Reconstruction of the form of a particle from its three-dimensional asymptotic form factor

The form of a particle, which is homogeneous, finite, strictly convex, smooth and centrosymmetric, can uniquely be determined if the leading asymptotic term of its form factor is known along each direction of reciprocal space. If the central symmetry is lacking, all the admissible particle forms are among the solutions of a partial differential equation with given boundary conditions. The possible practical relevance of this result is discussed.