Interpretation of the images from a point source electron microscope requires a detailed analysis of transmission low energy electron diffraction. Here we present a general approach for solutions to the mixed Bragg-Laue case in transmission LEED (100-1000eV), based on the dynamical diffraction theory of Bethe. However, the validity of the dynamical diffraction theory to low energy electrons can be justified by its connection to the band theory for low energy crystal electrons.Assume that the incident beam forms a plane wave and the crystal is a thin slab. According to Bethe, the total electron wavefield within crystal can be written as a linear combination of Bloch waves (equation 1). The Bloch wave excitation coefficients b(j) can be determined by matching the boundary conditions, the wave amplitudes Cg(j) and the wave vectors k(j) for each Bloch wave can be obtained by solving the time independent Schrodinger equations (equation 2).