On the reproducibility of the orientation distribution function of texture samples from pole figures (I). Relationship between the odf and pole figures

The explicit relationship between the orientation distribution function and the pole figures measured by means of diffraction experiments is derived and discussed. It is shown that these pole figures have a higher symmetry than the ODF, i.e. that it is impossible to reproduce unambiguously the ODF from pole figure datas only. From this circumstance follows that the ODF reproduced by help of usual methods are falsified and contain ghost phenomenas.