The optical transmission of antiferroelectric liquid crystal layers is non-trivial. For optical wavelengths we average the dielectric tensors. The aim is to provide a geometrical way for this averaging. By a thorough mathematical analysis, we are able to construct the representation ellipsoid for the final ε-tensor in most cases. In this way, we can easily predict the axes and indices of refraction of the structure. Especially the molecular states that occur during the hysteresis switching behaviour are studied.