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P. Torruella et al.
small as possible to avoid misidentification (as already discussed). Hence, to cover
large portions of the spectra, the quantity of required filtered images may be huge.
Nowadays, EDX-Tomo [17–19] is one of the most popular techniques to obtain
a 3D elemental reconstruction in nanostructured materials. The new generation
of detectors and the multi-detector geometries in the TEM column have largely
decreased acquisition times and improved collection efficiency. This way, X-ray
spectra can be collected fast enough to limit sample damage, as it is tilted to acquire
the projections required for the tomographic reconstruction. Nonetheless, EDX is
not as good as EELS in terms of spatial resolution and oxidation state information
is not available from EDX.
Finally, EELS spectrum image (SI) [20, 21]—tomography reconstruction has
become the option of choice to analytically reconstruct a 3D volume when high
spatial and energy resolution are required. The advances in TEM instrumentation
(e.g. Cs correctors [22], Cc correctors [23] and monochromators [24], Cold FEG [25]
and better spectrometers) has allowed the acquisition time for EELS SI to decrease in
recent years, as well as providing an access to higher resolution. Furthermore, EELSSI contain more information than solely the elemental composition. Fine structure
information about the local atomic environment in the sample is available through
the analysis of the energy loss near-edge structure (ELNES), such as the atomic
coordination, valence state, and type of bonding. Thus, the determination of the
oxidation state is made possible by analysing EELS-SI data. ELNES arises from
the quantum nature of the electronic excitation process for the electron in a certain
atomic shell interacting with the electron beam, within the atom probed. Physically,
the near-edge structure (spamming several tens of eV from the ionization edge) can be
directly linked to the density of (empty) states above the Fermi level [3, 26]. Some of
the more usually exploited ELNE-structures are the white lines (sharp peaks caused
by the ionization to well-defined empty energy states of electros in transition metals
and rare earths) [27].
In the following, a series of key experiments on the development of the EELS
tomography technique carried out in recent years is described, as well as the
mathematical and physical considerations that made them possible.
11.2.1 Compressed Sensing (CS)
Before the detailed description of the experiments, the introduction of one last reconstruction algorithm developed in recent times is advisable, due to the nature of the
experiments themselves. Given the increment of the data volume required for analytical electron tomography experiments, faster and more accurate approaches must be
pursued.
An alternative reconstruction method, based in the same theoretical background
as the image compression algorithms (JPEG and JPEG-2000) [28], is proposed:
compressed sensing (CS) [5, 29–32].
P. Torruella et al.
small as possible to avoid misidentification (as already discussed). Hence, to cover
large portions of the spectra, the quantity of required filtered images may be huge.
Nowadays, EDX-Tomo [17–19] is one of the most popular techniques to obtain
a 3D elemental reconstruction in nanostructured materials. The new generation
of detectors and the multi-detector geometries in the TEM column have largely
decreased acquisition times and improved collection efficiency. This way, X-ray
spectra can be collected fast enough to limit sample damage, as it is tilted to acquire
the projections required for the tomographic reconstruction. Nonetheless, EDX is
not as good as EELS in terms of spatial resolution and oxidation state information
is not available from EDX.
Finally, EELS spectrum image (SI) [20, 21]—tomography reconstruction has
become the option of choice to analytically reconstruct a 3D volume when high
spatial and energy resolution are required. The advances in TEM instrumentation
(e.g. Cs correctors [22], Cc correctors [23] and monochromators [24], Cold FEG [25]
and better spectrometers) has allowed the acquisition time for EELS SI to decrease in
recent years, as well as providing an access to higher resolution. Furthermore, EELSSI contain more information than solely the elemental composition. Fine structure
information about the local atomic environment in the sample is available through
the analysis of the energy loss near-edge structure (ELNES), such as the atomic
coordination, valence state, and type of bonding. Thus, the determination of the
oxidation state is made possible by analysing EELS-SI data. ELNES arises from
the quantum nature of the electronic excitation process for the electron in a certain
atomic shell interacting with the electron beam, within the atom probed. Physically,
the near-edge structure (spamming several tens of eV from the ionization edge) can be
directly linked to the density of (empty) states above the Fermi level [3, 26]. Some of
the more usually exploited ELNE-structures are the white lines (sharp peaks caused
by the ionization to well-defined empty energy states of electros in transition metals
and rare earths) [27].
In the following, a series of key experiments on the development of the EELS
tomography technique carried out in recent years is described, as well as the
mathematical and physical considerations that made them possible.
11.2.1 Compressed Sensing (CS)
Before the detailed description of the experiments, the introduction of one last reconstruction algorithm developed in recent times is advisable, due to the nature of the
experiments themselves. Given the increment of the data volume required for analytical electron tomography experiments, faster and more accurate approaches must be
pursued.
An alternative reconstruction method, based in the same theoretical background
as the image compression algorithms (JPEG and JPEG-2000) [28], is proposed:
compressed sensing (CS) [5, 29–32].