Two-dimensional ultrasonic tomography in nondestructive evaluation by using area functions

It is shown that the (normalized) area function based on the Born approximation offers a simple connection between the ultrasonic scattering response and the monochromatic ray sum in X-ray CT (computerized tomography). Because of this simple association, it is possible to apply the ultrasonic signals in the computationally direct and efficient parallel-beam X-ray CT algorithm to reproduce the vertical thickness function of an ultrasonic scatterer. The development of this imaging methodology is demonstrated for flaws of simple geometry; theoretical as well as experimental results for two model scatterers using this imaging technique are reported. Specifically, the area functions for a two-to-one spheroid and a circular cylinder are calculated and applied to a filtered backprojection algorithm of X-ray CT to obtain the vertical thickness function images. These images are then compared with the true vertical thickness functions of the targets based on their geometry. With theoretical data, this method was found to work very well. Even when experimental data containing creeping waves were used, the method produced satisfactory results for objects with continuously smooth surface.<>