A liquid crystal optical device is described configured to provide variable beam steering or refractive Fresnel lens control over light passing through an aperture of the device. The device includes at least one layer of liquid crystal material contained by substrates having alignment layers. An arrangement of electrodes is configured to provide a spatially varying electric field distribution within a number of zones within the liquid crystal layer. The liquid crystal optical device is structured to provide a spatial variation in optical phase delay with a transition at a boundary between zones which is an approximation of a sawtooth waveform across the boundaries of multiple zones. The arrangement of electrodes, device layered geometry and methods of driving the electrodes increase the effective aperture of the overall optical device.