Abstract
The inverse scattering problems of determining the shape of a cavity from observed waves are investigated by means of the Born inversion. The far-field amplitude of scattered waves is related to the spatial Fourier transform of a characteristic function of a cavity, which is equal to unity in the region occupied by a cavity and zero elsewhere. However, this method is based on the long-wavelength approximation. and is not adequate to the high frequency data. To improve the accuracy of inversion, we further propose the modified Born inversion which is applicable even for the high frequency data. In numerical examples, the data synthesized by the boundary integral equation are used to check the effect of some factors of incident and observed waves on the imaging of a cavity.
