In this thesis we present a combination of experimental and analytic approaches to improve the capabilities of polychromatic diffractive neutron imaging. This has been realized by following two relevant study cases: the transmitted neutron signal from powder crystals and the diffracted neutron signal from oligocrystals. In transmission imaging, powder crystals are among the most common samples of study, considering the importance of high-penetration non-destructive testing techniques for industrial applications and metallurgy. On the other hand, oligocrystals are interesting samples of study because they are currently stuck in a no "man's land" of scattering techniques: they have too few grains to produce powder diffraction patterns and too many grains to be indexed with single grain methods.