Skip to content

8.1. HRTEM simulation

seto edited this page Mar 23, 2026 · 2 revisions

HRTEM Simulation

Simulates high-resolution TEM lattice-fringe images. The primary mode of the 8. HRTEM/STEM simulator.


Calculation flow

  1. Bloch-wave method: compute electron wave propagation through the crystal potential; obtain exit-wave amplitude and phase
  2. Lens function: apply objective-lens aberrations (Cs, defocus Δf)
  3. Partial coherence: account for finite source size (spatial coherence) and energy spread (temporal coherence)
  4. Image formation: compute intensity |ψ(r)|²

Specimen parameters

Parameter Description
Thickness Specimen thickness (nm). HRTEM images are strongly thickness-dependent

Optical parameters

TEM conditions

Parameter Description
Acc. Vol. Accelerating voltage (kV). Relativistically corrected wavelength shown alongside
Defocus Defocus value (nm). Scherzer defocus displayed as reference

Intrinsic parameters

Parameter Description Typical
Cs Spherical aberration (mm) 0.5–1.0 (conventional); < 0.01 (Cs-corrected)
Cc Chromatic aberration (mm) 1.0–2.0
β Illumination semiangle (mrad) 0.1–1.0
ΔE Energy spread 1/e width (eV) 0.5–2.0

Phase Contrast Transfer Function (PCTF)

Displayed in the lens-function tab:

  • Sin[χ(u)]: phase contrast transfer function
  • Es(u): spatial coherence envelope
  • Ec(u): temporal coherence envelope

Scherzer defocus: Δf = −1.2 (Cs λ)^(1/2), the condition giving a broad negative PCTF band (dark contrast = atom positions).


Objective aperture

Set aperture size (mrad) and position. Open aperture removes it. The number of Bloch waves considered depends on aperture conditions.


Partial coherence models

Model Description
Quasi-coherent (linear image) Fast. Valid under the weak-phase approximation
TCC (Transmission Cross Coefficient) More accurate; longer computation

Simulation modes

Mode Description
Single image One image at current thickness and defocus
Serial image Matrix of images over thickness × defocus ranges (Start / Step / Num)

See also

Clone this wiki locally