Out-of-Plane Enhancement in a Discrete Random Halfspace
Open Access DepositedAlthough widely used to model wave propagation in random media, the accuracy of radiative transfer theory deteriorates when waves propagating in different directions exhibit strong correlation and comprise an appreciable portion of the total field. For active sensing in unbounded media, this degradation is isolated to a narrow region near backscatter. It will be shown that in a plane-stratified random medium, mechanisms not captured by radiative transfer lead to an enhancement that is significant at all azimuthal angles, although confined in zenith. The enhancement is examined for both electromagnetic and acoustic waves using the Foldy-Lax and distorted Born approximations in conjunction with the two-variable perturbation method. The mathematical evidence of an out-of-plane enhancement is significant for a multitude of active bistatic sensing applications, which have received comparatively little study relative to monostatic and passive applications until recently. As new technologies expand the role of bistatic sensing, the importance of rigorous physical models for bistatic configurations will likewise grow. The structure of this enhancement is derived systematically, beginning from the fundamental equations governing time-harmonic electromagnetic and acoustic waves. In a random medium, these fundamental equations lead to the Dyson and Bethe-Salpeter equations, which govern the first- and second-order ensemble statistics. Nondimensionalized forms of these equations are then approximated using the Foldy-Lax and distorted Born approximations, the latter of which would not predict an enhancement in an unbounded medium. Systematic analysis of the resulting integral expression confirms previous observations that the distorted Born approximation describes an enhancement in bounded media, but reveals that this enhancement is not confined to the plane of incidence. The azimuthally ubiquitous enhancement---appearing within a specular cone where the source and observer have the same zenith angle---is attributed to two pseudo-cyclic mechanisms which describe the correlation of the field interacting once with the boundary and with a single particle in forward and reversed sequence, After deriving the out-of-plane enhancement, numerical predictions are presented to illustrate the effect. It is then argued mechanistically that all multiple-scatter enhancements are narrowly confined to the vicinity of backscatter, including those that involve boundary interactions. This mechanistic argument is bolstered by mathematical analysis of a mechanism that is similar to the pseudo-cyclic mechanism but entails more than one particle. In order for the out-of-plane enhancement to be significant, the contribution of the pseudo-cyclic mechanisms must be similar in magnitude to the combined magnitude of all other scatter mechanisms. Circumstances when this would likely occur in practical remote sensing problems are discussed prior to concluding remarks. Rather than striving to produce high-fidelity predictions of specific applied sensing problems, this work seeks to provide fundamental mechanistic and mathematical insight into the enhancement effect. These fundamental observations are broadly applicable to a multitude of sensing applications in both electromagnetics and acoustics, but where specific applications are considered here they are for illustrative purposes. As such, the examples provided are idealized in order to simplify the mathematical presentation and to more clearly describe the enhancement structure.
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mccargar-dissertation_-_Reid_McCargar.pdf | 2020-12-11 | Open Access |
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