Statistical Distribution and Detection Limit of Time-Correlated Single-Photon Counting Echoes for Targets in Turbid Media

Strong scattering and absorption in turbid media severely limit the detection range and signal-to-noise ratio of conventional active optical detection methods. Leveraging the ultrahigh sensitivity and temporal resolution of single-photon detectors, this work establishes a statistical echo photon distribution model for targets in turbid media under the time-correlated single-photon counting (TCSPC) mode based on the diffusion equation, and proposes an object-to-background ratio (OBR) metric for quantitative performance evaluation. Experiments validate the model with a normalized cross-correlation coefficient above 0.97. Results show that effective detection and imaging ranges reach ~10 and ~5 times the scattering mean free path, respectively. Detection range increases logarithmically with laser repetition rate and single-pulse photon number, while noise and reflectivity show weaker influences. This study provides quantitative guidance for single-photon detection system design in turbid environments.