Inferring the properties of a scattering objective by analyzing the optical far-field responses within the framework of inverse problems is of great practical significance. However, it still faces major challenges when the parameter range is growing and involves inevitable experimental noises. Here, we propose a solving strategy containing robust neural-networks-based algorithms and informative photonic dispersions to overcome such challenges for a sort of inverse scattering problem—reconstructing grating profiles. Using two typical neural networks, forward-mapping type and inverse-mapping type, we reconstruct grating profiles whose geometric features span hundreds of nanometers with nanometric sensitivity and several seconds of time consumption. A forward-mapping neural network with a parameters-to-point architecture especially stands out in generating analytical photonic dispersions accurately, featured by sharp Fano-shaped spectra. Meanwhile, to implement the strategy experimentally, a Fourier-optics-based angle-resolved imaging spectroscopy with an all-fixed light path is developed to measure the dispersions by a single shot, acquiring adequate information. Our forward-mapping algorithm can enable real-time comparisons between robust predictions and experimental data with actual noises, showing an excellent linear correlation (R² > 0.982) with the measurements of atomic force microscopy. Our work provides a new strategy for reconstructing grating profiles in inverse scattering problems.

在逆问题的框架内通过分析光学远场响应来推断散射物镜的性质具有重要的实际意义。然而，当参数范围不断扩大并涉及不可避免的实验噪声时，它仍然面临重大挑战。在这里，我们提出了一种解决策略，其中包含基于神经网络的稳健算法和信息光子色散，以克服此类逆散射问题的挑战——重建光栅轮廓。使用两种典型的神经网络，正向映射类型和反向映射类型，我们重建光栅轮廓，其几何特征跨越数百纳米，具有纳米灵敏度和几秒钟的时间消耗。具有参数到点架构的前向映射神经网络在准确生成分析光子色散方面尤其突出，其特点是锋利的 Fano 形光谱。同时，为了通过实验实施该策略，开发了具有全固定光路的基于傅立叶光学的角分辨成像光谱，以通过单次拍摄测量色散，获取足够的信息。我们的前向映射算法可以将鲁棒预测和实验数据与实际噪声进行实时比较，显示出极好的线性相关性（开发了具有全固定光路的基于傅立叶光学的角分辨成像光谱，以通过单次拍摄测量色散，获取足够的信息。我们的前向映射算法可以将鲁棒预测和实验数据与实际噪声进行实时比较，显示出极好的线性相关性（开发了具有全固定光路的基于傅立叶光学的角分辨成像光谱，以通过单次拍摄测量色散，获取足够的信息。我们的前向映射算法可以将鲁棒预测和实验数据与实际噪声进行实时比较，显示出极好的线性相关性（R ²  > 0.982) 用原子力显微镜测量。我们的工作提供了一种在逆散射问题中重建光栅轮廓的新策略。