Abstract Computer generated optical volume elements have been investigated for information storage, spectral filtering, and imaging applications. Advancements in additive manufacturing (3D printing) allow the fabrication of multilayered diffractive volume elements in the micro-scale. For a micro-scale multilayer design, an optimization scheme is needed to calculate the layers. The conventional way is to optimize a stack of 2D phase distributions and implement them by translating the phase into thickness variation. Optimizing directly in 3D can improve field reconstruction accuracy. Here we propose an optimization method by inverting the intended use of Learning Tomography, which is a method to reconstruct 3D phase objects from experimental recordings of 2D projections of the 3D object. The forward model in the optimization is the beam propagation method (BPM). The iterative error reduction scheme and the multilayer structure of the BPM are similar to neural networks. Therefore, this method is referred to as Learning Tomography. Here, instead of imaging an object, we reconstruct the 3D structure that performs the desired task as defined by its input-output functionality. We present the optimization methodology, the comparison by simulation work and the experimental verification of the approach. We demonstrate an optical volume element that performs angular multiplexing of two plane waves to yield two linearly polarized fiber modes in a total volume of 128 μm by 128 μm by 170 μm.

中文翻译：

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通过增材制造计算机生成的光学体积元素

摘要 计算机生成的光学体积元素已被研究用于信息存储、光谱滤波和成像应用。增材制造（3D 打印）的进步允许在微观尺度上制造多层衍射体积元素。对于微尺度多层设计，需要优化方案来计算层。传统的方法是优化二维相位分布的堆栈，并通过将相位转换为厚度变化来实现它们。直接在 3D 中优化可以提高场重建精度。在这里，我们通过反转学习断层扫描的预期用途提出了一种优化方法，这是一种从 3D 对象的 2D 投影的实验记录中重建 3D 相位对象的方法。优化中的前向模型是光束传播方法（BPM）。BPM 的迭代误差减少方案和多层结构类似于神经网络。因此，这种方法被称为学习断层扫描。在这里，我们不是对对象进行成像，而是重建执行由其输入-输出功能定义的所需任务的 3D 结构。我们介绍了优化方法、模拟工作的比较和该方法的实验验证。我们展示了一个光学体积元件，它执行两个平面波的角度复用，以在 128 μm x 128 μm x 170 μm 的总体积中产生两个线性偏振光纤模式。这种方法被称为学习断层扫描。在这里，我们不是对对象进行成像，而是重建执行由其输入-输出功能定义的所需任务的 3D 结构。我们介绍了优化方法、模拟工作的比较和该方法的实验验证。我们展示了一个光学体积元件，它执行两个平面波的角度复用，以在 128 μm x 128 μm x 170 μm 的总体积中产生两个线性偏振光纤模式。这种方法被称为学习断层扫描。在这里，我们不是对对象进行成像，而是重建执行由其输入-输出功能定义的所需任务的 3D 结构。我们介绍了优化方法、模拟工作的比较和该方法的实验验证。我们展示了一个光学体积元件，它执行两个平面波的角度复用，以在 128 μm x 128 μm x 170 μm 的总体积中产生两个线性偏振光纤模式。