Superresolved image reconstruction from incomplete data

A finite thickness slab of a metamaterial having a refractive index close to n = -1, can be used for sub-wavelength scale imaging. In the image domain, the measured fields contain evanescent wave contributions from subwavelength scale features in the object but these have to be related to the intrinsic parameters describing the scatterer such as refractive index or permittivity. For weak scatterers there can be a simple relationship between the field distribution and the permittivity profile. However for strong (multiple) scatterers and, more importantly, for objects for which subwavelength features contribute to the scattered (near) field, there is no simple relationship between the measured data and the permittivity profile. This is a significant inverse scattering problem for which no immediate solution exists and given the metamaterial slab’s limitations one cannot assume that either angle or wavelength diversity will be available to apply an inverse scattering algorithm. We consider wavelength diversity in this paper to acquire the measured data necessary to estimate a superresolved solution to the inverse scattering problem.