WAVE PROPAGATION AND INVERSE SCATTERING IN HETEROGENOUS MEDIA
Abstract
This proposal is concerned with three research themes that are relevant to the Air Force- The first theme seeks to develop and analyze a robust, high resolution coherent interferometric methodology for imaging moving targets in random (cluttered) media with both synthetic aperture radar and active sensor arrays. It builds on the mathematics of wave propagation in random media and involves novel data processing based on the cross-correlations of the measured waves, calculated over proper time windows and aperture segments. The second theme uses an original active array data driven approach to learning how acoustic or electromagnetic waves propagate through a medium containing reflective structures like cracks in airplane wings or targets. The purpose of the learning is to estimate the Green’s function at points in the imaging domain and then use it for improving the existing inverse scattering methodology. The third theme is motivated by applications of imaging or communication through the turbulent atmosphere, using laser beams. The model of beam propagation is the paraxial wave equation, which is well understood in mixing random media. It is an Ito-Schrodinger equation with white noise potential, and the solution can be simulated numerically with the split-step Fourier (phase screen) method. We propose to study beam propagation in random media with long range correlations, which are more adequate models for atmospheric turbulence. The paraxial wave equation in such media is an Ito-Schrodinger equation with fractional white noise potential. It is not known how to analyze theoretically the solution of this equation. We propose to develop a novel numerical methodology for studying its statistics. The ultimate goal is to understand the important effects of long range correlations that are currently not accounted for in imaging and communications.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 07, 2023
- Source ID
- FA95502210077
Entities
People
- Liliana Borcea
Organizations
- Air Force Office of Scientific Research
- Board of Regents of the University of Michigan
- United States Air Force