Encoding lenses with focal lengths lower than the Nyquist limit using high phase-modulation displays

Liquid crystal displays allow the easy implementation of diffractive optical elements. However, the shortest focal lengths for lenses are limited by Nyquist conditions. In this work, we show that focal lengths much lower than this Nyquist limit can be encoded onto devices having a large phase-dynamic range. Experimental results are included with a display showing 10 pi phase modulation reducing the Nyquist limit by a factor of about 1/10. (C) 2019 Optical Society of America