Presumably this is a classic problem, but I would need an informed (but nevertheless elementary) answer or citation to start:
Assume a collection of hard, impenetrable 3-spheres (phase B), randomly distributed in a homogeneous medium (phase A). The distribution function of the radii R of the spheres is denoted p(R) and is not known.
A random plane P cuts through phase A and intersects phase B in a set of cuts, or 2-speres of different radii r, their distribution function q(r) being known.
Question: is it possible to reconstruct p(R) starting from the q(r) determined on a single plane?