Coherence and statistical insights for low electron count regimes in transmission electron microscopy

Abstract

We investigate coherent diffraction patterns from an amorphous SiO2 across a range of electron counting regimes, from sparse single-event detection to cumulative high-flux exposures. Low electron count rates, with a mean of approximately 0.017 electrons per pixel, reveal discrete electron events dominated by shot noise. In contrast, cumulative patterns acquired over 60 s exhibit pronounced speckle features reflecting atomic arrangements in the material. The count contrast Ck as a function of mean electron count K¯ transitions from a Poisson-dominated 1/K¯ trend at low K¯ to a stabilized Ck=0.23 beyond K¯=10, of which behavior is modeled effectively with a spatial degree of freedom M=32. This M value indicates partially coherent illumination, deviating from single-mode expectations of the electron beam. Our finding bridges a gap between statistical optics and applied TEM and introduces a framework with direct practical relevance for modern detector technologies.