Three-dimensional single-photon imaging through realistic fog in an outdoor environment during the day

Due to the strong scattering of fog and the strong background noise, the signal-to-background ratio (SBR) is extremely low, which severely limits the 3D imaging capability of single-photon detector array through fog. Here, we propose an outdoor three-dimensional imaging algorithm through fog, which can separate signal photons from non-signal photons (scattering and noise photons) with SBR as low as 0.003. This is achieved by using the observation model based on multinomial distribution to compensate for the pile-up, and using dual-Gamma estimation to eliminate non-signal photons. We show that the proposed algorithm enables accurate 3D imaging of 1.4 km in the visibility of 1.7 km. Compared with the traditional algorithms, the target recovery (TR) of the reconstructed image is improved by 20.5%, and the relative average ranging error (RARE) is reduced by 28.2%. It has been successfully demonstrated for targets at different distances and imaging times. This research successfully expands the fog scattering estimation model from indoor to outdoor environment, and improves the weather adaptability of the single-photon detector array.