Elsevier

Ultramicroscopy

Volume 158, November 2015, Pages 81-88
Ultramicroscopy

Electron tomography based on highly limited data using a neural network reconstruction technique

https://doi.org/10.1016/j.ultramic.2015.07.001Get rights and content

Highlights

  • We propose a new approach for electron tomography based on artifical neural networks, which reduces the number of projection images with a factor of 5 or more.

  • This reconstruction algorithm allows us to examine the 3D shape of a broad range of nanostructures in a statistical manner.

  • NN-FBP reconstructions of highly limited data yield comparable quality to full data SIRT reconstructions.

Abstract

Gold nanoparticles are studied extensively due to their unique optical and catalytical properties. Their exact shape determines the properties and thereby the possible applications. Electron tomography is therefore often used to examine the three-dimensional (3D) shape of nanoparticles. However, since the acquisition of the experimental tilt series and the 3D reconstructions are very time consuming, it is difficult to obtain statistical results concerning the 3D shape of nanoparticles. Here, we propose a new approach for electron tomography that is based on artificial neural networks. The use of a new reconstruction approach enables us to reduce the number of projection images with a factor of 5 or more. The decrease in acquisition time of the tilt series and use of an efficient reconstruction algorithm allows us to examine a large amount of nanoparticles in order to retrieve statistical results concerning the 3D shape.

Introduction

Gold nanoparticles (NPs) have truly unique electronic, optical as well as catalytic properties, rendering them ideal for numerous applications in fields as diverse as photovoltaics, optoelectronics and biomedicine [1], [2], [3], [4]. Furthermore, gold NPs can be prepared with almost any desired shape. Crucial to their application, however, is their exact structure, and specifically their anisotropy as well as the surface facets they expose. Currently, it is empirically understood how particle size and shape may be controlled during synthesis [5], [6], [7], [8]. Although transmission electron microscopy (TEM) has become a routine tool to investigate e.g. particle size, (atomic) structure and shape, increasingly advanced TEM is required for a more in-depth characterisation. For example, the surface facets of Au nanorods have a major influence on crucial effects such as reactivity and ligand adsorption and there has been controversy regarding facet indexing [9], [10], [11]. Indeed, TEM images are only two-dimensional (2D) projections of three-dimensional (3D) objects. To overcome this problem, 3D electron microscopy, or “electron tomography” was developed [12], [13]. In 2003, Paul Midgley and co-workers demonstrated the potential of the technique in materials science based on high angle annular dark field scanning transmission electron (HAADF-STEM) microscopy [14], [15]. Since then, different electron microscopy modes have been combined successfully with tomography, leading to a broad variety of 3D structural and compositional information at the nanoscale [16], [17], [18], [19], [20], [21]. Very often, electron tomography is used to determine the size and shape of the particles and nowadays, 3D reconstructions can even be obtained with a resolution at the atomic level [22], [23]. Although these investigations provide very precise information on the NP morphology, both the acquisition of tilt series as well as the 3D reconstruction is very time consuming and it is consequently not straightforward to acquire results in 3D that are statistically relevant, which is a major drawback e.g. when using electron tomography to optimize the synthesis of NPs. This problem will be even more essential for anisotropic NPs that are currently receiving a lot of attention because of the increased flexibility they provide to tune the final (optical) properties [24], [25], [26]. Since the optimization of the production of NPs with a specific shape would largely benefit from statistical 3D results with a nanometer resolution, one of the emerging challenges in the field of electron tomography is to increase the throughput of 3D reconstructions of NPs. At the same time, the quality of the reconstructions should be maintained and should enable one to obtain reliable and quantitative results concerning parameters such as particle size and surface morphology.

In this paper, we will determine the 3D shape and size of a large set of anisotropic Au NPs. We will make effective use of a new approach for electron tomographic reconstructions that is based on artificial neural networks. The neural network filtered backprojection method (NN-FBP) is a recently developed reconstruction technique that has been applied successfully to X-ray tomography [27]; however the implementation for electron tomography is completely new. The method that we propose will enable us to reduce the number of necessary projection images for a 3D reconstruction by a factor of 5 or more. In this manner, the acquisition time and time that is necessary for a 3D reconstruction is significantly reduced, enabling 3D results that are of statistical relevance.

Section snippets

Neural network filtered backprojection method

The sample that was investigated contains Au NPs yielding different morphologies: nanorods, nanotriangles, nanoprisms and nanospheres. An HAADF-STEM overview image of the sample is provided in Fig. 1a. Although this image only corresponds to a 2D projection of a set of 3D objects, it is already clear that different morphologies occur. In conventional electron tomography, a large set of 2D projection images is acquired from the same region of interest over a large tilt range with a tilt

Qualitative results

In a first experiment, tilt series of a nanosphere, a nanorod and a nanotriangle are acquired over an angular tilt range of ±75° with a tilt increment of 1°. These three series are used as training series, resulting in a set of filters that will be used during the NN-FBP approach. The resulting NN-FBP algorithm is applied to a limited tilt series that was acquired from a different nanotriangle. Although only 10 projection images obtained over a range of ±75° are used during the NN-FBP

Conclusion

We have shown that the NN-FBP reconstruction algorithm is able to yield electron tomography reconstructions based on highly limited data with a comparable quality to a reconstruction based on a full data series with a tilt increment of 1°. The decrease in acquisition time and the use of an efficient reconstruction method enables us to examine a broad range of nanostructures in a statistical manner. The NN-FBP algorithm also has promising prospects for the 3D investigation of beam sensitive

Supplementary information

Reconstructed volumes of a nanorod, histograms of the SIRT reconstructions, difference reconstructions of the nanorod, representations of the shape misinterpretation of the nanotriangle and plots of the relative error in the shape and the volume of the different nanostructures.

Acknowledgment

S.B. acknowledges financial support from European Research Council (ERC Starting Grant #335078-COLOURATOMS). E.B. gratefully acknowledges financial support by The Flemish Fund for Scientific Research (FWO Vlaanderen). D.M.P. and K.J.B. acknowledge financial support by The Netherlands Organisation for Scientific Research (NWO), Project number 639.072.005. The authors acknowledge COST Action MP1207 for networking support and the European Union under the Seventh Framework Program under a contract

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    E.B. and D.M.P. contributed equally.

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