The theory of super-resolution electron microscopy via Wigner-distribution deconvolution

The theory of deconvolving the microdiffraction data-set available in a scanning transmission electron microscope or, equivalently, the set of all bright- and dark-field images available in a conventional transmission electron microscope to obtain super- resolution micrographs (which are not limited by the transfer function of the objective lens) is developed and described with reference to holography and other phase-retrieval schemes. By the use of a Wigner distribution, influences of the instrument function can be entirely separated from the information pertaining to the specimen. The final solution yields an unambiguous estimate of the complex value of the specimen function at a resolution which in theory is only limited by the electron wavelength. The faithfulness of the image processing is shown to be not seriously affected by specimen thickness or partial coherence in the illuminating beam. The inversion procedure is remarkably noise insensitive, implying that it should result in a robust and practicable experimental technique, though one that will require very large computing facilities.