Introduction and problem statement.

The estimation of quality and structural perfection of single crystals is not possible without of application of modern diagnostic techniques, including X-ray topography and a polarization-optical analysis, which are the direct and non-destructive methods. Among all the methods of X-ray topography it is possible to highlight a method based on the Borrmann effect (XRBT method), which has high sensitivity at the study of crystals with low dislocation density and dislocation-free crystals [1].

The contrast formed by various type structure defects in the XRBT method has the form of intensity rosettes, shape and number of lobes of which depends on the type of defect and its location in the volume of a single crystal, and the size of the rosettes depends on the type of the investigated crystal. The decoding of topography contrast images is carried out visually and complicated because of the noise factors - background inhomogeneity and granularity of experimental topographs, making it difficult to identify defects with dimensions comparable to the grain of nuclear emulsion plates, as well as defects in highly bright or dark areas. The use of different photographic techniques of eliminating of noise factors often does not lead to the desired result, but the process is generally laborious and inefficient. The result of crystal diagnostic depends on the skills, experience, and the visual acuity of the researcher.

Eliminating of noise factors and improving of reliability at the identification of structural defects is achieved by increasing the quality of the analyzed contrast through the use of digital methods of treatment [2]. Digital processing can be based on an analysis of brightness characteristics of experimental contrast or frequency characteristics at use Fourier and wavelet analysis.

Digital processing based on analysis of the brightness characteristics.

The method based on a filter with recursive accumulation has a high efficiency at granularity removal. The principle of the filter operation is based on the recognition of signal and noise regions in the image from difference between their average values. This allows us to do signal amplification and noise reduction through recursive accumulation with different weights for the signal and noise (Fig. 1).

Fig. 1. Initial (a, c) and processed by filter (b, d) topographs containing images of structural defects: microdefects of interstitial type (a) and edge dislocations (c).

Effective elimination of background heterogeneity is achieved by using a high-frequency filter with pre-processing of the analyzed image by non-linear filter (with taking the logarithm or exponentiation of image). Filtering is done by mathematical processing of each pixel of the original image. The specific form of the selected processing function will depend from the average pixel values ​​of the initial image (Fig. 2).

Fig. 2. The result of background inhomogeneity eliminating for single crystal 6H-SiC polarization-optical image: a – the original image; b – the image after high-frequency filtering with use image exponentiation only; c – the image after high-frequency filtering with taking the logarithm of image only; d – the high-frequency filtering with pre-processing by non-linear filter then taking the logarithm, and exponentiation do together.

Comparison of the structure defect images processed by these methods with the theoretically simulated from the modified Indenbom–Chamrov's equations ones shows that low-frequency peculiarities of experimental contrast (some lobes of intensity rosettes) may be lost, the processed contrast can be seen as a visual binary. However, digital processing stores all the basic features of the contrast formed by defects of various types, simplifies decoding and increases the reliability of the identification of structural defects.

Digital processing based on discrete wavelet analysis.

The most complete information about studied signal may exist in its frequency range. Discrete wavelet analysis is a kind of frequency analysis of complex signals, which include topography and birefringence experimental images. Experimental studies have shown a distinct advantage of the wavelet analysis in comparison with Fourier analysis [2].

At the core of the discrete wavelet analysis lays decomposition of the investigated contrast on a number of levels, depending on its size. As a result of the decomposition we obtain two types of factors that characterize the frequency spectrum of the image: scale factors containing low-frequency characteristics, and detailed (diagonal, vertical and horizontal) factors containing high-frequency image features. Selecting the optimal bandwidth at filtering and zeroing coefficients relating to the noise factors we obtain contrast at reconstruction (restoration), containing purified from the noise images of structural defects. Background inhomogeneity refers to the low-frequency characteristics of the contrast and emulsion granularity – to high ones.

In comparison to methods based on the analysis of brightness characteristics, discrete wavelet analysis allows to keep the low-frequency characteristics of images of structure defects and improve the reliability of identification of the defect and its location in the crystal volume, reveals additional features of experimental contrast, not detected previously.

In this work we compare two methods of elimination of background inhomogeneity using the discrete wavelet analysis [2]. The first method is based on zeroing of scale factors at the signal decomposition. Further work is carried out with the detailing coefficients only at signal reconstruction with optimal selection of bandwidth. The second method involves four stages and can improve performance of wavelet processing by 10–12 times, as well as eliminate the aliasing phenomenon (intensity fluctuations at the boundaries of the single crystal and at the defects occurred during the surface processing): stage 1 – zeroing of detailing coefficients and selection only background inhomogeneity after processing; stage 2 – construction of a difference between the original contrast and contrast obtained at the first stage; stage 3 – gauss blur of difference contrast (value is selected experimentally); stage 4 – construct the final difference contrast between obtained at stage 3 (blurred contrast) and the difference contrast obtained at stage 2. For a better visual perception of the final contrast and for better details, optimal dynamic range is selected (Fig. 3).

Fig. 3. The result of the wavelet processing of polarization-optical image of 6H-SiC single crystal and its fragments: a – the original image; b, c – images after digital processing with use of sym8 wavelet, through the first and second methods, respectively.

Best detailing of contrast is obtained by its rescaling and representation in 32-bit format (High-dynamic-range images or HDR-images). The processing time at this operation does not increase much.

The main result of the digital processing is the removal of noise factors, as well as more complete and reliable identification of crystal defects.

Acknowledgments.

This work was performed in joint with Ioffe Physical Technical Institute RAS Laboratories "Computer technology in the diffraction diagnostics of materials" of SPbSUSE (Novgorod branch) and "X-ray topography methods at research of materials for electronic engineering" of NovSU with the support of RFBR grant № 12-02-00201.

1. L. Danilchuk, A. Okunev, V. Tkal, X-Ray topography on base of Borrmann effect (LAP LAMBERT Academic Publishing, Saarbrücken, 2012), p. 348.

2. V. Tkal, A. Okunev, I. Zhukovskaya, The Brightness and Frequency Analysis of Images of Structure Defects (LAP  LAMBERT Academic Publishing, Saarbrücken, 2012), p. 392.

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