In CTEMs, the defocus spread
(Δ) (sometimes called defocus fluctuation) is the spread mainly caused by the current
instability (δI/I0) of the objective lens, the overall energy spread of the incident electron beam (δV/V0), and the incident
electron energy (δE/E0). Δ is given by,
V0 -- The accelerating voltage of the electrons.
I0 -- Objective lens current
E0 -- Accelerating voltage of the incident beam
δ -- Fluctuations of V0, I0, and E0
Cc -- Cchromatic aberration coefficient
Note that the defocus spread, in CTEMs with LaB6 or W electron guns and FE-EMs, affects the intensity of diffractogram and real images. The temporal coherence affects the envelope function because of the energy spread of the electrons, which induces a defocus spread Δ because of the chromatic aberration. In EMs (especially in TEMs), the temporal coherency effects comes from the small instabilities in the accelerating voltage and electron gun emission over time, which will give the illumination a small energy spread, and from variations in the lens currents, which induces focus variation with time. Because the electrons with different energy are focused at different planes, the total effect of the temporal coherency variations is to create a defocus spread Δ (usually in the order of a few nm) due to the chromatic aberration.
In STEM mode, the focal spread can be given by,
Δ = α x Δz ----------------------- [4164b]
α -- The beam convergence semi-angle,
Δz -- The defocus.
Any defocus change, e.g. induced by a wedged or other non-uniform thickness in the TEM film, results in a defocus spread affecting the quality of the Thon ring pattern and deteriorate the high-frequency information that is needed for accurate aberration measurement, for instance, based on diffractogram.
Note that the variation of the high voltage generated for electron microscopes (especially TEMs) should be kept as small as possible because it induces defocusing of EM images due to the chromatic aberrations.