We analysed the light propagation through alignment-patterned liquid crystal films where the alignment is planar and homeotropic for different domains, respectively. Using elastic theory the nematic director field can be analytically calculated with the method of conformal mapping in the one elastic constant approximation. A smooth change of the nematic director field is found with defect points at the substrate surfaces. In order to investigate the propagation of light passing through such a liquid crystalline thin film with spatially varying birefringence, we use a rigorous method. The use of rigorous methods allows the simulation of the time-dependent electric and magnetic fields for a region that is two-dimensional and possibly anisotropic. Simulations are made by the finite-difference time-domain method (FDTD), which is a numerical approach for the rigorous solution of the Maxwell equations. This method, in contrast to methods of geometrical and matrix optics, delivers results which include diffraction and scattering.