Models of Direct Time-of-Flight Sensor Precision That Enable Optimal Design and Dynamic Configuration

Direct time-of-flight (dToF) sensors that measure depth by pulsing a laser and timing the photon return are used in many applications, including consumer electronics for proximity sensing and depth map generation. A histogram of photon return times is measured and then processed to estimate object depth. By collecting many photons that span multiple bins of the histogram the final depth estimate interpolates between time-to-digital converter (TDC) bins to produce a result that is more precise than the converter resolution. The precision of this interpolation depends on the temporal spread of the measurement, the resolution of the TDC, and the number of signal and background photons measured. There is a need for dToF depth precision models to guide design and predict and tune performance during use. In this article, we present models that estimate sensor depth precision versus dToF design parameters and photons measured. We use Monte Carlo simulations and experimental measurements to prove the accuracy of the models. With proven models in hand, we investigate a dToF sensor design by first presenting the dependence of precision upon the TDC resolution and the signal-to-noise ratio. Second, we experimentally measure the depth precision versus the intensity of background illumination. The models closely match the measurements of background susceptibility and locate a transition point of background intensity below which precision is constant and above which the precision continuously degrades. Finally, experimental measurements demonstrate how the modeling enables dynamic tuning: from a single histogram we estimate precision, thus enabling sensor exposure time tuning for a target precision or prediction of the precision given a change in object distance or background illumination. This work presents straightforward models verified by simulation and measurement. These models guide dToF design and enable dynamic adjustments that benefit power-constrained usage scenarios.