258
P. Torruella et al.
of electron tomography strategies applied to magnetic nanomaterials, beginning in a
chronologically ordered description of some of the commonly used algorithms and
their underlying mathematical principles: from the historical Radon transform and
the WBP, to the iterative ART and SIRT algorithms, the later DART and recently
added compressed sensing-based algorithms with superior performance. Regarding
the spectral reconstruction, dimensionality reduction techniques such as PCA and
ICA are also presented here as a viable way to reduce the problem complexity, by
applying the reconstruction algorithms to the weighted mappings of the physically
meaningful resolved components. In this sense, the recent addition of clustering algorithms to the possible spectral unmixing tools is also described, as a proof of concept
of its potentiality as part of an analytical electron tomography routine. Throughout the
text, a series of published experiments are described, in which electron tomography
and advanced EELS data treatment techniques are used in conjunction to retrieve
the spectrum volume of several magnetic nanomaterials, revealing details of the NPs
under study such as the 3D distribution of oxidation states.
11.1 Introduction: Fundamentals of Electron Tomography
and Overview of Classic Reconstruction Methods
Electron tomography in the transmission electron microscope (TEM) refers to the
reconstruction of 3D volumes from the 2D projection images obtained in the microscope. TEM tomography was first applied to the field of biology [1]. In the last
couple of decades, the operational and instrumental advances, as well as the formulation of new reconstruction algorithms, have introduce tomography into the realm
of materials and physical sciences. Nowadays, it plays a central role in the study and
fabrication of nanostructured materials. Moreover, the combination of tomographic
techniques with TEM spectroscopic techniques (electron energy loss spectroscopy
EELS and energy-dispersive X-ray spectroscopy EDX/EDS) has recently opened
new perspectives for the characterization of nanomaterials.
In order to successfully carry out tomography experiments in the TEM, the signal
acquired (projected images) must fulfil the projection requirement: the contrast in
the image must change monotonically with given property of the sample (e.g. thickness or Z number) [2]. This automatically discards high resolution TEM images,
formed through phase contrast, and specifically bright and dark field diffraction
contrast imaging modes. For crystalline samples, scanning-TEM high-angle annular
dark field (STEM-HAADF) images are preferred, as HAADF incoherent signal is
monotonically dependent on the thickness and the Z number.
Experimentally, tomography in the TEM is carried out through the acquisition
of a set of images obtained at different tilt angles [3]. Hence, a certain degree of
discretization is inherently introduced and, thus, the quality of the reconstruction
will be affected by the number of projections (the angle step) and the considered
angular range. The resolution in TEM tomography is anisotropic. For simplicity, let
P. Torruella et al.
of electron tomography strategies applied to magnetic nanomaterials, beginning in a
chronologically ordered description of some of the commonly used algorithms and
their underlying mathematical principles: from the historical Radon transform and
the WBP, to the iterative ART and SIRT algorithms, the later DART and recently
added compressed sensing-based algorithms with superior performance. Regarding
the spectral reconstruction, dimensionality reduction techniques such as PCA and
ICA are also presented here as a viable way to reduce the problem complexity, by
applying the reconstruction algorithms to the weighted mappings of the physically
meaningful resolved components. In this sense, the recent addition of clustering algorithms to the possible spectral unmixing tools is also described, as a proof of concept
of its potentiality as part of an analytical electron tomography routine. Throughout the
text, a series of published experiments are described, in which electron tomography
and advanced EELS data treatment techniques are used in conjunction to retrieve
the spectrum volume of several magnetic nanomaterials, revealing details of the NPs
under study such as the 3D distribution of oxidation states.
11.1 Introduction: Fundamentals of Electron Tomography
and Overview of Classic Reconstruction Methods
Electron tomography in the transmission electron microscope (TEM) refers to the
reconstruction of 3D volumes from the 2D projection images obtained in the microscope. TEM tomography was first applied to the field of biology [1]. In the last
couple of decades, the operational and instrumental advances, as well as the formulation of new reconstruction algorithms, have introduce tomography into the realm
of materials and physical sciences. Nowadays, it plays a central role in the study and
fabrication of nanostructured materials. Moreover, the combination of tomographic
techniques with TEM spectroscopic techniques (electron energy loss spectroscopy
EELS and energy-dispersive X-ray spectroscopy EDX/EDS) has recently opened
new perspectives for the characterization of nanomaterials.
In order to successfully carry out tomography experiments in the TEM, the signal
acquired (projected images) must fulfil the projection requirement: the contrast in
the image must change monotonically with given property of the sample (e.g. thickness or Z number) [2]. This automatically discards high resolution TEM images,
formed through phase contrast, and specifically bright and dark field diffraction
contrast imaging modes. For crystalline samples, scanning-TEM high-angle annular
dark field (STEM-HAADF) images are preferred, as HAADF incoherent signal is
monotonically dependent on the thickness and the Z number.
Experimentally, tomography in the TEM is carried out through the acquisition
of a set of images obtained at different tilt angles [3]. Hence, a certain degree of
discretization is inherently introduced and, thus, the quality of the reconstruction
will be affected by the number of projections (the angle step) and the considered
angular range. The resolution in TEM tomography is anisotropic. For simplicity, let