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：我们引入多普勒飞行时间（D-ToF）渲染，这是针对动态场景的ToF渲染扩展，应用于模拟D-ToF相机。D-ToF相机采用高频调制照明与曝光，通过测量多普勒频移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结构和所使用的调制函数，使得现有ToF渲染算法难以准确高效地模拟其测量结果。本文通过双重方法克服这些挑战：为实现准确性，我们推导了全局光照下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；为实现高效性，我们开发了一种定制的时间路径采样技术，将反时间采样与相关路径采样相结合。实验表明，与朴素的时间路径采样相比，我们的采样技术可将方差降低两个数量级。我们提供了开源模拟器作为D-ToF成像系统的数字孪生，使成像研究人员能够首次研究调制函数、材料属性和全局光照对D-ToF成像性能的影响。