Resolution defocusing

Spatial resolution is a function of altitude of the backscattering region Hi, since the size of the defocus image writes D Hj — Hi)/ HfHi). With Hf 25km and Hi =11 km and if the spot is observed with a resolution of 1 arcsec, then when projected to the pupil the resolution is 5 x Hf Hi)/ Hf — Hi) 0.26m. At a 32 m, the defocus image is 2 arcmin wide. 

Our SIMS data is taken using a VGQ8 quadrupole with unit mass resolution between 0-300 amu and a differentially pumped argon ion gun used in a defocused mode. A current of l-2x 10 A in a 0.S cm spot area is used. 

For the high resolution case, the phase-contrast effects are automatically introduced owing to the combined effect of defocus and spherical aberration, which gives rise to an image of a structure complicated by the fact that also the amplitude term, resulting from the propagation process, interacts in a non-linear way with the phase term [16,89,90,96]. 

A direct removal of image Fourier coefficients from a reconstructed electron exit wave seems a most suitable way for resolution verification. Here, Figure 2 shows for the first time the contribution of Si (444) image Fourier coefficients to the separation of the 0.78A dumbbell distance in Si [112] in the phase of an electron exit wave. The focal series was recorded at Lichte defocus with the 0AM and reconstructed in 2001. 

Phase extension proves that the second model gives better and more reasonable results. Fig. 3c shows the final projected potential map of the crystal along [010] with resolution up to 1 A that is obtained after performing the phase extension for two cycles in combination with the diffraction data correction based on the second proposed mode. Hence, it is supposed that, in the examined structure, B atoms replace those Cu atoms sited in the Cu-0 chains. Image simulations based on the multislice theory were performed to confirm the proposed model in Fig. 3e. The simulated image calculated with the crystal thickness of 46 A and defocus value of -650 A is presented in Fig. 3d, which matches the contrast of the averaged experimental image (Fig. 3a) pretty well. 

For an image taken at Scherzer defocus, where T(u) -1 over a large range of resolution, the structure factor F(u) can be obtained from the Fourier transform of the HREM image lim(u) ... 

As mentioned in section 6, the structure factors F(u) are proportional to the Fourier components lim(u) of the HREM image and the projected potential is proportional to the negative of the image intensity, if the image is taken Scherzer defocus where the contrast transfer function T(u) -1. In general, the Fourier components lim(u) are proportional to the structure factors F(u) multiplied by the contrast transfer function (CTF). The contrast transfer function T(u) = D(u)sinx(u) is not a linear function. It contains two parts an envelope part D(u) which dampens the amplitudes of the high resolution components ... 

The first zero transition of the CTF at this defocus is called the point resolution, d, of the TEM and can be shown to be... 

Figure 2.6. An example of a contrast transfer function (CTF). The calculated CTF of a 200CX HRTEM at Scherzer defocus and Cs = 1.2 mm. The first zero is arrowed (corresponding to 0.23 nm resolution) and the resolution in angstrdms is shown on the horizontal axis. A-D are envelope functions plotted as a function of convergence angle (0) of the beam and beam energy spread (A V). Parallel illumination is necessary for high resolution (after Boyes et al 1980).

---