In the ab-initio indexing of powder diffraction, the unitcell parameters are determined from the values of d-spacings of reflections. From a Kikuchi map of electron backscattering diffraction (EBSD), the orientations of the corresponding reciprocal lattice vectors can be obtained, instead of the d-values. As fundamental tools for indexing analyses that can be commonly used in such different situations, we have recently developed the following.

(i) algorithm for error-stable Bravais lattice determination,
(ii) generalization of the de Wolff figure of merit for powder diffraction to higher-dimensional data, including EBSD images.
(iii) rules on forbidden hkl's that can be used even when the space group is not known.

In particular, handling of symmetries and observational error of experimental data are central topics in crystallography. We explain how indexing algorithms (including theoretical discussion such as (iii)) can be simplified by using (i). Our indexing software is now available on the web.

Powder diffraction: https://z-code.kek.jp/zrg/ (CONOGRAPH with graphic user interface)

EBSD: https://osdn.net/projects/ebsd-conograph/ (only command-line interface, upgrade is planned)