  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 3-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 first 4-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 with no laser scanning, camera translation, interpolation, nor
dark noise subtraction. A machine learning technique is applied to analyze the
measured spatio-temporal data set. A theoretical formula is introduced to
perform least-square regression, 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 a
good agreement with the actual geometry of the light path. Our approach could
potentially provide novel functionalities to high speed imaging applications
such as non-line-of-sight imaging and time-resolved optical tomography.
