Differential Frequency Heterodyne Time-of-Flight Imaging for Instantaneous Depth and Velocity Estimation

In this study, we discuss the imaging of depth and velocity using heterodyne-mode time-of-flight (ToF) cameras. In particular, Doppler ToF (D-ToF) imaging utilizes heterodyne modulation to measure the velocity from the Doppler frequency shift, which uniquely facilitates the instantaneous radial velocity estimation. However, theoretical discussion on D-ToF is limited to orthogonal frequency and sinusoidal waveform modulation. This study extends the formulation of the D-ToF imaging, and proposes an arbitrary-frequency, arbitrary-waveform framework considering a phase-compensated, symmetrical two-dimensional correlation map. With the proposed framework, the optimal heterodyne frequency for frequency decoding is found. A differential frequency sampling and decoding method is then proposed, which computes the frequency and phase from as few as four simultaneously captured images. With an experiment platform we built, it is confirmed that the minimum velocity sensing error is half that of the orthogonal frequency method, and the sensible phase range is approximately 2.5 times larger. The conclusions in this study allow the ToF velocity imaging to be applied at the optimal sample frequencies for a wide range of ToF sensors. This pushes one step further to the practical use of ToF velocity imaging.