Recent progress in the material sciences has led to an increasing amount of interest in the role of textures for the behaviour of materials and in the mechanisms controlling the texture formation. This development was supported by a rather powerfull development taking place in the area of texture studies itself: Besides the usual, more qualitative, characterization of a texture by pole figures a fully quantitative description by a three-dimensional orientation distribution function (ODF) has been increasingly applied. There are two sides to the problem of quantitative representation of textures. One involves the mathematical technique associated with the acquisition of an ODF, and its transforms, from the experimental data, whereas the other concerns the methods of a rational description and interpretation of an ODF. The fust side can be considered from the practicaf point of view as experimental-data processing which is accomplished by a computer and is sort of a continuation of the measurement itself. Much attention has been paid to this problem, particulary by Bunge, who has written up achievements in this field in this extensive monograph /1/ and in conference proceedings /2/. There is also avaiable a rather detailed presen· tation of a system of subroutines written in Fortran /3/ which allows standard computations to be made without having to go into the mathematical details of the method.

A Review of the Representation of Orientations and Orientation Distributions

B The Tables
Table I: The General Miller-Indices {HKL} 'UVW' for H,K,L,U,V,W ? 15
Table II: From the {001}-Pole Figure to Miller Indices
Table III: From {011} Pole Figure to Miller Indices
Table IV: From {111} Pole Figure to Miller Indices
Table V: From Miller Indices into Euler Angles
Table VI: From Euler Angles into Miller Indices
Table VII: Angles between Sample and Crystal Axes.