Advances in high-speed imaging techniques have opened new possibilities for capturing ultrafast phenomena such as light propagation in air or through media. Capturing light in flight in three-dimensional $xyt$ space has been reported based on various types of imaging systems, whereas reconstruction of light-in-flight information in the fourth dimension $z$ has been a challenge. We demonstrate the four-dimensional light-in-flight imaging based on the observation of a superluminal motion captured by a new time-gated megapixel single-photon avalanche diode camera. A high-resolution light-in-flight video is generated without laser scanning, camera translation, interpolation, or dark noise subtraction. An unsupervised machine-learning technique is applied to analyze the measured spatiotemporal data set. A theoretical formula is introduced to perform least-square regression for numerically solving a nonlinear inverse problem, and extra-dimensional information is recovered without prior knowledge. The algorithm relies on the mathematical formulation equivalent to the superluminal motion in astrophysics, which is scaled by a factor of a quadrillionth. The reconstructed light-in-flight trajectory shows good agreement with the actual geometry of the light path. Applicability of the reconstruction approach to more complex scenes with multiple overlapped light trajectories is verified based on a data set generated by Monte Carlo simulations. Our approach could potentially provide novel functionalities to high-speed imaging applications such as non-line-of-sight imaging and time-resolved optical tomography.

中文翻译：

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超光速运动辅助的四维飞行中成像

高速成像技术的进步为捕获超快现象（例如光在空气中或通过介质的传播）开辟了新的可能性。捕捉飞行中的三维光$XÿŤ$ 已根据各种类型的成像系统报告了空间，而在第四维重建了飞行中的光信息 $ž$一直是一个挑战。我们演示了基于新的时间门控百万像素单光子雪崩二极管相机捕获的超光速运动的观察的三维飞行中的成像。无需激光扫描，摄像机平移，插值或暗噪声扣除，即可生成高分辨率的飞行中视频。一种无监督的机器学习技术被应用于分析测得的时空数据集。引入理论公式以执行最小二乘回归，以数值方式求解非线性逆问题，并且无需先验知识即可恢复超维信息。该算法依赖于相当于天体物理学中超腔运动的数学公式，该公式按四分之一的比例缩放。重建的飞行中光轨迹与光路的实际几何形状显示出良好的一致性。基于蒙特卡洛模拟生成的数据集，验证了重构方法对具有多个重叠光轨迹的更复杂场景的适用性。我们的方法可能为高速成像应用（如非视距成像和时间分辨光学层析成像）提供新颖的功能。