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    Area of Science:

    • Photon-counting lidar technology
    • Optical remote sensing
    • Statistical modeling in physics

    Background:

    • Current ranging performance models for photon-counting lidars rely on Poisson statistics.
    • Poisson statistics represent a simplified case of the more general negative-binomial (NB) distribution.
    • Existing models do not fully account for factors like target speckle, noise, and detector dead-time.

    Purpose of the Study:

    • To derive a novel ranging performance model for photon-counting lidars from the NB distribution.
    • To incorporate the effects of target speckle, noise, and detector dead-time into the model.
    • To analyze the impact of target speckle on different lidar systems.

    Main Methods:

    • Derivation of a new ranging performance model based on the negative-binomial distribution.
    • Experimental verification using a Geiger-mode avalanche photodiode (GM-APD) lidar.
    • Simulation using a recursive method for validation.
    • Analysis of space-borne (ICESat-2) and ground-based (SHAO) lidar systems.

    Main Results:

    • The new NB-distribution-based model accurately predicts ranging performance, considering speckle, noise, and dead-time.
    • For space-borne/airborne lidars, the model approximates traditional Poisson-based models.
    • For ground-based lidars, the NB model reveals differences of ~1 cm bias and 4.8 cm precision compared to approximations.
    • The model is universal and converges to the Poisson model for speckle diversity > 100.

    Conclusions:

    • The derived NB-distribution model provides a more comprehensive understanding of photon-counting lidar ranging performance.
    • Target speckle significantly impacts ground-based lidar systems, necessitating the use of the NB model.
    • The model's compatibility with the Poisson model ensures its broad applicability across different lidar scenarios.