short (in time) reception is made, that the turbulence-induced complex phase errors are either small or have a correlation distance short relative to the receiving aperture extent, and that the object is within an isoplanatic region. The method of maximum likelihood (ML) is used as a criterion; its applicability is discussed. The ML image-processing structure is found and is nonlinear. Asymptotic cases are examined; among other conclusions, it is shown that the ML processing of independent receptions is more complex than an ML processing of the sum of the receptions. A coherent optical system that realizes the ML image processor is described; it includes the capability to generate the scattered field. Simplifications are pointed out.