Optical Characterization of the Director Field in a Distorted Nematic Layer

We develop new optical methods using transmitted polarized light for the characterization of the out of plane component $n_z$ of the director field in a weakly distorted planar nematic layer. In extraordinary light, we relate the angles of aperture of the caustic surface to the local amplitudes of the $n_z$ distortion. In ordinary light, a new type of contrast due to the anisotropic light scattering is shown to give the map of $n_z^2$. We apply our methods to the study of the director distortions occuring in the thermal convection