Optimization of the Positivity Method in Quantitative Texture Analysis

The direct calculation of the three-dimensional orientation density function (ODF), from its two-dimensional projections, the pole figures, yields only the reduced or even ODF, (g), which has usually negative values. The positivity method allows the determination of a physical acceptable positive ODF, f(g), best compatible with the experimental pole figures. The algorithm for the searching of the positive solution can be substantially improved in computing at each iteration step, the solution having the minimal distance to the set of positive functions.