Noise estimation for off-axis electron holography

Off-axis electron holography provides access to the phase of the elastically scattered wave in a transmission electron microscope at scales ranging from several hundreds of nanometres down to 0.1 nm. In many cases the reconstructed phase shift is directly proportional to projected electric and magnetic potentials rendering electron holography a useful and established characterisation method for materials science. However, quantitative interpretation of experimental phase shifts requires quantitative knowledge about the noise, which has been previously established for some limiting cases only. Here, we present a general noise transfer formalism for off-axis electron holography allowing to compute the covariance (noise) of reconstructed amplitude and phase from characteristic detector functions and general properties of the reconstruction process. Experimentally, we verify the presented noise transfer formulas for two different cameras with and without objects within the errors given by the experimental noise determination.