  Consider an opaque medium which contains 3D particles. All particles are
convex bodies of the same shape, but they vary in size. The particles are
randomly positioned and oriented within the medium and cannot be observed
directly. Taking a planar section of the medium we obtain a sample of observed
2D section profile areas of the intersected particles. In this paper the
distribution of interest is the underlying 3D particle size distribution for
which an identifiability result is obtained. Moreover, a nonparametric
estimator is proposed for this size distribution. The estimator is proven to be
consistent and its performance is assessed in a simulation study.
