Fog Effects on Time-of-Flight Imaging Investigated by Ray-Tracing Simulations^†

Time-of-Flight (ToF) sensors are a key technology for autonomous vehicles and autonomous mobile robotics. Quantifying the extent of perturbation induced by atmospheric phenomena on ToF imaging is critical to identify effective correction strategies. Here we present an approach that uses optical ray-tracing to simulate the ToF image, while the distance information is recovered by analyzing the optical path of each ray. Such an approach allows, for example, understanding the effects of different ray paths on the ToF image, or testing various retrieval/correction algorithms upon running a single ray-tracing simulation. By modelling several scattering scenarios, we show that ranging errors arise mostly from light backscattered to the sensor prior reaching the scene. Scattering events close to the sensors (<1 m) have the largest influence, therefore strategies capable of filtering out signals from distances shorter than the range of interest can significantly improve the accuracy of ToF sensors.