large specimen thickness, so that the beam diameter at the exit face is roughly the
same for both semi-convergence angles. Although incident beam convergence of
9.7 mrad produces a smaller probe focus in vacuum, a smaller semi-convergence
angle should be used for tomographic experiments, in order to utilize the larger
depth of focus that is proportional to 1/a
2 , and to reduce the electron dose for
radiation-sensitive material that scales with a
2 .
Figure 2.3e shows the beam diameter defined as the area that contains 68% of
the electrons as a function of the specimen depth for a = 9.7 mrad and a = 2.9
mrad. The figure indicates that a resolution in the range of a few nanometers can be
obtained with an electron probe of small convergence angle in biological samples
even if they are a micrometer thick. In agreement with the previous discussion, the
smaller semi-convergence angle is the better compromise for the resolution
throughout the sample. A refined calculation would take into account multiple
inelastic scattering, which leads to an additional broadening of the STEM beam in
thicker specimens [30], but does not change this major conclusion. The quantitative
broadening displayed in Fig. 2.3e will be slightly worse when multiple inelastic
scattering is to be included. In fact, nanometer-resolution has been demonstrated in
STEM for micrometer-thick plastic sections [31], stained samples [32], and
liquid-cells [16]. It should be stressed that a similar resolution cannot be obtained in
phase contrast TEM unless zero-loss filtering is applied [26], upon which the
majority of electrons that suffer from one or more inelastic scattering events will not
contribute to the image, but do heavily contribute to radiation damage.
In the presence of multiple scattering, object details will be imaged with better
resolution when they are located on the surface facing the probe forming lens in
STEM, and facing the objective lens in TEM [26, 33, 34]. In STEM mode this
top-bottom effect results in a poorer resolution for specimen details at the bottom of
a thick layer, whereas details at the top are imaged with a resolution given by the
diameter of the scanning beam. In TEM-mode, details at the bottom are imaged
with additional chromatic error, whereas details at the top show the additional
influence of multiple scattering [34]. In STEM mode the resolution throughout the
sample thickness can be optimized by an appropriate focus which reduces the
resolution at the top surface but improves the resolution at the bottom surface by
balancing with the geometrical broadening. This situation is shown in Fig. 2.4,
where the probe is focused roughly at the center of the sample. In practice, this is
hard to achieve because the depth of the area of focus is unknown during standard
tomographic experimental protocols. However it is possible to combine a series of
acquisitions at multiple focus values in order to extend the depth of field [35, 36].
With increasing thickness, the resolution in STEM ADF or HAADF images
tends to degrade more than in a BF image because the dark field detectors collect an
increasing fraction of multiply scattered electrons, while a small BF detector ideally
does not distinguish between events that take electrons out of the direction of
transmission. It was therefore suggested that STEM tomography tilt series of thick
stained sections is optimally performed with a BF detector [28, 31, 37]. Care must
be taken because multiple (in)elastic scattering can lead to contrast inversion in the
2 STEM Tomography in Biology
41
same for both semi-convergence angles. Although incident beam convergence of
9.7 mrad produces a smaller probe focus in vacuum, a smaller semi-convergence
angle should be used for tomographic experiments, in order to utilize the larger
depth of focus that is proportional to 1/a
2 , and to reduce the electron dose for
radiation-sensitive material that scales with a
2 .
Figure 2.3e shows the beam diameter defined as the area that contains 68% of
the electrons as a function of the specimen depth for a = 9.7 mrad and a = 2.9
mrad. The figure indicates that a resolution in the range of a few nanometers can be
obtained with an electron probe of small convergence angle in biological samples
even if they are a micrometer thick. In agreement with the previous discussion, the
smaller semi-convergence angle is the better compromise for the resolution
throughout the sample. A refined calculation would take into account multiple
inelastic scattering, which leads to an additional broadening of the STEM beam in
thicker specimens [30], but does not change this major conclusion. The quantitative
broadening displayed in Fig. 2.3e will be slightly worse when multiple inelastic
scattering is to be included. In fact, nanometer-resolution has been demonstrated in
STEM for micrometer-thick plastic sections [31], stained samples [32], and
liquid-cells [16]. It should be stressed that a similar resolution cannot be obtained in
phase contrast TEM unless zero-loss filtering is applied [26], upon which the
majority of electrons that suffer from one or more inelastic scattering events will not
contribute to the image, but do heavily contribute to radiation damage.
In the presence of multiple scattering, object details will be imaged with better
resolution when they are located on the surface facing the probe forming lens in
STEM, and facing the objective lens in TEM [26, 33, 34]. In STEM mode this
top-bottom effect results in a poorer resolution for specimen details at the bottom of
a thick layer, whereas details at the top are imaged with a resolution given by the
diameter of the scanning beam. In TEM-mode, details at the bottom are imaged
with additional chromatic error, whereas details at the top show the additional
influence of multiple scattering [34]. In STEM mode the resolution throughout the
sample thickness can be optimized by an appropriate focus which reduces the
resolution at the top surface but improves the resolution at the bottom surface by
balancing with the geometrical broadening. This situation is shown in Fig. 2.4,
where the probe is focused roughly at the center of the sample. In practice, this is
hard to achieve because the depth of the area of focus is unknown during standard
tomographic experimental protocols. However it is possible to combine a series of
acquisitions at multiple focus values in order to extend the depth of field [35, 36].
With increasing thickness, the resolution in STEM ADF or HAADF images
tends to degrade more than in a BF image because the dark field detectors collect an
increasing fraction of multiply scattered electrons, while a small BF detector ideally
does not distinguish between events that take electrons out of the direction of
transmission. It was therefore suggested that STEM tomography tilt series of thick
stained sections is optimally performed with a BF detector [28, 31, 37]. Care must
be taken because multiple (in)elastic scattering can lead to contrast inversion in the
2 STEM Tomography in Biology
41