Signal flux and time-of-flight estimation based on waveform optimization for single-photon LiDAR

Single-photon LiDAR is widely used for target detection and 3D imaging. Traditional flux inversion methods, which count the echo photons of the signal, struggle with high signal fluxes due to dead time and a detection probability close to 100 %. This paper presents a new approach that uses the temporal information of the echo photons to estimate LiDAR fluxes in the range [0.5, 21] photons instead of simply counting the echo signal photons. The calibration of the laser pulse shape is performed using the GMM (Gaussian Mixture Model) method, which allows for the optimal signal flux value to be identified for describing the measured histogram. The waveform optimization is used to compensate for walking errors and improve range accuracy. Simulation results show that the method achieves a mean absolute error (MRE) within 9.55 % and a distance estimation accuracy of 12.01 mm. Changing the noise from 10 kHz to 100 kHz did not significantly degrade the algorithm performance. In the experiment, the depth precision can be better than 15.07 mm. Under the condition of different signal fluxes, the inversion values of signal flux and distance of the proposed method will converge to the ground truth with higher accuracy, which will more suitable for high dynamic range scene ranging and imaging.