Phasor Imaging: A Generalization of Correlation-Based Time-of-Flight Imaging

In correlation-based time-of-flight (C-ToF) imaging systems, light sources with temporally varying intensities illuminate the scene. Due to global illumination, the temporally varying radiance received at the sensor is a combination of light received along multiple paths. Recovering scene properties (e.g., scene depths) from the received radiance requires separating these contributions, which is challenging due to the complexity of global illumination and the additional temporal dimension of the radiance. We propose phasor imaging, a framework for performing fast inverse light transport analysis using C-ToF sensors. Phasor imaging is based on the idea that, by representing light transport quantities as phasors and light transport events as phasor transformations, light transport analysis can be simplified in the temporal frequency domain. We study the effect of temporal illumination frequencies on light transport and show that, for a broad range of scenes, global radiance (inter-reflections and volumetric scattering) vanishes for frequencies higher than a scene-dependent threshold. We use this observation for developing two novel scene recovery techniques. First, we present micro-ToF imaging, a ToF-based shape recovery technique that is robust to errors due to inter-reflections (multipath interference) and volumetric scattering. Second, we present a technique for separating the direct and global components of radiance. Both techniques require capturing as few as 3-4 images and minimal computations. We demonstrate the validity of the presented techniques via simulations and experiments performed with our hardware prototype.