We explore the properties of elastic and inelastic scattering in a thick organic specimen, together with the mechanisms that provide contrast in a transmission electron microscope (TEM) and scanning-transmission electron microscope (STEM). Experimental data recorded from amorphous carbon are used to predict the bright-field image intensity, mass-thickness contrast and dose-limited resolution as a function of thickness, objective-aperture size, and primary-electron energy E0. Combining this information with estimates of chromatic aberration, objective-aperture diffraction and beam broadening in the specimen, we calculate the achievable TEM and STEM resolution to be around 4 nm at E0 = 300 keV (or below 3 nm at MeV energies) for a 10 µm-diameter objective aperture and 1 – 2 µm thickness of hydrated biological tissue. The 3 MeV resolution for a 10-μm tissue sample is probably closer to 10 nm. We also comment on the error involved in quadrature addition of resolution factors, when one or more of the point-spread functions are non-Gaussian. •Electron scattering in a thick TEM specimen is reviewed, including the effect of a collection aperture.•Experimental data are used to predict image intensity, contrast and dose-limited resolution.•Including instrumental effects, bright-field resolution is estimated for accelerating voltages a up to 3 MV.•Linear and quadratic addition of resolution components are discussed and compared.