Voxel dose-limited resolution for thick beam-sensitive specimens imaged in a TEM or STEM

The resolution limit imposed by radiation damage is quantified in terms of a voxel dose-limited resolution (DLR), applicable to small features within a thick specimen. An analytical formula for this DLR is derived and applied to bright-field mass-thickness contrast from organic (polymer or biological) specimens of thickness between 400 nm and 20 µm. For a permissible dose of 330 MGy (typical of frozen-hydrated tissue), the TEM or STEM image resolution is determined by radiation damage rather than by lens aberrations or beam-broadening effects, which can be restricted by use of a small angle-limiting aperture. DLR is improved by a up to factor of 2 by increasing the primary-electron energy from 300 keV to 3 MeV, or by up to a factor of 3 by heavy-metal staining. For stained samples, a higher electron fluence allows better resolution but the improvement is modest because the voxel DLR is proportional to the 1/4 power of electron dose. The relevance of voxel and columnar DLR is discussed, for both thick and thin samples.