Noise estimation for off-axis electron holography

• We derive a general noise transfer for the off-axis holographic reconstruction.
• Noise transfer formulas given by F. Lenz are included as a special case.
• We estimate the covariance of a hologram using the noise spread function.
• We experimentally verify the derived noise transfer formulas.

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.