Computer diffraction tomography. Digital image processing and analysis based on the 1D-, 2D-sized guided and wavelet-function filter processing

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Resumo

One presents and analyzes the results of computer processing for a plane-wave X-ray topography imaging of a point defect of the Coulomb-types in the Si(111) crystal recorded by an X-ray detector against a background of the Gaussian noise, and their subsequent filtering by using the 1D-, 2D-sized guided and a heuristic wavelet 4th-order Daubechie’s atomic function. The filtering efficiency of a topography image is determined by the parameter of the averaged over all pixels relative square deviations of the pixel intensities (RMS.) of the processed and reference (noise-free) 2D image. Practical methods for selecting filtration parameters are proposed, using which the considered methods work well enough to be used in practice for the noise processing of plane-wave X-ray topography images, meaning their use for the 3D digital recovering nanosized crystal defects.

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Sobre autores

V. Bondarenko

National Research Center “Kurchatov Institute”

Autor responsável pela correspondência
Email: bondarenko.v@crys.ras.ru

Shubnikov Institute of Crystallography of the Kurchatov Complex Crystallography and Photonics

Rússia, Moscow

S. Rekhviashvili

National Research Center “Kurchatov Institute”

Email: bondarenko.v@crys.ras.ru

Shubnikov Institute of Crystallography of the Kurchatov Complex Crystallography and Photonics

Rússia, Moscow

F. Chukhovskii

National Research Center “Kurchatov Institute”; Kabardin-Balkar Scientific Center of Russian Academy of Sciences

Email: bondarenko.v@crys.ras.ru

Shubnikov Institute of Crystallography of the Kurchatov Complex Crystallography and Photonics, Institute of Applied Mathematics and Automation

Rússia, Moscow; Nalchik

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2. Fig. 1. Functions in the D4 transform.

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3. Fig. 2. RMS as a function of the parameter ε. 1D-controlled filter, filter window size ρ = 1, a – full image, b – area near the defect. Filter options: 1 – noisy image is used as a reference image; 2 – reference image coincides with the exact image; 3 – reference image is generated automatically; 4 – interpolation, ρ = 2.

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4. Fig. 3. RMS as a function of the parameter ε. 2D-controlled filter, filter window size ρ = 1, a – full image, b – area near the defect. Filter options: 1 – noisy image is used as a reference image; 2 – reference image coincides with the exact image; 3 – reference image is generated automatically; 4 – interpolation, ρ = 2.

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5. Fig. 4. 2D images: a – accurate, b – noisy, c – filtered, 2D-controlled filter, automatically generated reference image.

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6. Fig. 5. 2D images: a – accurate, b – noisy. Wavelet filtering: c – algorithm of the first type [7], d – algorithm of the second type.

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7. Fig. 6. Image intensity profiles taken along a segment passing horizontally through the center of the defect. Solid line – accurate image, dotted line – noisy image, dotted line – filtering result: a – for a controlled filter with automatic generation of reference image, b – algorithm of the first type of wavelet filtering (∆ = 80), c – algorithm of the second type of wavelet filtering (∆ = 80).

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