Nonlinear Inverse Scattering and Three-Dimensional Near-Field Optical Imaging
G. Panasyuk and J. Schotland (University of Pennsylvania) and P.S. Carney (University of Illinois, Urbana-Champaign)
Three-dimensional optical imaging at the nanoscale presents a formidable challenge with correspondingly great scientific rewards. Potential applications range across multiple fields within both the physical and biological sciences. In micro- and nano-fabrication, for example, manufacturing processes are transitioning from planar to stacked platforms. In cell biology, the study of subcellular nanostructures is recognized as increasingly important. In these and numerous other examples, near-field microscopy realizes nanometer resolution but with a significant limitation, namely only surface features of the sample are visualized.
Near-field tomography (NFT) is a recently proposed computed imaging modality for three-dimensional optical imaging with subwavelength resolution and achieves nanoscale resolution by combining the experimental methods of near-field optics with the mathematical tools of inverse scattering theory. In NFT the sample is illuminated sequentially by a series of incident waves while the scattered field is measured in the near zone. Using the data gathered from such an experiment, it is possible to reconstruct the three-dimensional sample structure. In previous work we have studied this inverse scattering problem (ISP) within a linearization of scattering theory. The purpose of the current study is to extend these results to account for the effects of multiple scattering. This situation, in which the ISP is nonlinear is of interest when variations in the susceptibility are not small or when the sample is sufficiently large, conditions which characterize a large class of physical systems.
Panasyuk, Carney and Schotland Appl. Phys. Lett. (2006)