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（D-ToF）渲染技术，作为针对动态场景的ToF渲染扩展，应用于模拟D-ToF相机。D-ToF相机通过高频调制照明与曝光，测量多普勒频移以计算动态物体的径向速度。此类相机中时变场景几何与高频调制函数的存在，使得现有ToF渲染算法难以准确高效地模拟其测量数据。我们通过双重策略克服这些挑战：在精度方面，推导出全局光照下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；在效率方面，开发了一种将对立时间采样与关联路径采样相结合的自适应时间-路径采样技术。实验表明，与朴素的时间-路径采样相比，本采样技术可实现方差降低达两个数量级。我们提供开源模拟器作为D-ToF成像系统的数字孪生，首次使成像研究人员能够探究调制函数、材料属性和全局光照对D-ToF成像性能的影响。