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A large aperture tunable lens based on liquid crystals, which is considered for near-to-eye applications, is designed, built, and characterized. Large liquid crystal lenses with high quality are limited by very slow switching speeds due to the large optical path difference (OPD) required. To reduce the switching time of the lens, the thickness is controlled through the application of several phase resets, similar to the design of a Fresnel lens. A main point of the paper is the design of the Fresnel structure to have a minimal effect on the image quality. Our modeling and experimental results demonstrate that minimal image degradation due to the phase resets is observable when the segment spacing is chosen by taking into account human eye resolution. Such lenses have applications related to presbyopia and, in virtual reality systems, to solve the well-known issue of accommodation–convergence mismatch.