3D Imaging Algorithm of Directional Borehole Radar Based on Root-MUSIC

A directional borehole radar consists of one transmitting antenna in the borehole and four receiving antennas distributed at equal angles in a ring. The receiving antennas can determine the depth and orientation of targets beside the borehole. However, the problem of target orientation determination and 3D imaging algorithms remains a technological challenge. The MUSIC (multiple signal classification) algorithm requires a peak search, so the accuracy of the operation is limited by the angle interval. Based on the MUSIC algorithm, the Root-MUSIC algorithm is proposed and implemented. By replacing the spectral peak search with calculating the roots of the polynomials greatly improves the orientation recognition accuracy. Finally, the results obtained using the above algorithm are verified with synthetic data and compared with the results of the MUSIC algorithm. The results show that both the MUSIC algorithm and the Root-MUSIC algorithm can achieve very good orientation determination and 3D imaging results. In terms of accuracy, the Root-MUSIC algorithm has an obvious improvement compared with the MUSIC algorithm.

Distribution rules of systematic absences and generalized de Wolff figures of merit applied to electron backscatter diffraction ab initio indexing

A new method for electron backscatter diffraction ab initio indexing is reported that adopts several methods originally invented for powder indexing. Distribution rules of systematic absences and error-stable Bravais lattice determination are used to eliminate the negative influence of non-visible bands and erroneous information from visible bands. In addition, generalized versions of the de Wolff figures of merit are proposed as a new sorting criterion for the obtained unit-cell parameters, which can be used in both orientation determination and ab initio indexing from Kikuchi patterns. Computational results show that the new figures of merit work well, similar to the original de Wolff Mn . The ambiguity of the indexing solutions is also pointed out, which happens in particular for low-symmetry cells and may generate multiple distinct solutions even if very accurate positions of band centre lines and the projection centre are given. It is supposed that this is the reason why indexing was successful in an orthorhombic case but not in a triclinic cell.