A Coding Theory of Time-of-Flight 3D Imaging

The depth resolution achieved by a continuous wave time-of-flight (C-ToF) imaging system is determined by the coding (modulation and demodulation) functions that it uses. Almost all current C ToF systems use sinusoid or square coding functions, resulting in a limited depth resolution. We present a mathematical framework for exploring and characterizing the space of C-ToF coding functions in a geometrically intuitive space. Using this framework, we design families of novel coding functions that are based on Hamiltonian cycles on hypercube graphs. Given a fixed power and acquisition time, the new Hamiltonian coding scheme can achieve up to an order of magnitude higher resolution as compared to the current state-of-the-art methods, especially in low signal-to-noise ratio (SNR) settings. Since most off-the-shelf C-ToF sensors use sinusoid or square functions, we develop a hardware prototype that can implement a wide range of coding functions. Using this prototype, we demonstrate the performance advantages of the proposed Hamiltonian coding functions in a wide range of imaging settings.