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The concept of spatial filtering as applied to remote sensing of the transverse flow velocity and refractive-index spectrum along a line-of-sight propagation path was first outlined in 1974. The technique was applied to optical propagation through the turbulent atmosphere. Random fluctuations in the field were produced by irregularities advected across the optical path by a mean flow. We extend and modify this earlier work to include source and receiver motion, temporal filtering, and dispersion of the refractive index structure. The technique described in this study can be applied to the remote probing of random atmospheric, ionospheric, and oceanic flows using either electromagnetic or acoustic sources. It can also be used for the remote sensing of rough surfaces such as the sea surface. The analysis indicates that this technique is a new, powerful tool with a unique capability for probing the spatial and temporal structure, and evolution of geophysical flows.