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Indexing of Kikuchi and Kossel lines is a crucial step in K-line pattern analysis. Previous approaches mostly rely on the knowledge of unit-cell parameters and experimental geometry. An auto-indexing procedure is introduced that is able to find the unknown lattice, its orientation and the indices of the lines. To achieve this, the unbiased extraction of the precise conical geometrical information from the patterns is combined with existing auto-indexing procedures developed in the field of crystallography. A subsequent lattice-constrained refinement of all lines to the experimental pattern yields reliable lattice and experimental parameters simultaneously. Beyond providing detailed mathematical formulae, the procedure is also demonstrated on an experimental Kossel line pattern.

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Mathematical formulae for cones and conic sections, the coordinate system and sets of parameters and the three use cases.

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