QUANTITATIVE RECONSTRUCTION OF INTERNAL DENSITY DISTRIBUTIONS FROM LASER ULTRASONIC DATA

An ultrasonic method has been investigated for the quantitative recove ry of density distributions of porous bodies similar to those produced by pressure-assisted sintering of powders. It relies upon the strong relationship between the ultrasonic velocity and the density of a poro us body. Noncontact laser-generated/interferometrically detected ultra sound has been propagated along ray paths in a planar cross section of model samples and ultrasonic time-of-flight projections obtained. Two approaches have been explored for reconstructing the internal velocit y (and thus density) distribution from the projection data. The first approach was a standard convolution backprojection algorithm used freq uently in computerized tomographic reconstruction. A combination of ra y bending (due to refraction by the velocity gradient within the sampl e), noise in the projections, and practical limits upon the number of projections that can be obtained have all adversely affected the recon struction quality of this method. The second approach explored a (nont omographic) nonlinear least-squares approach. It utilized a priori inf ormation about the general functional form of the velocity (density) d istribution (which is available from predictive models of the densific ation process) and gave significantly better results for samples with simple geometry even when projection data were sparse.