Repladed TEM imaging example specimen with Au and added diffraction e…

…xample.

TEM.md

@@ -12,33 +12,49 @@ numbering:
 ### Wavefunctions
 After building an atomic potential as described in the [](#algorithms_page), the first step in a TEM simulation is to choose the wavefunction ({math}`\Psi`) for the simulation. The simplest case for the incident beam is to set {math}`\Psi` to unity everywhere in the plane, which means perfectly even illumination across the sample. However, it is possible to introduce more complications, such as a slightly [titled plane wave](https://abtem.readthedocs.io/en/main/user_guide/walkthrough/multislice.html#small-angle-beam-tilt). The sampling is set by the gridpoint and extent as described in seciton [](#sim_inputs_page).
 
-In [](#fig_potential_wave_image) we show an interactive visualization of the potential of the STO/LTO interface we created in [](#manipulating-atoms), the corresponding exit wave function, and the resulting image with a reasonable [contrast transfer function](#CTF_page) applied, as a function of the slices through the specimen.
+### Imaging
 
-```{figure} #app:tem_potential_wave_image
-:name: fig_potential_wave_image
-:placeholder: ./static/potential_wave_image.png
+A TEM image is simulated by propagating the wavefunction through the specimen potential using the multislice algorithm, which calculates how the wave evolves due to scattering by the specimen atoms and the propagation through it. The resulting exit-wave is complex, but can be visualized via its intensity. For a more realistic image, a [contrast transfer function](#CTF_page) can be applied to model the optics of the microscope; note that this is done after the computationally time-consuming multislice run which described the physics of hte interaction.
+
+In [](#fig_tem_Au_potential_wave_image) we show an interactive visualization of the potential of gold with a lattice constant of 4.08 Å in the <100> zone axis, the corresponding exit wave function, and the resulting image as a function of depth through the specimen.
+
+```{figure} #app:tem_Au_potential_wave_image
+:name: fig_tem_Au_potential_wave_image
+:placeholder: ./static/tem_Au_potential_wave_image.png
 **Visualization of slicing through the specimen for the potential, the exit wave, and the image with a CTF applied.**
 ```
 
-### Imaging 
+%#### Imaging example 
+%
+%```{figure} #app:tem_imaging
+%:name: fig_tem_phase
+%:placeholder: ./static/tem_imaging.png
+%**TEM imaging of SrTiO$_3$ grains**: 
+%```
 
-```{figure} #app:tem_imaging
-:name: fig_tem_phase
-:placeholder: ./static/tem_imaging.png
-**TEM imaging of SrTiO$_3$ grains**: 
-```
+### Electron diffraction patterns
 
+Instead of an image, we can instead simulate a selected area diffraction (SAD) experiment by using the `DiffractionPatterns` method. We use `block_direct=True` to block the direct beam: it typically has a much higher intensity than the scattered beams, and thus it is typically not possible to show it on the same scale.
 
+You may wonder; why do the diffraction spots look like squares? This is because the incoming wave function is a periodic and infinite plane wave, hence the intersection with the Ewald sphere is pointlike. However, since we are discretizing the wave function on a square grid (i.e. pixels), the spots can only be as small as single pixels. In real SAD experiments, the spot size is broadened due to the finite extent of the crystal as well instrumental effects.
 
-### Diffraction 
+We can use the `index_diffraction_spots` method to create a represention of SAD patterns as a mapping of Miller indices to the intensity of the corresponding reflections. The *conventional* unit cell have to be provided in order to index the pattern, we can provide this as the unit cell of the gold crystal we created earlier, we cannot use the the repeated cell.
 
-```{figure} #app:tem_diffraction
-:name: fig_tem_diffraction
-:placeholder: ./static/tem_diffraction.png
-**TEM diffraction of STO as a function of thickness**: 
-```
+In [](#fig_tem_Au_diffraction) we show an interactive visualization of the diffraction intensities and indexed diffraction spots as function of the depth through the specimen. We see that the {100} reflections are extinguished, as is expected from the selection rules of an F-centered crystal. We can also observe that the <220> spots end up with significantly higher intensity than the <200> spots; this is due to dynamical scattering — which is accounted for by the multislice algorithm.
 
+```{figure} #app:tem_Au_potential_wave_image
+:name: fig_tem_Au_diffraction
+:placeholder: ./static/tem_Au_diffraction.png
+**Visualization of redistribution of diffraction intensity as function of depth through an Au <100> specimen, and the Miller indexing of the resulting diffraction spots.**
+```
 
+%#### Diffraction example
+%
+%```{figure} #app:tem_diffraction
+%:name: fig_tem_diffraction
+%:placeholder: ./static/tem_diffraction.png
+%**TEM diffraction of STO as a function of thickness**: 
+%```
 
 ### Contrast transfer and phase contrast STEM
 Thus far we have been considering how to form images and diffraction patterns with perfect incident illumination. However, often we're interested in seeing how aberrations or other beam modifications impacts imaging conditions. There are a variety of aberration functions ({math}`\chi(\bm{k})`) we may be interested in including as described in [](#CTF_page).