Electron Tomography (ET) is a key technique to perform 3D characterization at the nanometer scale [1]. 2D projections at different tilt angles are first acquired in an electron microscope, then an inversion algorithm is used to reconstruct the 3D volume of the sample from the dataset. Classically, ET is performed in a HAADF STEM mode in materials science leading to 3D Z-contrast reconstructions. 3D elemental mapping based on EELS or EDS acquisitions is also possible in reconstruction theory [2]. Yet, reconstruction theory needs several hundreds of projections and 2D chemical mapping needs an important acquisition time and electron dose, therefore 3D elemental mapping is challenging. Nowadays, microscopes improvements limit the acquisition time of 2D chemical mapping. Moreover, powerful state-of-the-art reconstruction algorithms make possible the reconstruction from a limited dataset of a few dozens of projections only. As a consequence 3D elemental mapping is now possible with a reasonable acquisition time of a day or less.  

        New reconstruction algorithms add prior knowledge on the object to compensate for the lack of information due to limited number of available projections. The prior knowledge can be a limited number of possible grey levels in the reconstruction to perform discrete tomography [3]. This correspond to a limited number of known materials in the sample. In the case of Compressed Sensing (CS) algorithms [4], the prior knowledge is a sparsity of the object expressed in a particular basis. A special case of CS reconstruction is the use of the gradient sparsity of the object to perform Total Variation Minimization (TVM) algorithms [5]. In that case, objects constant by parts are preferably reconstructed.

        We propose a mixed approach suited for EDS acquisition. That mixed approach combines both projection denoising [6] and a TVM based algorithm that uses the reconstructions of each element all together. This new approach leads to higher reconstruction accuracy since a new kind of prior knowledge is used. Indeed, reconstructions of different elements should not be independent since a variation of an element is most of the time correlated to a variation of at least another element. The algorithm will be introduced. Simulations using projections with high Poisson noise and strong misalignment will be used to show the accuracy of our approach. Experimental results for a GaN – TiAl intermetallic sample in EDS tomography will also be presented.

        This work was supported by the French “Recherche Technologie de Base” (RTB) program. The authors acknowledge access to the nanocharacterization platform (PFNC) at the Minatec Campus in Grenoble. The authors thank Alphonse Torres from CEA Leti for providing the intermetallic specimen.

[1] P. A. Midgley and M. Weyland, “3D electron microscopy in the physical sciences: the development of Z-contrast and EFTEM tomography.,” Ultramicroscopy, vol. 96, no. 3–4, pp. 413–31, Sep. 2003.

[2] G. Haberfehlner, A. Orthacker, M. Albu, J. Li, and G. Kothleitner, “Nanoscale voxel spectroscopy by simultaneous EELS and EDS tomography,” Nanoscale, vol. 6, no. 23, pp. 14563–14569, Oct. 2014.

[3] K. J. Batenburg and J. Sijbers, “DART: a practical reconstruction algorithm for discrete tomography.,” IEEE Trans. Image Process., vol. 20, no. 9, pp. 2542–53, 2011.

[4] R. Leary, Z. Saghi, P. A. Midgley, and D. Holland, “Compressed sensing electron tomography,” Ultramicroscopy, vol. 131, pp. 70–91, Aug. 2013.

[5] B. Goris, W. Van den Broek, K. J. Batenburg, H. Heidari Mezerji, and S. Bals, “Electron tomography based on a total variation minimization reconstruction technique,” Ultramicroscopy, vol. 113, pp. 120–130, Feb. 2012.

[6] T. Printemps, G. Mula, D. Sette, P. Bleuet, V. Delaye, N. Bernier, A. Grenier, G. Audoit, N. Gambacorti, and L. Hervé, “Self-adapting denoising, alignment and reconstruction in electron tomography in materials science,” Ultramicroscopy, vol. 160, pp. 23–34, 2016. 

Figures:

Complete EDS tomography process. (a) Projection at -90° for Al, Ga and Ti elements, (b) Same denoised projection, (c) representation of the 3D reconstructed volumes, (d) a sagitall slice in each reconstructed volume, (e) an axial slice in each reconstructed volume

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EMC Abstracts - https://emc-proceedings.com/abstract/3d-elemental-and-interdependent-reconstructions-based-on-a-novel-compressed-sensing-algorithm-in-electron-tomography/