With progressing resolution of dot matrix displays, effects of inhomogeneous electric fields at the edges of structured electrodes become more and more important in the optical performance. We present a new method of polarizing microscopy for the study of the director field in two-dimensionally inhomogeneous nematic LC layers. Planar cells with electrode strips are investigated. The novel effects observed in these systems are two types of inversion walls, depending upon the preferred director orientation at the glass plates with respect to the electrodes.