This paper is concerned with the inverse problem of reconstructing a small object from far-field measurements. The inverse problem is severely ill-posed because of the diffraction limit and low signal to noise ratio. We propose a novel methodology to solve this type of inverse problem based on an idea from plasmonic sensing. By using the field interaction with a known plasmonic particle, the fine detail information of the small object can be encoded into the shift of the resonant frequencies of the two particle system in the far field. In the intermediate interaction regime, we show that this information is exactly the generalized polarization tensors associated with the small object, from which one can perform the reconstruction. Our theoretical findings are supplemented by a variety of numerical results. The results in the paper also provide a mathematical foundation for plasmonic sensing.
- Far-field measurement
- Generalized polarization tensors
- Plasmonic sensing
ASJC Scopus subject areas
- Applied Mathematics