Abstract. The MATLAB™ toolbox MTEX provides a unique way to represent, analyse and interpret crystallographic preferred orientation, i.e. texture, based on integral ("pole figure") or individual orientation ("EBSD") measurements. In particular, MTEX comprises functions to import, analyse and visualize diffraction pole figure data as well as EBSD data, to estimate an orientation density function from either kind of data, to compute texture characteristics, to model orientation density functions in terms of model functions or Fourier coefficients, to simulate pole figure or EBSD data, to create publication ready plots, to write scripts for multiple use, and others. Thus MTEX is a versatile free and open-source software toolbox for texture analysis and modeling.

A novel algorithm for ODF (orientation density function) estimation from diffraction pole figures is presented which is especially well suited for sharp textures and high‐resolution pole figures measured with respect to arbitrarily scattered specimen directions, e.g. by area detectors. The estimated ODF is computed as the solution of a minimization problem which is based on a model of the diffraction counts as a Poisson process. The algorithm applies discretization by radially symmetric functions and fast Fourier techniques to guarantee smooth approximation and high performance. An implementation of the algorithm is freely available as part of the texture analysis software MTEX.

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This paper presents the background for the calculation of various numbers that can be used to characterize crystal-preferred orientation (CPO), also known as texture in materials science, for large datasets using the combined scripting possibilities of MTEX and MatLab w . The paper is focused on three aspects in particular: the strength of CPO represented by orientation and misorientation distribution functions (ODFs, MDFs) or pole figures (PFs); symmetry of PFs and components of ODFs; and elastic tensors. The traditional measurements of texture strength of ODFs, MDFs and PFs are integral measurements of the distribution squared. The M-index is a partial measure of the MDF as the difference between uniform and measured misorientation angles. In addition there other parameters based on eigen analysis, but there are restrictions on their use. Eigen analysis does provide some shape factors for the distributions. The maxima of an ODF provides information on the modes. MTEX provides an estimate of the lower bound uniform fraction of an ODF. Finally, we illustrate the decomposition of arbitrary elastic tensor into symmetry components as an example of components in anisotropic physical properties. Ten examples scripts and their output are provided in the appendix.