To calculate HREM images:

1. Load a crystal of small lattice parameters (like BaTiO₃).
2. Select a [uvw] zone axis (any zone axis is possible with Bloch-wave method).
3. Open the Bloch-wave window (menu Imaging).
4. Select the HREM map pane (Fig. 1).
5. Start with a as simple as possible calculation, use a small number of reflections, i.e. of the order of 50.

The toolbox contains 3 controls to adjust the camera length, the number of reflections and Laue zones.

The calculation is controlled by buttons

• Start the calculation.
• Stop the calculation.
• Reset the parameters of calculation.

Figure 1 shows the HREM pane of the Bloch-wave calculations. This pane that controls the calculation of High Resolution Electron Microscope images. It is in essence similar to the pane of the multislice approach. On its left part of the pane, there are controls to define the HREM calculation parameters and on its right part 3 panels to display the kinematical diffraction pattern, the HREM image map and the associated beam plot and images. The toolbox, activated by tool button, depends on the panel which selected.

The controls are distributed in 9 panes and used to introduce:

• Camera MTF: The MTF of the camera (Fig. 2a).
• Illumination: The beam half-convergence, defocus spread and objective aperture diameter (Fig. 2b).
• Imaging: The initial defocus and the defocus between two images of a series (Fig. 2c). Also the size of the defocus series, the image duplication and noise (Fig. 2d).
• Iteration: The starting thickness, the number of thickness steps and the step thickness (Fig. 2e).
• Obj. lens: The 2-Fold astigmatism, coma or 3-fold astigmatism (Fig. 2f).
• Holography: The bi-prism voltage and orientation (Fig. 2g).
• Cs & C5: The defocus, C_s and C_{5 spherical Aberrations (Fig. 2h).}
• Shift: Image shift (W11) and phase of a beam stop (Fig. 2i).
• Vibration: Drift, thermal magnetic noise (Fig. 2j)), x and y vibrations (Fig. 2k)

The iteration pane 2e shows the controls to set the specimen thickness and number of reflections included in the Bloch wave calculation. The following settings have been used to calculate the HREM map shown on Map pane:

• Minimum thickness 1.0 nm, thickness steps 0.5 nm, 20 steps (i.e. final thickness 1 nm + (20 - 1) * 0.5 nm = 10.5 nm).
• Mhe minimum number of Bloch waves (50). In fact 61 strong reflections perturbed by 216 weak reflections have been used.
• The atomic form factor.

Figure 2g Holography.	Figure 2h Spherical Aberrations.

Figure 2i Shift.	Figure 2j Vibration.

The Illuminationpane displays the coherent transfer function (intensity) attenuated by the 4 first order envelopes (temporal, spatial, cross and phase) as well as the attenuation due to thermal magnetic Noise.

Other microscope or specimen related parameters are accessed using the microscope and specimen settings. Many transfer function parameters are set using the transfer function settings.

Faster calculations are obtained when the Envelope illumination model is used. The coherent illumination model only takes into account the defocus and spherical aberration induced phase changes (transfer function>). The lines shown on the transfer function plot are indexed when the mouse hits them. The black, red, green, blue curves are respectively, the overall transfer function the product of the envelopes, the partial spatial and the partial temporal coherence envelopes and the TM noise.

The precise position of the Center of Laue Circle that fix the specimen tilt is set in a manner similar to that of the CBED>. This pane helps define:

• the starting defocus of a defocus series, the defocus step and the number of steps,

• the x and y image tiling.

• the noise.

Figure 3a HRTEM BaTiO3.	Figure 3b HRTEM BaTiO3 with coma (W31).

Before the calculation selecting the checkbox Plot option and the radio button Image, together with Atomic columns option makes possible to observe in the Plot result panel the effect of specimen thickness, defocus, several aberations, shift, vibration (Fig. 6a).

Figure 4 Observing Aberrations (Plot panel).

Figure 5 shows the phase of the wave function. The specimen thickness can be changed using the thickness slider of the toolBox, the right one the gamma correction.

Figure 5 Wave-function phase image.

Saving the wave-function and starting the HRTEM imager more optical Aberrations, illumination tilt, aperture centering, ... can be observed (Fig. 6b).

Figure 6a Plot option for real time observations.	Figure 6b Transfering the wave-function to the HRTEM imager.

Figure 7 HRTEM imager, coma aberration.

Figure 8a Transfer function.	Figure b wave-function (phase).