  Single-photon Light Detection and Ranging (LiDAR) systems are often equipped
with an array of detectors for improved spatial resolution and sensing speed.
However, given a fixed amount of flux produced by the laser transmitter across
the scene, the per-pixel Signal-to-Noise Ratio (SNR) will decrease when more
pixels are packed in a unit space. This presents a fundamental trade-off
between the spatial resolution of the sensor array and the SNR received at each
pixel. Theoretical characterization of this fundamental limit is explored. By
deriving the photon arrival statistics and introducing a series of new
approximation techniques, the Mean Squared Error (MSE) of the
maximum-likelihood estimator of the time delay is derived. The theoretical
predictions align well with simulations and real data.
