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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.

We present an implementation of a semi-device-independent protocol of the generation of quantum random numbers in a fully integrated silicon chip. The system is based on a prepare-and-measure scheme, where we integrate a partially trusted source of photons and an untrusted single photon detector. The source is a silicon photomultiplier, which emits photons during the avalanche impact ionization process, while the detector is a single photon avalanche diode. The proposed protocol requires only a few and reasonable assumptions on the generated states. It is sufficient to measure the statistics of generation and detection in order to evaluate the min-entropy of the output sequence, conditioned on all possible classical side information. We demonstrate that this protocol, previously realized with a bulky laboratory setup, is totally applicable to a compact and fully integrated chip with an estimated throughput of 6 kHz of the certified quantum random bit rate.

We present a Montecarlo simulator developed in Matlab® for the analysis of a Single Photon Avalanche Diode (SPAD)-based Complementary Metal-Oxide Semiconductor (CMOS) flash Light Detection and Ranging (LIDAR) system. The simulation environment has been developed to accurately model the components of a flash LIDAR system, such as illumination source, optics, and the architecture of the designated SPAD-based CMOS image sensor. Together with the modeling of the background noise and target topology, all of the fundamental factors that are involved in a typical LIDAR acquisition system have been included in order to predict the achievable system performance and verified with an existing sensor.