Scan-free time-of-flight-based three-dimensional imaging through a scattering layer.

Reconstructing an object's three-dimensional shape behind a scattering layer with a single exposure is of great significance in real-life applications. However, due to the little information captured by a single exposure while strongly perturbed by the scattering layer and encoded by free-space propagation, existing methods cannot achieve scan-free three-dimensional reconstruction through the scattering layer in macroscopic scenarios using a short acquisition time of seconds. In this paper, we proposed a scan-free time-of-flight-based three-dimensional reconstruction method based on explicitly modeling and inverting the time-of-flight-based scattering light propagation in a non-confocal imaging system. The non-confocal time-of-flight-based scattering imaging model is developed to map the three-dimensional object shape information to the time-resolved measurements, by encoding the three-dimensional object shape into the free-space propagation result and then convolving with the scattering blur kernel derived from the diffusion equation. To solve the inverse problem, a three-dimensional shape reconstruction algorithm consisting of the deconvolution and diffractive wave propagation is developed to invert the effects caused by the scattering diffusion and the free-space propagation, which reshapes the temporal and spatial distribution of scattered signal photons and recovers the object shape information. Experiments on a real scattering imaging system are conducted to demonstrate the effectiveness of the proposed method. The single exposure used in the experiment only takes 3.5 s, which is more than 200 times faster than confocal scanning methods. Experimental results show that the proposed method outperforms existing methods in terms of three-dimensional reconstruction accuracy and imaging limit subjectively and objectively. Even though the signal photons captured by a single exposure are too highly scattered and attenuated to present any valid information in time gating, the proposed method can reconstruct three-dimensional objects located behind the scattering layer of 9.6 transport mean free paths (TMFPs), corresponding to the round-trip scattering length of 19.2 TMFPs.