Multi‐modal electron tomography for
3D
spectroscopic analysis using limited projections
Authors: Collins Sean , Einsle Joshua , Saghi Zineb , Blukis Robert , Harrison Richard , Midgley Paul 
Published: December 2016

Electron tomography applied to spectroscopic signals in the scanning transmission electron microscope (STEM) offers the possibility for quantitative determination of structure‐chemistry relationships with nanometre spatial resolution. Electron energy loss spectroscopy (EELS) and X‐ray energy dispersive spectroscopy (EDS), however, often require long exposure times or high beam currents for sufficient data quality for spectral tomography. Many materials samples are not sufficiently stable under the electron beam for the prolonged irradiation times necessary for conventional tilt‐series acquisition and back‐projection tomographic reconstruction schemes using STEM spectrum imaging signals. Reduced dose acquisition strategies will, in general, require the use of fewer projections for tilt‐series electron tomography because signals with sufficient signal‐to‐noise must be recorded on the respective detectors for quantitative chemical reconstructions, establishing a limit on the minimum acquisition time for individual spectrum images using current detector technologies. While methods such as compressive sensing electron tomography (CS‐ET) [1] show promise for reducing the number of projections required for successful tomographic reconstructions, combining information from multiple simultaneous imaging modes in the STEM provides a complementary strategy for further reducing electron dose in spectral tomography. Simultaneously acquired signals that offer structural contrast information (e.g. ADF STEM, low‐loss EELS, qualitative EDS tomography) in many cases enable the spectral tomography problem to be re‐cast as a recovery problem with reduced dimensionality. The 3D reconstruction of spectral data can then be recovered quantitatively from substantially fewer spectrum images. In the case of surface plasmon modes of silver particles, ADF STEM tomography has already been applied in conjunction with EELS spectrum imaging to reconstruct the surface charge distributions [2], a two‐dimensional reconstruction problem (on a surface) defined in three‐dimensional spatial coordinates.
This approach has been extended to the recovery of voxel spectra from the cloudy zone, a spinodal decomposition of Fe‐Ni in the Tazewell meteorite (Figure 1). Due to minimal ADF STEM contrast, qualitative EDS tomography using the Ni K‐alpha signal was analysed for structural segmentation of the sample volume. Re‐projections of the extracted binarized volumes for each of the two phases were then used as a thickness‐series to re‐cast the recovery problem as an overdetermined system of linear equations, assuming homogeneous composition within each phase. The spectral intensity at each energy channel was decomposed according to the thickness data for each phase available at each pixel in the two‐dimensional spectrum images, allowing relative spectral intensities to be attributed to the voxels assigned to each of the two phases. The resulting tomographically unmixed spectra enabled improved EDS quantification of the relative Fe‐Ni ratios in each phase, giving results within 2% of quantification by atom probe tomography of similar material from the cloudy zone of the Tazewell meteorite.
Applications to core‐loss STEM‐EELS analyses will be presented, further extending this family of methods to cases involving plural‐scattering corrections implemented in conjunction with the linear thickness unmixing approach. Comparisons of signal unmixing determined from multi‐modal structural and spectral tomography and blind‐source separation methods (e.g. non‐negative matrix factorization or independent component analysis) of two‐dimensional spectrum image data will also be discussed.