부산대학교 도서관

Summary: ``In a large number of measuring and characterization methods, the sphere size distribution of particles embedded in a medium has to be estimated from profile radii observed in cross sections or thin slices. On the one hand, this is a typical problem of density estimation. For that reason, kernel estimators may be applied. On the other hand, the computation of the sphere size distribution from the profile size distribution requires the inversion of an integral equation. In the case of cross sections or infinitely thin slices, this is an ill-posed problem which can be solved with specific methods as, e.g., Tikhonov regularization. In this contribution we propose a method for unfolding the sphere size distribution given a sample of profile radii which combines the advantages of kernel estimators with those of regularization methods. In order to study and test this method, Monte Carlo simulations have been performed. The results demonstrate that the method is reliable and leads to properly unfolded sphere size distributions. Finally, the method has been applied to experimental data obtained from transmission electron microscopy images of several polymer blends. The results demonstrate that the new method is a valuable tool for data analysis.''