Grain size estimation in polycrystals: Solving the corpuscle problem using Maximum Likelihood Estimation

In materials science, the microstructures of materials are generally characterized by 2D observation (e.g. electron microscopy). For polycrystalline materials, such as crystalline rocks or ceramics, those observations can be used to measure the grain size distribution. However, the fact that grain sizes are measured in planar cuts introduces a statistical bias, since the real (3D) grain sizes cannot be directly measured. For almost spherical grains, this bias can be computed thanks to the so-called Wicksell's equation. This paper proposes a method, based on Maximum Likelihood Estimation (MLE) for unfolding the apparent 2D distribution. The efficiency of this method is extensively investigated in the special case of lognormal distribution. In this case, 10% uncertainty on the distribution parameters can be reached with only 580 empirical values.