The Polymer Society of Korea

Abstract

Particle size distribution plays an important role in advanced materials. However, some materials do not allow direct measurement of particle size distribution but only 2D cross-sectional images are available. Therefore, we propose a numerical algorithm that converts 2D distribution to 3D one by solving Wicksell's corpuscle problem, a type of Abel's integral equation. 
Our algorithm is to approximate 3D size distribution by B-spline and to make the Abel integral equation to a system of linear equations. To solve the linear equations without magnification of error effect and the negativity of distribution function, we adopted fixed-point iteration which was developed for the estimation of relaxation time distribution.
Our algorithm is superior to the histogram approach because the size distributions are considered as continuous functions and to the other approaches in stabilization error. It should be noteworthy that our algorithm does not rely on any distribution models.