In TEM imaging, the conventional modes of high-resolution imaging are mainly determined by the objective lens defocus. There are four generally used defocus settings:
Except the first defocus is in-focus, underfocuses are applied to all the other defocus settings because of the existing, positive spherical aberration of the objective lens, which has to be counterbalanced in a certain way by a negative defocus aberration related to underfocus.
i) “Standard” defocus.
ii) Scherzer defocus maximizing the phase contrast of a weak-phase object,
iii) Lichte defocus of least confusion, minimizing contrast delocalization,
iv) Minimum phase-contrast defocus.
The defocus value (Δf) can be determined from the position of the first crossover of contrast transfer function (refer to Equation 4974b):
Here, n = 0, ±1. That means different integers n give different defoci. For instance, a TEM system has a spherical aberration constant Cs 1.38 mm, is operating at 200 kV (the wavelength is 0.0025 nm), and has the first crossover of Fourier transform at u = 2.75 nm-1. Therefore, three possible defocus values are -15 nm (for n = -1), -70 nm (for n = 0), and 53 nm (for n = 1).
The values of Δf (defocus value), Cs (spherical aberration coefficient), and D (standard deviation of the Gaussian distribution of defocus due to the chromatic aberration) can be obtained by TEM image deconvolution.
Table 3874. Selections of focusing/defocusing conditions in TEM imaging.
|Best/optimum defocus condition for HRTEM imaging
|Optimal defocus for minimizing the delocalization in (HR)TEM imaging
|Minimum (phase-)contrast in (HR)TEM imaging with Gaussian defocus
|Maximum (phase-)contrast in (HR)TEM imaging (with Scherzer defocus)