268
P. Torruella et al.
The first approximation to the spectrum volume reconstruction was carried out by
acquiring sets of spectrum images (SI) at different tilt angles, simultaneous with the
acquisition of HAADF images [37]. To avoid sample damage, the experiments are
usually performed using short acquisition times for the EEL spectra. These conditions
reduce the signal to noise ratio (SNR) of the spectra; thus, statistical treatment is
routinely required to retrieve significant information. The large number of spectra
acquired for the complete set of projections increases the statistics, allowing the
successful retrieval of a denoised signal through multivariable analysis methods
(MVA) [20, 38–40].
The information fed to the tomographic reconstruction algorithms is intended to
be the intensity of the EELS edges on the spectrum images acquired I (x, y, θ) (i.e.
the integrated area under the curve for each edge). This way, a map of separated
elements according to EELS edge intensities is available for each projected image.
The intensity of EELS edges in the core-loss region is given by:
I k
A
(β, ,) = N
A
σ k
A
(β, ,) l T (β) e
(−t/λ)
for the k edge of element A integrating over a collection angle β along an energy
range , I K
A is the integrated intensity, N
A is the areal density, σ k
A is the ionization
cross-section and l T is the total transmitted beam intensity; t is the sample thickness and λ the inelastic mean free path. (If t/λ 0.3, plural scattering events are
expected, and the equation may not hold ). Avoiding plural scattering, the edge intensities will vary monotonically with thickness (material property), and the signals are
suitable for tomographic reconstruction. This will be the usual scenario for magnetic
nanoparticles due to their reduced size.
In cases where plural scattering is relevant (thicker or larger samples), some problems may arise. One clear example is the case of the ‘cupping artefact’, characterized
by an inversion of the spectrum image contrast in thicker zones of the sample [41].
This leads to a miscalculation of the edge intensity and, thus, of the elemental quantification. Hence, in those cases, EELS edge intensities may no longer be suitable
signals for tomography reconstruction.
The correct identification of cupping artefact effects in SI is not always straightforward, since they can be mistaken by a structural effect on the image (e.g. core-shell
structure). Thereby, a thorough study of the material is required before undertaking
the tomographic reconstruction. Although the spectrum volume cannot be retrieved if
EELS edge intensities are unsuitable for tomographic reconstruction, 3D information
for the elemental distribution in the samples can still be extracted [37].
11.2.2.1 Multivariable Analysis Methods (MVA)
SNR is usually low in EELS-SI experiments, due to image acquisition constraints
to avoid sample damage. Hence, statistical treatment of the signals in the SI and
P. Torruella et al.
The first approximation to the spectrum volume reconstruction was carried out by
acquiring sets of spectrum images (SI) at different tilt angles, simultaneous with the
acquisition of HAADF images [37]. To avoid sample damage, the experiments are
usually performed using short acquisition times for the EEL spectra. These conditions
reduce the signal to noise ratio (SNR) of the spectra; thus, statistical treatment is
routinely required to retrieve significant information. The large number of spectra
acquired for the complete set of projections increases the statistics, allowing the
successful retrieval of a denoised signal through multivariable analysis methods
(MVA) [20, 38–40].
The information fed to the tomographic reconstruction algorithms is intended to
be the intensity of the EELS edges on the spectrum images acquired I (x, y, θ) (i.e.
the integrated area under the curve for each edge). This way, a map of separated
elements according to EELS edge intensities is available for each projected image.
The intensity of EELS edges in the core-loss region is given by:
I k
A
(β, ,) = N
A
σ k
A
(β, ,) l T (β) e
(−t/λ)
for the k edge of element A integrating over a collection angle β along an energy
range , I K
A is the integrated intensity, N
A is the areal density, σ k
A is the ionization
cross-section and l T is the total transmitted beam intensity; t is the sample thickness and λ the inelastic mean free path. (If t/λ 0.3, plural scattering events are
expected, and the equation may not hold ). Avoiding plural scattering, the edge intensities will vary monotonically with thickness (material property), and the signals are
suitable for tomographic reconstruction. This will be the usual scenario for magnetic
nanoparticles due to their reduced size.
In cases where plural scattering is relevant (thicker or larger samples), some problems may arise. One clear example is the case of the ‘cupping artefact’, characterized
by an inversion of the spectrum image contrast in thicker zones of the sample [41].
This leads to a miscalculation of the edge intensity and, thus, of the elemental quantification. Hence, in those cases, EELS edge intensities may no longer be suitable
signals for tomography reconstruction.
The correct identification of cupping artefact effects in SI is not always straightforward, since they can be mistaken by a structural effect on the image (e.g. core-shell
structure). Thereby, a thorough study of the material is required before undertaking
the tomographic reconstruction. Although the spectrum volume cannot be retrieved if
EELS edge intensities are unsuitable for tomographic reconstruction, 3D information
for the elemental distribution in the samples can still be extracted [37].
11.2.2.1 Multivariable Analysis Methods (MVA)
SNR is usually low in EELS-SI experiments, due to image acquisition constraints
to avoid sample damage. Hence, statistical treatment of the signals in the SI and