Nonlinear diffraction tomography: The use of inverse scattering for imaging

Our recent inverse scattering work has been to derive inverse scattering theory and algorithms that can be used to process practical experimental data. The theory makes use of computation of the forward scattering solution. Therefore, an eecient forward solver is instrumental to the rapid solution of the inverse scattering problem. The advantage of the more sophisticated theory over a linear theory is that it accounts for multiple scattering eeects within the scat-terers which often give rise to distortions in an image. A new method to invert strong scatterers, such as metallic scatterers, is presented. 1 Introduction In inverse scattering, one attempts to infer the pro-le of an object from measurement data collected away from the scatterer see Figure 1]. Needless to say, this is very important for a number of sensing and remote sensing applications. For instance, it nds applications in nondestructive testing, geophysical probing, medical imaging, and target identiication. In addition to obtaining the image of an object, a quantitative description of the scatterer such as its permittiv-ity, velocity, or conductivity proole is also obtainable from an inverse scattering experiment and can be an extremely valuable diagnostic information. Most imaging modalities use elds or waves to probe an object. In inverse scattering, one attempts to infer the object from the eld perturbation, or the scattered eld induced by the presence of the object. ε ε o x y T R ρ ρ T R Figure 1: An inverse scattering experiment where an object is illuminated by the transmitted eld, and the scattered eld is measured at the receivers. The inverse scattering problem is often quite diicult, especially when wave interactions are present. It is often non-unique because high spatial frequency portions of the object give rise to evanescent waves that cannot be measured. Multiple scattering causes the scattered eld to be nonlinearly related to the scat-terer. Many methods have been proposed in the past to solve particular classes of inverse scattering problems by making certain underlying assumptions about the object or scattering process. For example, in computed tomography (CT) a ray picture is used whereby it is assumed that waves propagate in straight lines and all diiraction and multiple scattering eeects are ignored. Diiraction tomography (DT) takes into account diiraction, but ignores multiple scattering and assumes that the object contrast is small. Many methods have been proposed to solve the inverse scattering problem \exactly" for 1-D objects (objects such …