A post-processing histogram compensation method for SPAD-based d-ToF LiDAR systems for high photon flux measurements

In this study, we introduce a histogram post-processing technique for Single Photon Avalanche Diode (SPAD)-based direct Time of Flight (d-ToF) depth measurement systems, designed to address the nonlinearity inherent in SPAD behavior. The technique has been developed to mitigate the distortion of the histogram of timestamps known as pile-up, which results in non-existing fluctuations of the recorded background and reflected laser light. Because of pile-up, accuracy issues arise in the target depth estimation, ultimately limiting the measurement range. The problem is typically addressed implementing sophisticated algorithms to process the histogram of timestamps, with a direct impact on system complexity, frame rate and power consumption. Our method approximates a linear behavior of the SPAD over time by compensating the histogram of timestamps with its own cumulative distribution function (CDF), thereby producing a linearized histogram even in the presence of intense background illumination or strong laser echo, beyond the commonly recognized limit of 5% detection ratio. We first demonstrate the compensation process 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 wide range of values. Then, we validate the method performance using real data obtained from an existing d-ToF sensor. The experimental validation confirms the validity of the method to mitigate accuracy errors due to pile-up with varying target reflectivities, with an improvement of ≈73% and ≈57% for Lambertian and retroreflective surfaces, respectively. Finally, we analyze the behavior of the method over three different ToF extraction algorithms, demonstrating that the measurement range can be extended by more than 50%. Moreover, thanks to the linear shape of the compensated histogram, even a lightweight and computationally inexpensive ToF extraction algorithm as a peak detector can be successfully employed with benefits in terms of system complexity, frame rate and power consumption.