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P. Torruella et al.
technique, such as PCA, within a Bayesian framework. This is ought to reduce the
degrees of freedom in the parameters.
Although both methods described have proven to solve the BSS problem for
tomography reconstruction, new advances are expected in the field, driven by the
growing resources dedicated to the treatment of big data in a wide spectrum of
scientific and technological fields [45].
11.2.2.2 EELS-SV. Tomographic Reconstruction from the Elemental
Maps
After the PCA noise reduction and the EEL Spectra separation as a sum of weighted
spectral components identified by ICA/BLU, these are set as the orthogonal axes of
the new spectral basis. Every single EEL spectrum on every SI of the tilt series dataset
acquired is represented as a weighted sum of the identified spectral components.
The final step is the tomographic reconstruction itself, using the spectral weighted
component map separated from the SI as the projections fed to the algorithms.
The quality of the reconstruction, the number of projections and the computational
resources available, will determine the algorithm of choice, as already discussed.
At this point, EELS-SV is already available, since the full spectra in each
reconstructed voxel have been calculated from the separated components and the
corresponding weighting factors.
As a paradigmatic example, let us briefly revise the results achieved on the reconstruction of ferromagnetic (FM) CoFe 2 O 4 (CFO) nanocolumns embedded in a ferroelectric (FE) BiFeO 3 (BFO) matrix grown on a LaNiO 3 buffered LaAlO 3 substrate
(BFO–CFO//LNO/LAO) (see Fig. 11.5a). It is a prototypical multiferroic vertical
nanostructure, where the magnetic properties are strongly dependent of the substrate
material and orientation, ferroic phases, and phase ratio. Thus, a complete characterization, expected to bind functional properties and material structure, requires precise
knowledge of the local composition (EELS) coupled with 3D structure reconstruction
(electron tomography) [36].
A focus ion beam (FIB) [46] preparation of a nanopillar TEM specimen ensured
almost constant thickness in the projections regardless the tilt angle. Electron mean
free path exceeds sample thickness in all possible transmitted trajectories. Hence,
multiple scattering events should remain as a residual contribution to EELS signal.
This is confirmed by the absence of contrast inversion towards the centre of the
nanocolumn in the SI and, thus, enables the use of EELS component as the input
dataset for tomographic reconstruction.
BLU along with PCA where carried out for the endmember separation, and SIRT
was the algorithm of choice for tomographic reconstruction, requiring 20 iterations
before convergence. The parametric basis extracted after MVA consisted of four
components, identified as: (1) iron oxide (Fe x O y ), (2) lanthanum oxide(La x O y ), (3)
background contribution, and (4) noise in vacuum contribution (kept for calculations but not reconstructed), as shown in Fig. 11.5b. The results of the volume
reconstructions for each component in the basis in Fig. 11.5b are shown in Fig. 11.5d.
P. Torruella et al.
technique, such as PCA, within a Bayesian framework. This is ought to reduce the
degrees of freedom in the parameters.
Although both methods described have proven to solve the BSS problem for
tomography reconstruction, new advances are expected in the field, driven by the
growing resources dedicated to the treatment of big data in a wide spectrum of
scientific and technological fields [45].
11.2.2.2 EELS-SV. Tomographic Reconstruction from the Elemental
Maps
After the PCA noise reduction and the EEL Spectra separation as a sum of weighted
spectral components identified by ICA/BLU, these are set as the orthogonal axes of
the new spectral basis. Every single EEL spectrum on every SI of the tilt series dataset
acquired is represented as a weighted sum of the identified spectral components.
The final step is the tomographic reconstruction itself, using the spectral weighted
component map separated from the SI as the projections fed to the algorithms.
The quality of the reconstruction, the number of projections and the computational
resources available, will determine the algorithm of choice, as already discussed.
At this point, EELS-SV is already available, since the full spectra in each
reconstructed voxel have been calculated from the separated components and the
corresponding weighting factors.
As a paradigmatic example, let us briefly revise the results achieved on the reconstruction of ferromagnetic (FM) CoFe 2 O 4 (CFO) nanocolumns embedded in a ferroelectric (FE) BiFeO 3 (BFO) matrix grown on a LaNiO 3 buffered LaAlO 3 substrate
(BFO–CFO//LNO/LAO) (see Fig. 11.5a). It is a prototypical multiferroic vertical
nanostructure, where the magnetic properties are strongly dependent of the substrate
material and orientation, ferroic phases, and phase ratio. Thus, a complete characterization, expected to bind functional properties and material structure, requires precise
knowledge of the local composition (EELS) coupled with 3D structure reconstruction
(electron tomography) [36].
A focus ion beam (FIB) [46] preparation of a nanopillar TEM specimen ensured
almost constant thickness in the projections regardless the tilt angle. Electron mean
free path exceeds sample thickness in all possible transmitted trajectories. Hence,
multiple scattering events should remain as a residual contribution to EELS signal.
This is confirmed by the absence of contrast inversion towards the centre of the
nanocolumn in the SI and, thus, enables the use of EELS component as the input
dataset for tomographic reconstruction.
BLU along with PCA where carried out for the endmember separation, and SIRT
was the algorithm of choice for tomographic reconstruction, requiring 20 iterations
before convergence. The parametric basis extracted after MVA consisted of four
components, identified as: (1) iron oxide (Fe x O y ), (2) lanthanum oxide(La x O y ), (3)
background contribution, and (4) noise in vacuum contribution (kept for calculations but not reconstructed), as shown in Fig. 11.5b. The results of the volume
reconstructions for each component in the basis in Fig. 11.5b are shown in Fig. 11.5d.