Fundamental radar properties. II. Coherent phenomena in space-time

A previous publication [J. Opt. Soc. Am. A19, 946-956 (2002)] presented a general formulation of radiative systems based on special relativity, and properties of imaging radar were derived as examples. Complex and diverse properties of radar images were shown to have a simple and unified origin when viewed as lower-dimensional (temporal) projections of the space-time structure of a radar observation. A diagram was developed that could be manipulated for a simple, intuitive view of the underlying structure of radar observations and phenomena. That treatment is here extended to include coherent phenomena as they appear in the lower time dimensions of the image. Various known coherent properties of imaging radar and interferometry are derived. The formulation is shown to be a generalization of a conventional echo correlation and is extended to a second spatial dimension. From this perspective, coherent properties also have a surprisingly simple and unified structure; their observed complexity is somewhat illusory, also a consequence of projection onto the lower temporal dimension of the receiver. While this formulation and the rules governing it are quite different from the standard treatments, they have the considerable advantage of providing a much simpler, intuitive, and unified description of radiative (radar and optical) systems that is rooted in fundamental physics.