Synthetic aperture diffraction tomography for three-dimensional imaging

Tomography of complex three-dimensional objects with ultrasound or microwave has been a long-standing goal since the introduction of these technologies after World War II. While current state-of-the-art systems can provide high-resolution images of cylindrical objects characterized by a two-dimensional structure, the three-dimensional case remains an open challenge owing to current limitations of sensor technology and computer power. Here, this problem is addressed by means of a synthetic aperture technique that, while using hardware technology developed for two-dimensional problems, accounts for the complexity of three-dimensional scattering and leads to high-resolution three-dimensional reconstructions. In this paper, we present the theoretical formulation of this new approach and illustrate it by means of a numerical example.