We introduce Doppler time-of-flight (D-ToF) rendering, an extension of ToF rendering for dynamic scenes, with applications in simulating D-ToF cameras. D-ToF cameras use high-frequency modulation of illumination and exposure, and measure the Doppler frequency shift to compute the radial velocity of dynamic objects. The time-varying scene geometry and high-frequency modulation functions used in such cameras make it challenging to accurately and efficiently simulate their measurements with existing ToF rendering algorithms. We overcome these challenges in a twofold manner: To achieve accuracy, we derive path integral expressions for D-ToF measurements under global illumination and form unbiased Monte Carlo estimates of these integrals. To achieve efficiency, we develop a tailored time-path sampling technique that combines antithetic time sampling with correlated path sampling. We show experimentally that our sampling technique achieves up to two orders of magnitude lower variance compared to naive time-path sampling. We provide an open-source simulator that serves as a digital twin for D-ToF imaging systems, allowing imaging researchers, for the first time, to investigate the impact of modulation functions, material properties, and global illumination on D-ToF imaging performance.

翻译：我们提出多普勒飞行时间渲染（Doppler time-of-flight rendering, D-ToF rendering），这是针对动态场景的飞行时间渲染扩展，用于模拟D-ToF相机。D-ToF相机采用高频照明与曝光调制，通过测量多普勒频移来计算动态物体的径向速度。此类相机中随时间变化的场景几何与高频调制函数，使得现有飞行时间渲染算法难以精确高效地模拟其测量过程。我们通过双向方法克服这些挑战：为提升精度，推导全局光照下D-ToF测量的路径积分表达式，并构建这些积分的无偏蒙特卡洛估计；为提升效率，开发了一种结合对偶时间采样与关联路径采样的定制化时间-路径采样技术。实验表明，与朴素时间-路径采样相比，该采样技术的方差降低可达两个数量级。我们提供开源模拟器作为D-ToF成像系统的数字孪生，使成像研究者首次能够探究调制函数、材料属性及全局光照对D-ToF成像性能的影响。