Liquid crystal (LC) devices including displays, beam-steering devices, electrically- and optically-controlled spatial light modulators, are widely used in a variety of applications. Some important operational properties of these devices, such as spatial resolution and diffraction efficiency, are severely limited by the influence of fringing electrical fields, generated between adjacent pixel electrodes. This work combines the results of three recent studies encompassing computer simulation, the development of an approximate analytical model and its experimental verification. The approximate analytical model ties the fringing-field-dependent broadening kernel, to the physical LC Cell properties. In particular, it is shown that, the broadening of the phase profile due to the fringing field is proportional to the LC cell thickness. These results are found to be in an excellent agreement both with high-precision computer simulations and experimental results. Finally, the phase broadening kernel is found to be independent of the particular shape of the phase profile, allowing the model to be used for other LC device architectures such as LCDs.