stereological correction of mineral liberation grade distributions estimated by single sectioning of particles

The liberation distribution of ore samples is of considerable interest for process optimisation in the minerals industry. A scanning electron microscope-based automatic mineral analyser such as the LEO QEMSCAN system developed by CSIRO Minerals is a powerful tool for the estimation of linear or areal grade distributions of a population of ore particles based upon polished single particle sections. Stereological correction of a single section mineralogical grade distribution is recognised as an ill-posed inverse problem. The transformation kernel method with constrained entropy regularisation (King and Schneider, 1998) is adopted for the correction of stereological error in binary systems. An enhanced transformation kernel correction scheme is developed with an additional equality constraint for average grade as determined by section and volumetric sampling, in accordance with Delesse's fundamental stereological theorem. The usefulness of both correction methods is limited by the availability of kernels that appropriately model the relationship between volumetric and section grade distributions for the mineralogical sample of interest. The transformation kernel stereological correction methods are implemented in software available for use as part of the LEO QEMSCAN system. Both correction procedures are applied to areal section grade distributions of feed and concentrate from a mineral processing plant. The corrected grade distributions are in some instances found to be sensitive to the application of the average grade constraint. The statistical significance of differences in the corrected solutions is discussed.