When originally developed decades ago, care was taken to orient the crystals correctly to ensure satisfactory signal detection between the crystals, but more modern versions of sonomicrometer hardware ( typically dating from 1995 to the present ) do not require such attention to crystal orientation.
32.
Since CIP on single HREM images works only smoothly for layer-structures with at least one short ( 3 to 5 ?) crystal axis, the method was extended to work also with data from different crystal orientations ( = atomic resolution electron tomography ).
33.
The Christoffel Equation is essentially an eigenvalue problem which relates the elastic tensor, c _ { ijkl }, to the crystal orientation and the orientation of the incident light, \ Lambda _ { kl }, to a matrix, \ lambda _ { kl }, whose eigenvalues are equal to ?V2, where ? is density and V is acoustic velocity ..
34.
With EBSD software, pattern bands are typically detected via a mathematical routine using a modified Hough transform, in which every pixel in Hough space denotes a unique line / band in the EBSP . The Hough transform is used to enable band detection, which are difficult to locate by computer in the original EBSP . Once the band locations have been detected it is possible to relate these locations to the underlying crystal orientation, as angles between bands represent angles between lattice planes.
