Texture analysis of heterogeneous data—a farewell to F-coefficients

This contribution describes the mathematical and numerical possibility to analyse heterogeneous data, e.g. experimental intensity data measured for many crystallographic but few sample directions, adaptively refined high resolution intensity data, or a mixture of diffraction intensity data and individual orientation data from scanning electron microscopy. possibilities are put forward within the dual approach to texture analysis provided by the differential equation governing pole figures. The general solution of this differential equation is represented both in terms of spherical harmonics or characteristics. The resulting systems of equations are capable of considering such heterogeneous data as mentioned above. entual aim of this contribution is to show that (i) the mostly tacit ‘paradigm’ of texture analysis that additional pole figures can be calculated from experimental pole figures only by using a detour via the ODF is not correct, and (ii) any function satisfying the differential equation governing pole figures is the actual pole figure projection, or X-ray transform, of a common function defined in a higher dimensional space. ily, it is shown that the two dual approaches to texture analysis provided by the projection formula or the differential equation are equivalent, but put emphasis on different issues of the same problem.