Limited aperture effects on ultrasonic image reconstruction

In the inverse Born approximation the shape of a weak scatterer can be determined from a knowledge of the backscattered ultrasonic amplitude for all directions of incidence and all frequencies. Two questions are considered. First, what information on the scatterer shape is preserved and what is degraded if the scattering data are available only within a limited set of incident directions (limited aperture). This problem is addressed for a spherical weakly scattering uniform flaw. It is shown that the problem of a general uniform ellipsoidal flaw can be reduced to the spherical case by a scale transformation; however, the apertures in these two cases must be related by the same transformation. Second, limited aperture and finite bandwidth Born inversions were performed for strongly scattering flaws (voids and cracks) using numerically generated scattering amplitudes. These inversions were then compared with the weak scattering analytic results, which show many common features