A technique to study randomly varying media

Abstract

A randomly varying medium causes both amplitude and phase fluctuations on a wave propagating through it. The time variations of the medium are shown to provide a mechanism for viewing isolated regions along the propagation path. A general technique for locating the refractive index variation regions and mapping their position versus distance along the propagation path is introduced in this paper. The novel feature of the new technique is that this mapping is obtained from an end view of the propagation path rather than an overview; thus, only one antenna is required at each end of the path. In developing the description of the technique, a nonlinear wave equation is derived to include the time variations in addition to the usual spatial variations. This equation leads to the retarded potential solution and to the autocorrelation function which is the desired mapping. The resolution of a source region in the medium is shown to be inversely proportional to its spectral bandwidth. An experiment at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</tex> band is proposed to measure filamentary electron density structures in the solar wind over a path length on the order of one AU. Processing ten hours of data will give a unity signal-to-noise ratio for 36 resolution cells in 4/10 of an AU path length or for 14 resolution cells in a one AU path length.