A new expression of Takagi-Taupin equations is applied to nearly perfect crystals with statistical lattice distortion, with which a formalism of the dynamical diffraction is proposed. A static Debye-Waller factor E is introduced to characterize the crystal. A solution of the equations is presented which describe the intensity distribution due to a narrow incident wave in the topography of a statistically homogeneous crystal. The application of this theory to the measuring of the micro-defects in crvstals is discussed.