It is intended in this Phase II of the project to continue and complete the development of the general formulation of diffraction tomography that was initiated in Phase I. This formulation is applicable to weak and strongly scattering objects, to general experimental configurations employing plane, fan beam or other types of incident wavefields and to applications where the data is sparse either because of a limited number of experiments (limited views) or under sampling of the waveforms over the measurement surfaces. The general formulation will be implemented in software codes on a microprocessor equipped with an array processor and will be extensively tested in computer simulations and on experimental data drawn from seismic, electromagnetic, ultrasound and optical tomographic applications. Major emphasis will be given to applications for which follow-on funding commitments are obtained. This project is aimed at developing mathematical and computational techniques for the so called diffraction tomography. This is a generalized formulation of tomography for applications involving radiation other than x-rays, such as for example, ultrasound tomography, optical tomography and geophysical tomography. Earlier studies in diffraction tomography assumed plane wave illumination of the object and worked with the linearized version of the wave equation. More recent approaches, including this one, work with the complex phase of the transmitted field. Potential applications of this research include ultrasound tomographic scanners for medical and industrial applications, coherent optical tomographic scanners for monitoring combustion processes and a host of geophysical applications including seismic imaging, well-to- well tomography and ocean acoustic tomography.
