The Ill-Posedness of the Inverse Problem of Texture Goniometry: the Variation Width of Feasible Orientation Density Functions Revisited

The problem of determining the set of all solutions of a well specified inverse problem of texture goniometry and providing a measure of its size by its variation width is revisited. This communication also clarifies the ambiguity and ill-posed nature of the inverse problem of texture goniometry. Starting with a standard orientation density function of the von Mises-Fisher type and its corresponding pole density function, another orientation density function is constructed exhibiting much more variation than the initial one, yet the pole density function remains basically unchanged. Comparison of the initial orientation density function with its wiggly variant provides a rough estimate of the lower bound of the variation width of the corresponding inverse problem.