Resolution Limit of Single-Photon LIDAR

Single-photon Light Detection and Ranging (LiDAR) systems are often equippedwith an array of detectors for improved spatial resolution and sensing speed.However, given a fixed amount of flux produced by the laser transmitter acrossthe scene, the per-pixel Signal-to-Noise Ratio (SNR) will decrease when morepixels are packed in a unit space. This presents a fundamental trade-offbetween the spatial resolution of the sensor array and the SNR received at eachpixel. Theoretical characterization of this fundamental limit is explored. Byderiving the photon arrival statistics and introducing a series of newapproximation techniques, the Mean Squared Error (MSE) of themaximum-likelihood estimator of the time delay is derived. The theoreticalpredictions align well with simulations and real data.