Reducing Berreman's 4 × 4 formulation of liquid-crystal-display optics to 2 × 2 Jones vector equations

We use a perturbation expansion to obtain a generalized 2 x 2 Jones vector description that is equivalent to Berreman's description. We show that for typical liquid-crystal displays (LCD's) the bulk reflections are weak so that the first-order 2 x 2 Jones solution is generally sufficient and affords fast and reasonably accurate computations of the overall optical properties of LCD devices.