Comments on absorption in Takagi–Taupin equations

The Takagi-Taupin theory of X-ray diffraction leaves an ambiguity in the choice of the wave vector inside the crystal. This holds also for its imaginary part which describes absorption. One consequence of this ambiguity is that the wave vector k0 inside the crystal need not always satisfy the continuity conditions for the tangential component of the wave vector at the entrance surface. But if the direction of the imaginary part is once fixed then it determines the particular manner of solution of the Takagi-Taupin equations. Thus a direction of the imaginary part of the wave vector in the crystal parallel to the reflecting net planes will in general ensure that the continuity condition is not satisfied; only a wave vector with an imaginary part perpendicular to the crystal surface can satisfy this condition.