Inverse scattering with subwavelength resolution in the near-zone

In classical microscopy and inverse scattering, images are made from far field measurements. It will be shown that the standard Abbe or Rayleigh resolution limits arise as a result of assumptions which do not hold in the near field. Existing technologies such as TIRM and PSTM that exploit these properties of the near field produce two dimensional images which exhibit structure on a subwavelength scale. These images have proven difficult to interpret when the sample presents variations in structure and optical properties simultaneously in three dimensions. We present the analytic singular value decomposition of the linearized scattering operator. This representation leads to a robust inversion algorithm for the inverse scattering problem in the near zone. Numerical implementation of the algorithm is demonstrated using simulated noisy data to produce tomographic images of a three dimensional scatterer.