Determination of localized visibility in off-axis electron holography

• Report on a new statistical metric to determine holographic fringe visibility.
• Adds new signal to electron holography: measure of electron coherence loss in 2-D.
• Provide algorithm to calculate 2-D local visibility map.
• Show that amplitude and visibility may be used for compositional analysis and segmentation.
• Corrected for data bias such as shot noise.

Off-axis electron holography is a wavefront-split interference method for the transmission electron microscope that allows the phase shift and amplitude of the electron wavefront to be separated and quantitatively measured. An additional, third component of the holographic signal is the coherence of the electron wavefront. Historically, wavefront coherence has been evaluated by measurement of the holographic fringe visibility (or contrast) based on the minimum and maximum intensity values. We present a method based on statistical moments is presented that allows allow the visibility to be measured in a deterministic and reproducible fashion suitable for quantitative analysis. We also present an algorithm, based on the Fourier-ratio method, which allows the visibility to be resolved in two-dimensions, which we term the local visibility. The local visibility may be used to evaluate the loss of coherence due to electron scattering within a specimen, or as an aid in image analysis and segmentation. The relationship between amplitude and visibility may be used to evaluate the composition and mass thickness of a specimen by means of a 2-D histogram. Results for a selection of elements (C, Al, Si, Ti, Cr, Cu, Ge, and Au) are provided. All presented visibility metrics are biased at low-dose conditions by the presence of shot-noise, for which we provide methods for empirical normalization to achieve linear response.