Role of self-coherence in single-electron phase contrast imaging

Abstract

The extension of coherent lattice contrast into the energy loss region in high-resolution transmission electron microscopy (HRTEM) is described by a pulse-like electron-sample interaction in the energy/time uncertainty limit. It generates a wave packet by electron self-interference in any coherent-inelastic scattering event with energy loss. The width of this wave packet is characterized by a self-coherence length ls(ΔE) that is predictable because an intrinsic decoherence phase around one radian is set by the expectation value for phase fluctuations. In this case the visibility of interference contrast from a crystalline sample with lattice parameter a is limited by a Rayleigh-like transfer factor P(ls, a) in the self-coherently illuminated sample area. The model is verified by energy-filtered HRTEM images of hexagonal BN and identifies energy-loss-induced phase noise as a single-electron visibility limit distinct from resolution limitations caused by ensemble-coherence or counting-statistical noise.