Energy-filtered phase retrieval using the transport of intensity equation

Energy-filtered imaging was combined with phase retrieval to study plasmon scattering contributions to electron phase shifts surrounding gold nanoparticles. Spectral windows with sufficient energy resolution to exclude plasmon scattering were used to measure through-focal intensity derivatives and retrieve phase maps via the transport of intensity equation. Phase excursions in the phase maps that included plasmon scattering were found to disagree with theory by at least an order of magnitude. This discrepancy was attributed to subtle particle instabilities under the electron beam, which lead to systematic errors in the retrieved phase maps.