In-phase sub-Nyquist lenslet arrays encoded onto spatial light modulators.

Abstract

When encoding diffractive lenses onto a spatial light modulator (SLM), there is a Nyquist limit to the smallest focal length that can be formed. When this limit is surpassed, a two-dimensional array of lenslets is formed. There have been very few discussions on the performance of these lenslets. In this work, we focus on the phase distribution of these lenses in the array. We show that, for certain values of the focal length, the lenslets are all in perfect phase. We show that this situation happens for a total number of N/4 different discrete equidistant sub-Nyquist focal lengths, where N×N is the number of pixels in the SLM. We find other distances in between where the array is composed of two sets of lenslets with a relative π phase among them. Finally, we illustrate these phase distributions in the application to generate an array of vortex producing lenses. We expect that these results might be useful for high-accuracy interferometric or multiple imaging where this phase must be exactly the same for each replica.