Progress on a Mathematical Inversion Technique for Non-Destructive Evaluation

Last year, computer output was presented for synthetic pulse-echo data which was processed according to a mathematical imaging technique. This technique was based on the physical optics farfield inverse scattering (acronym, POFFIS) formalism for scattering by volume defects. This year, a number of theoretical advances have been made in the POFFIS formalism, with attendant revisions in the computer algorithm. Firstly, a revised POFFIS formalism was developed in which the surface of the scatterer is directly related to the scattering data. In this formalism, aperture limited scattering data yields an image of a corresponding aperture of the scattering surface of the defect. Secondly, this formalism will also yield an image of the scatterina surface of a crack. Thirdly, for true amplitude data, the impedance or reflection coefficient may be read directly from the computer output. Related to this last result was the elimination of an "image fading" phenomenon at certain critical angles. Fourthly, the computer algorithm, which was originally designed to process data for a spherically symmetric "trailer hitch", was modified (and tested) to process data when the range to the center of the coordinate system was different at each observation angle. Fifthly, the algorithm was modified (and tested) to process data when the average propagation speed varied with anqle. Implementation on a real data set is discussed.