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Optimization of Texture Measurements. III. Statistical Relevance of ODF Represented by Individual Orientations

The object of investigation in real texture experiments is always a sample with some finite number of grains N (see discussion in [1]). In previous papers [2, 3] the statistical properties of pole densities obtained from such experiments are highlighted. Two approaches were used to analyze quantitatively the statistical relevance of the experimental pole densities. In this paper, these approaches are applied for an analysis of the orientational distribution density (ODF) to compare quantitatively sampling and actual ODFs. Statistical analysis of ODF may be of use in individual orientation methods and of pole densities (PFs) is of interest in the conventional diffraction techniques.