A histogram compensation process for SPAD-based d-ToF LiDAR systems for high photon flux measurements

In this work, we present a histogram post-processing method for Single Photon Avalanche Diode (SPAD)-based direct Time of Flight (d-ToF) depth measurement systems that compensates for the nonlinear behavior of the SPAD. The proposed compensation method approximates a linear behavior of the SPAD detector over time, resulting in a linearized histogram of timestamps even under strong background illumination conditions. The process can compensate for the distortion problem known as pile-up, which causes the corruption of the histogram of timestamps due to the variability of the intensity of the background and reflected laser light. The proposed approach has been first demonstrated with simulations, based on a physical model for the computation of the optical power budget and a numerical engine for the generation of the simulated train of timestamps. In particular, we consider a set of realistic parameters for typical SPAD-based d-ToF sensors, allowing us to validate the compensation method over a wider range of values. Finally, the method is validated with data from a real d-ToF sensor to demonstrate the effectiveness in mitigating the pile-up distortion phenomenon in the computation of the ToF.