Diffractive achromats (DAs) promise ultra-thin and light-weight form factors for full-color computational imaging systems. However, designing DAs with the optimal optical transfer function (OTF) distribution suitable for image reconstruction algorithms has been a difficult challenge. Emerging end-to-end optimization paradigms of diffractive optics and processing algorithms have achieved impressive results, but these approaches require immense computational resources and solve non-convex inverse problems with millions of parameters. Here, we propose a learned rotational symmetric DA design using a concentric ring decomposition that reduces the computational complexity and memory requirements by one order of magnitude compared with conventional end-to-end optimization procedures, which simplifies the optimization significantly. With this approach, we realize the joint learning of a DA with an aperture size of 8 mm and an image recovery neural network, i.e., Res-Unet, in an end-to-end manner across the full visible spectrum (429–699 nm). The peak signal-to-noise ratio of the recovered images of our learned DA is 1.3 dB higher than that of DAs designed by conventional sequential approaches. This is because the learned DA exhibits higher amplitudes of the OTF at high frequencies over the full spectrum. We fabricate the learned DA using imprinting lithography. Experiments show that it resolves both fine details and color fidelity of diverse real-world scenes under natural illumination. The proposed design paradigm paves the way for incorporating DAs for thinner, lighter, and more compact full-spectrum imaging systems.

中文翻译：

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用于全光谱计算成像的旋转对称衍射消色差技术

衍射消色差透镜（DA）有望为全色计算成像系统提供超薄和轻巧的外形尺寸。然而，设计具有适用于图像重建算法的最佳光学传递函数（OTF）分布的DA一直是一项艰巨的挑战。新兴的衍射光学端到端优化范例和处理算法已经取得了令人印象深刻的结果，但是这些方法需要大量的计算资源，并且需要解决具有数百万个参数的非凸逆问题。在这里，我们提出了一种使用同心环分解的学习型旋转对称DA设计，与传统的端到端优化程序相比，该设计将计算复杂性和内存需求降低了一个数量级，从而显着简化了优化过程。用这种方法 我们实现了对孔径为8 mm的DA和图像恢复神经网络（即Res-Unet）的端到端在整个可见光谱（429–699 nm）中的联合学习。我们学习到的DA的恢复图像的峰值信噪比比常规顺序方法设计的DA高1.3 dB。这是因为学习到的DA在整个频谱上的高频下显示出更高的OTF幅度。我们使用压印光刻技术来制作学习到的DA。实验表明，它可以在自然光照下解决现实世界中各种场景的精细细节和色彩逼真度。提出的设计范例为将DA集成到更薄，更轻和更紧凑的全光谱成像系统中铺平了道路。