Coherence Recovery in Random Environments Using the Autoproduct

Abstract

The study of wave propagation is a mature field of research with numerous avenues of theoretical, numerical, and experimental investigation. A prominent application is remote sensing, where recorded acoustic or electromagnetic waves are analyzed to elucidate information about their source or the environment with which they have interacted. The success of remote sensing tasks is often limited by the coherence of the recorded field, and the coherence of the recorded field is generally reduced by random fluctuations in the propagating medium. In this thesis, the recovery of coherence in wave propagation through random media is studied. Coherence recovery is facilitated by the frequency-difference autoproduct, a quadratic product of complex fields at nearby frequencies, which synthetically estimates field content at the difference frequency of the two constituent fields. By downshifting to sufficiently low difference frequencies, the effects of random media, which typically scale with frequency, are mitigated or entirely removed. Here, the capability of the frequency-difference autoproduct to recover coherence is primarily assessed in underwater acoustic scattering from the sea surface. Theoretical predictions, numerical simulations, and laboratory experiments demonstrate the frequency-difference autoproduct restores coherent reflection even when the constituent scattered fields are nearly completely incoherent. Acoustic measurements collected in the Pacific Ocean and Atlantic Ocean further verify the conclusion. Analytical development of this concept revealed autoproduct-based recovery depends strongly on the autocorrelation function, or power spectrum by Fourier transform, of the randomly rough surface. A simple inversion strategy, designed to exploit this dependence for the measurements collected at sea, identified minor adjustments to the nominal surface characteristics within experimental uncertainty and in agreement with a previous study of the Pacific Ocean dataset. Comparisons of frequency-difference autoproduct, frequency-sum autoproduct, and genuine acoustic field spatial coherence, determined from ocean recordings, conclude this portion of the thesis. Notably, autoproduct spatial coherence exists outside the recorded signal bandwidth, and the coherence lengths of the autoproducts were generally greater than that of the constituent acoustic field for the bottom-reflected sound analyzed here. The second objective of the thesis research focuses on extensions to standard autoproduct theory. Higher-order autoproducts are discussed first, and the cubic frequency-difference autoproduct, capable of mimicking frequency content within the recorded signal bandwidth, receives primary consideration. Mathematical analyses of the governing field equations and examination of the cubic frequency-difference autoproduct’s properties in simple propagation environments highlights the similarities with the quadratic autoproduct. Serendipitously, noise suppression is inherent in the bandwidth-averaging step of the cubic frequency-difference autoproduct construction. Using acoustic recordings and ambient ocean noise measurements, cubic autoproduct-based direction of arrival estimation is shown to outperform conventional methods in noisy environments. The other extension considered here is the electromagnetic frequency-difference autoproduct. Constructed as an outer product of the electric field vector with itself at nearby frequencies, the dyadic autoproduct quantity is explored theoretically, numerically, and experimentally. The frequency-shifting concept is maintained in electromagnetics, as confirmed by numerical computation of autoproducts generated from scattering of a TM-polarized plane wave by perfectly conducting infinite cylinders. Active target localization experiments conducted in forested areas on campus demonstrate remote sensing problems associated with array sparsity and random scattering may be mitigated by the electromagnetic frequency-difference autoproduct, as they are for remote sensing with the acoustic frequency-difference autoproduct.