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

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

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.

Full Text

Restricted Access

About the authors

V. I. Bondarenko

National Research Center “Kurchatov Institute”

Author for correspondence.
Email: bondarenko.v@crys.ras.ru

Shubnikov Institute of Crystallography of the Kurchatov Complex Crystallography and Photonics

Russian Federation, Moscow

S. S. Rekhviashvili

National Research Center “Kurchatov Institute”

Email: bondarenko.v@crys.ras.ru

Shubnikov Institute of Crystallography of the Kurchatov Complex Crystallography and Photonics

Russian Federation, Moscow

F. N. 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

Russian Federation, Moscow; Nalchik

References

  1. Authier A. Dynamical Theory of X-ray Diffraction. New York: Oxford University Press, 2001. 680 p.
  2. Asadchikov V., Buzmakov A., Chukhovskii F. et al. // J. Appl. Cryst. 2018. V. 51. P. 1616. https://doi.org/10.1107/S160057671801419X
  3. Бондаренко В.И., Конарев П.В., Чуховский Ф.Н. // Кристаллография. 2020. Т. 65. № 6. С. 845. https://doi.org/10.31857/S0023476120060090
  4. Chukhovskii F.N., Konarev P.V., Volkov V.V. // Acta Cryst. A. 2020. V. 76. P. 16. https://doi.org/10.1107/S2053273320000145
  5. Hendriksen A.A., Bührer M., Leone L. et al. // Sci. Rep. 2021. V. 11. P. 11895. https://doi.org/10.1038/s41598-021-91084-8
  6. Chukhovskii F.N., Konarev P.V., Volkov V.V. // Crystals. 2024. V. 14. P. 29. https://doi.org/10.3390/cryst14010029
  7. Бондаренко В.И., Рехвиашвили C.Ш., Чуховский Ф.Н. // Кристаллография. 2024. Т. 69. № 5. С. 755. https://doi.org/10.31857/S0023476124050012
  8. Welstead S. Fractal and Wavelet Image Compression Techniques. SPIE Publications, 1999. 254 p.
  9. He K., Sun J., Tang X. // IEEE Trans. Pattern Anal. Machine Intell. 2013. V. 35. № 6. P. 1397. https://doi.org/10.1109/TPAMI.2012.213
  10. Nagajyothi G., Raghuveera E. // Int. J. Adv. Res. Electron. Commun. Eng. 2016. V. 5. P. 2362.
  11. Li Z., Zheng J., Zhu Z. et al. // IEEE Trans. Image Process. 2015. V. 24. P. 120. https://doi.org/10.1109/TIP.2014.2371234
  12. Zhang Y.Q., Ding Y., Liu J. // IET Image Process. 2013. V. 7. № 3. P. 270. https://doi.org/10.1049/iet-ipr.2012.0351
  13. Zhu S., Yu Z. // IET Image Process. 2020. V. 14. № 11. P. 2561. https://doi.org/10.1049/iet-ipr.2019.1471
  14. Малла С. Вейвлеты в обработке сигналов. М.: Мир, 2005. 671 с.
  15. Гонсалес Р., Вудс Р. Цифровая обработка изображений. М.: Техносфера, 2005. 1072 с.
  16. Дремин И.М., Иванов О.В., Нечитайло В.А. // Успехи физ. наук. 2001. Т. 171. № 5. С. 465. https://doi.org/10.3367/UFNr.0171.200105a.0465
  17. Уэлстид С. Фракталы и вейвлеты для сжатия изображений в действии. М.: Триумф, 2003. 320 с.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Fig. 1. Functions in the D4 transform.

Download (80KB)
Indexing metadata
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.

Download (112KB)
Indexing metadata
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.

Download (109KB)
Indexing metadata
5. Fig. 4. 2D images: a – accurate, b – noisy, c – filtered, 2D-controlled filter, automatically generated reference image.

Download (182KB)
Indexing metadata
6. Fig. 5. 2D images: a – accurate, b – noisy. Wavelet filtering: c – algorithm of the first type [7], d – algorithm of the second type.

Download (121KB)
Indexing metadata
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).

Download (234KB)
Indexing metadata

Copyright (c) 2025 Russian Academy of Sciences