Electron tomography for sintered ceramic materials by a neural network algebraic reconstruction technique

doi:10.1016/j.jmst.2021.05.051

Abstract

Abstract:

The missing wedge effect in electron tomography introduces various types of artifacts in the tomograms and lowers the reconstruction resolution and quality. The artifacts produced in tomographic reconstruction of bulk materials can be very severe, particularly for sintered bulk ceramic materials in which there are often nano-pores or pore-like microstructure features. Here, we report a neural network algebraic reconstruction algorithm with no prior knowledge to perform electron tomography for a sintered SiC material with nano carbon zones. The results show that the proposed algorithm has a great suppressive effect on the missing wedge artifacts and a high tolerance for noise. The information in the missing wedge can be partly recovered by this technique. Thus, both the shape of the bulk SiC specimen and its irregular inner pore-like features are correctly retrieved in the obtained 3D image. Our study shows the effectiveness of the neural network algorithm for improving the reconstruction accuracy of electron tomography, in order to reveal sophisticated 3D microstructures generally existing in sintered ceramic materials.

Key words: Neural network, Missing wedge, Electron tomography, Sintered ceramics

R.H. Shen, Y.T. He, W.Q. Ming, Y. Zhang, X.D. Xu, J.H. Chen. Electron tomography for sintered ceramic materials by a neural network algebraic reconstruction technique[J]. J. Mater. Sci. Technol., 2022, 100: 75-81.

Figures/Tables 10

Fig. 1. (a, e) Model 1 and Model 2. (b, f) The tomograms reconstructed by SIRT with 100 iterations from the sinograms of Model 1 and Model 2. The tilt range is from -70° to +70° with 1° increment. (c, g) The central part of FFTs of (a) and (e). (d, h) The central part of FFTs of (b) and (f).

Fig. 2. (a) The flow chart of NNART algorithm. (b) The full connection feedforward neural network. In (a), I represents the predicted image in size of N × N pixels reshaped from the output layer L(4) which is a vector with N2 elements. R represents Radon transformation. S and Sexp represent the predicted and experimental sinograms respectively. Symbol t is the iteration number and tmax is a predefined maximum iteration number. Iavg is the final result averaged from several repetitive reconstructions.

Fig. 3. (a) The loss profile during iterations in logarithm scale. (b-e) The predicted tomograms at various iteration numbers: (b) 10, (c) 40, (d) 400 and (e) 3000. (f-k) Comparison between the FFTs of the original image (f) and the predicted tomograms after various iterations: (g) 10, (h) 40, (i) 400 and (j) 3000. Only the central parts (60 × 30 pixels) of the FFTs are displayed with the same absolute grayscale contrast limits for comparison. (k) The line profiles along the z-axis of the images (f-j). All results are averaged from 20 repeats as mentioned above.

Fig. 4. (a) Experimental setting of the tilted HAADF-STEM images acquisition. The incident electron beam is along the z-axis. (b, c) HAADF-STEM images of the SiC specimen at 0° and 70°. The region between the red dashed lines (c) is the field of view of (b). The white dashed rectangle (a) and lines (b, c) all indicate the same slice of the specimen that will be analyzed in following.

Fig. 5. A slice of the SiC specimen reconstructed by (a) NNART and (c) TVM. (b, d) The enlarged views of the central area in the FFTs (the insert images) of (a, c).

Fig. 6. (a, b) The side view of the tomograms reconstructed by NNART and TVM. (c) The HAADF image at 0° tilt. The black arrows in (a, b) represent the observation directions of (d-g). (d, e) The front and back view of the volume indicated by the black dashed polygon marked in (a). (f, g) The front and back views of the same volume in (b). The area marked by a blue dashed rectangle in (d) will be analyzed in the following.

Fig. 7. Comparison of the 3D renderings by NNART and experimental images of the graphite phase at different tilt angles of (a, a’) 0°. (b, b’) 15°. (c, c’) 30°. (d, d’) 45°. (e, e’) 60°.

Fig. 8. (a-e) Slice illustrations at different depths to show a void (or graphite phase) embedded in the SiC matrix.

Fig. 9. Comparison between the NNART and the TVM algorithms with various tilt ranges of (a, e) -70° to +70°. (b, f) -60° to +60°. (c, g) -50° to +50°. (d, h) -40° to +40°. The tilt increment is 1°. The iteration numbers of NNART and TVM were 6000 and 5000 to ensure convergence, respectively. The MSEs between the reconstructed images and the raw image are shown at the right bottom corner. All images share the same absolute grayscale contrast limit for comparison.

Fig. 10. Results reconstructed by (a, c) NNART and (b, d) TVM. The noise levels are indicated by the SNR in the sinograms: (a, b) SNR = 30, (c, d) SNR = 20. The tilt range of the sinogram is from -60° to 60° with an increment of 1°. The MSEs between the reconstructed images and the raw image are shown at the right bottom corner.

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