HRTEM Simulation¶
Simulates high-resolution TEM lattice-fringe images. The primary mode of the HRTEM/STEM simulator.
Calculation flow¶
- Bloch-wave method: compute electron wave propagation through the crystal potential; obtain exit-wave amplitude and phase
- Lens function: apply objective-lens aberrations (spherical aberration \(C_s\), defocus \(\Delta f\))
- Partial coherence: account for finite source size (spatial coherence) and energy spread (temporal coherence)
- Image formation: compute intensity \(|\psi(\mathbf{r})|^2\)
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:
- \(\sin\chi(u)\): phase contrast transfer function (\(\chi(u)\) is the lens aberration function)
- \(E_\text{s}(u)\): spatial coherence envelope
- \(E_\text{c}(u)\): temporal coherence envelope
Scherzer defocus: \(\Delta f = -\sqrt{\tfrac{4}{3}\,C_s \lambda}\ (\approx -1.155\,\sqrt{C_s \lambda})\), the condition giving a broad negative PCTF band (dark contrast = atom positions). ReciPro uses this original Scherzer value — derived by setting the minimum of the aberration phase \(\chi\) to \(-2\pi/3\) — and the value shown in the GUI follows this formula; some references instead use the extended Scherzer value \(-1.2\sqrt{C_s\lambda}\).
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) |
Image adjustment¶
| Setting | Description |
|---|---|
| Min / Max | Display range (image-adjustment trackbars) |
| Colour | Greyscale or Cold-Warm |
| Gaussian blur (FWHM) | Apply a Gaussian filter |
| Unit cell | Overlay unit-cell grid |
| Scale | Show scale bar |