Improvements on the recovery of 3D particle size distributions from 2D sections

The recovery of underlying 3D particle size distributions by analyzing only 2D sections (such as thin layers or scanning electron microscopy images) has been thoroughly investigated in the last forty years. However, with the advent of increasingly more powerful computers, flexible programming languages and readily available source code, very interesting studies have recently been published on this topic. In this paper, we implement and discuss some key improvements to one particularly promising approach, which is based on the linear representation of the effect of each particle on the smaller apparent sizes that are measurable in the 2D plane. Two main improvements are examined: (i) the inclusion of either a parametric or a nonparametric fit to the measured data and (ii) the utilization of optimization tools to solve the resulting linear system. We endeavor to prove that the new method produces reliable results both in simulations and in an experimental validation example, while also reducing the number of required measurements.