`Exact' formulation for π-polarization waves of dynamical X-ray diffraction

Self-consistent formulae for treating the π-polarization waves in two-beam X-ray diffraction from single crystals are refined within the Laue formalism. These formulae overcome the ∇ · D ≠ 0 problem and avoid all the unnecessary approximations in previous dynamical theories. Therefore, they are as accurate as the formulae for σ-polarization waves.