LabAdviser/314/Microscopy 314-307/SEM/Nova/Transmission Kikuchi diffraction: Difference between revisions
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An example is shown in Fig. 3. Consider four pixels along a Kikuchi line. For each pixel in the line, all possible values of ''ρ'' are calculated for ''θ'' ranging from 0° to 180° using Eq. 1, which produces four sinusoidal curves. These curves intersect at a point with (''ρ'', ''θ'') coordinates (green rectangle), corresponding to the angle of the line (''θ'') and its position relative to the origin (''ρ''). The grey-scale intensity I(xi; yi) of the image pixels is accumulated in each quantized point H(''ρ''; ''θ'') 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 in the Hough space, which is easily detected by the indexing software over the at background. For a correct indexing, the crystal system, chemical composition, unit cell dimensions and atomic positions of the material must be supplied to the analysis software. | An example is shown in Fig. 3. Consider four pixels along a Kikuchi line. For each pixel in the line, all possible values of ''ρ'' are calculated for ''θ'' ranging from 0° to 180° using Eq. 1, which produces four sinusoidal curves. These curves intersect at a point with (''ρ'', ''θ'') coordinates (green rectangle), corresponding to the angle of the line (''θ'') and its position relative to the origin (''ρ''). The grey-scale intensity I(xi; yi) of the image pixels is accumulated in each quantized point H(''ρ''; ''θ'') 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 in the Hough space, which is easily detected by the indexing software over the at background. For a correct indexing, the crystal system, chemical composition, unit cell dimensions and atomic positions of the material must be supplied to the analysis software. | ||
[[File:Picture2.png| | [[File:Picture2.png|550px|center|thumb|Fig. 3: Example of use of Hough transform for indexing of Kikuchi patterns: the points on a Kikuchi line (left) form sinusoidal curves in Hough space (right). The intersection of these curves is a point in the Hough space having (''ρ'', ''θ'') coordinates, directly connected to the position and tilt of the Kikuchi line.]] | ||