Variational and active surface techniques for acoustic and electromagnetic imaging

Abstract

This research seeks to expand the role of variational and adjoint processing methods into segments of the sonar, radar, and nondestructive testing communities where they have not yet been widely introduced. First, synthetic aperture reconstruction is expressed in terms of the adjoint operator. Many, if not all, practical imaging modalities can be traced back to this general result, as the adjoint is the foundation for backprojection-type algorithms.

Next, active surfaces are developed in the context of the Helmholtz equation for the cases of opaque scatterers (i.e., with no interior field) embedded in free space, and penetrable scatterers embedded in a volume which may be bounded. The latter are demonstrated numerically using closed-form solutions based on spherical harmonics. The former case was chosen as the basis for a laboratory experiment using Lamb waves in an aluminum plate. Lamb wave propagation in plates is accurately described by the Helmholtz equation, where the field quantity is the displacement potential. However, the boundary conditions associated with the displacement potential formulation of Lamb waves are incompatible with the shape gradient derived for the Helmholtz equation, except for very long or very short wavelengths.

Lastly, optical flow is used to solve a new and unique problem in the field of synthetic aperture sonar. Areas of acoustic focusing and dilution attributable to refraction can sometimes resemble the natural bathymetry of the ocean floor. The difference is often visually indistinguishable, so it is desirable to have a means of detecting these transient refractive effects without having to repeat the survey. Optical flow proved to be effective for this purpose, and it is shown that the parameters used to control the algorithm can be linked to known properties of the data collection and scattering physics.