Optical metasurfaces performing analog image processing – such as spatial differentiation and edge detection – hold the potential to reduce processing times and power consumption, while avoiding bulky 4 F lens systems. However, current designs have been suffering from trade-offs between spatial resolution, throughput, polarization asymmetry, operational bandwidth, and isotropy. Here, we show that dispersion engineering provides an elegant way to design metasurfaces where all these critical metrics are simultaneously optimized. We experimentally demonstrate silicon metasurfaces performing isotropic and dual-polarization edge detection, with numerical apertures above 0.35 and spectral bandwidths of 35 nm around 1500 nm. Moreover, we introduce quantitative metrics to assess the efficiency of these devices. Thanks to the low loss nature and dual-polarization response, our metasurfaces feature large throughput efficiencies, approaching the theoretical maximum for a given NA. Our results pave the way for low-loss, high-efficiency and broadband optical computing and image processing with free-space metasurfaces.

执行模拟图像处理（例如空间微分和边缘检测）的光学超表面有可能减少处理时间和功耗，同时避免使用笨重的 4 F 透镜系统。然而，当前的设计一直在空间分辨率、吞吐量、偏振不对称性、工作带宽和各向同性之间进行权衡。在这里，我们展示了色散工程提供了一种设计超表面的优雅方法，其中所有这些关键指标都得到同时优化。我们通过实验证明了硅超表面执行各向同性和双偏振边缘检测，其数值孔径高于 0.35，光谱带宽在 1500 nm 左右为 35 nm。此外，我们引入了定量指标来评估这些设备的效率。由于低损耗特性和双偏振响应，我们的超表面具有很高的吞吐量效率，接近给定 NA 的理论最大值。我们的研究结果为利用自由空间超表面进行低损耗、高效和宽带光学计算和图像处理铺平了道路。