The reconstructed light-in-flight trajectory shows good agreement with the actual geometry of the light path. The algorithm relies on the mathematical formulation equivalent to the superluminal motion in astrophysics, which is scaled by a factor of a quadrillionth. 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. An unsupervised machine-learning technique is applied to analyze the measured spatiotemporal data set. A high-resolution light-in-flight video is generated without laser scanning, camera translation, interpolation, or dark noise subtraction. 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. Capturing light in flight in three-dimensional x y t 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. Advances in high-speed imaging techniques have opened new possibilities for capturing ultrafast phenomena such as light propagation in air or through media.
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