LabAdviser/314/Microscopy 314-307/SEM/Nova/Transmission Kikuchi diffraction: Difference between revisions
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= Indexing of Kikuchi patterns = | = Indexing of Kikuchi patterns = | ||
The automated determination of the position of Kikuchi lines in a diffraction pattern (and consequently of lattice planes in the crystal) has enabled the practical use of Kikuchi diffraction for the study of micro- and nanomaterials. An algorithm known as the Hough transform was introduced by Krieger Lassen to recognize the edges of the Kikuchi bands [1,2]. The Hough transform is a mathematical tool which can be used to isolate features of a particular shape, such as lines, circles and ellipses, within an image. The main advantage of the Hough transform is that it is relatively unaffected by image noise. The essential idea of the the Hough transform consists of applying to each pixel of the Kikuchi pattern the equation: | The automated determination of the position of Kikuchi lines in a diffraction pattern (and consequently of lattice planes in the crystal) has enabled the practical use of Kikuchi diffraction for the study of micro- and nanomaterials. An algorithm known as the Hough transform was introduced by Krieger Lassen to recognize the edges of the Kikuchi bands [1,2]. The Hough transform is a mathematical tool which can be used to isolate features of a particular shape, such as lines, circles and ellipses, within an image. The main advantage of the Hough transform is that it is relatively unaffected by image noise. The essential idea of the the Hough transform consists of applying to each pixel of the Kikuchi pattern the equation: ''ρ''i = xcos�i + ysin�i (3.1) where (x, y) are the coordinates of a pixel in the original image and (�i, �i) are the parameters of a straight line passing through (x, y). From Eq. 3.1 it is evident that the set of possible lines passing through the chosen pixel is represented by a sinusoid in the Hough space. | ||
An example is shown in Fig. 3.4. Consider four pixels along a Kikuchi line. For each pixel in the line, all possible values of � are calculated for � ranging from 0° to 180° using Eq. 3.1, which produces four sinusoidal curves. These curves intersect at a point with (�, �) coordinates (green rectangle), corresponding to the angle of the line (�) and its position relative to the origin (�). The grey-scale intensity I(xi; yi) of the image pixels is accumulated in each quantized point H(�; �) of the Hough space, so that I(xi; yi) serves as a measure of evidence for a line passing through the pixel (x, y). In this way, a line in the pattern space transforms to a point having a certain intensity | An example is shown in Fig. 3.4. Consider four pixels along a Kikuchi line. For each pixel in the line, all possible values of � are calculated for � ranging from 0° to 180° using Eq. 3.1, which produces four sinusoidal curves. These curves intersect at a point with (�, �) coordinates (green rectangle), corresponding to the angle of the line (�) and its position relative to the origin (�). The grey-scale intensity I(xi; yi) of the image pixels is accumulated in each quantized point H(�; �) of the Hough space, so that I(xi; yi) serves as a measure of evidence for a line passing through the pixel (x, y). In this way, a line in the pattern space transforms to a point having a certain intensity | ||