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 \times 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 $\pi $ 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.

中文翻译：

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同相亚奈奎斯特小透镜阵列编码到空间光调制器上。

当将衍射透镜编码到空间光调制器（SLM）上时，奈奎斯特（Nyquist）限制可形成的最小焦距。当超过该极限时，形成小透镜的二维阵列。关于这些小透镜性能的讨论很少。在这项工作中，我们专注于阵列中这些透镜的相位分布。我们表明，对于某些焦距值，小透镜都处于完美相位。我们表明，这种情况发生在总数为N / 4的不同离散等距子奈奎斯特焦距总数中，其中N × N是SLM中的像素数。我们在阵列由两组相对的$ \ pi $小透镜组成的阵列之间找到其他距离。其中的相位。最后，我们在应用中说明了这些相位分布，以生成产生涡流的透镜阵列。我们希望这些结果可能对高精度干涉仪或多重成像有用，其中每个复制品的这一阶段必须完全相同。