Ranging performance models based on negative-binomial distribution for photon-counting lidars


Advanced sensitive sensors have been used in the development of high-performance photon-counting lidars which have found applications in numerous areas such as ground-based debris detection systems and airborne laser altimeter systems. This has led to the development of several theoretical models for analyzing the detection probability and ranging performance of these systems. Considering the importance of the ranging performance in evaluating a lidar, the corresponding theoretical models can be used to optimize systematic parameters. However, the presently available ranging performance models are based on Poisson statistics that do not fully describe the effects of some parameters such as noise and the dead time.

Recently, Wuhan University-based researchers: Professor Song Li, Zhiyu Zhang, Dr. Yue Ma, Haomin Zeng, Pufan Zhao, and Wenhao Zhang developed a new ranging performance model from the negative binomial distribution for photon-counting lidars. In particular, the authors extended the previously obtained results by taking into consideration the effects of a target speckle, noise, and dead-time of photo-counting detectors. Next, the derived ranging performance model was validated both experimentally and numerically based on the Geiger mode avalanche photodiode (GM-APD) lidar and recursive simulation method respectively. The research work is currently published in the journal, Optics Express.

The mutual agreement between the theoretical model results and the experimental and recursive calculation results showed the reliability of the proposed ranging performance model. As a concept proof, the model was used to analyses the effects of the target speckles in two photon-counting ranging systems with different targets. This included detection of the Earth’s surface using space-borne ICESat-2 and detecting space debris at the Shanghai Astronomical Observatory (SHAO) station using a ground-based laser ranging system. The effects of the speckle diversity of the two systems were also analyzed. For instance, the ranging performance model could be approximated to the classical models based on Poison statistics for airborne lidars as opposed to ground-based laser ranging systems.

The new model was regarded as universal owing to its compatibility with the classic model of Poison distribution. For example, speckle diversity larger than 100, the new model produced similar results as that of the classical model. Based on the ranging performance model, the system parameters of a photon-counting lidar could be optimized to achieve a balance between the range performance and detection probability.

Whereas it was possible to determine the ranging performance of a ranging system aimed at area targets like that for airborne, it was significantly difficult to simplify the ranging performance of a laser ranging system aimed at point targets. This was attributed to the difficulty in deriving the analytical solution to speckle diversity of a recto-reflector due to the effects of the incident and dihedral angles on the far-field diffraction.

Nonetheless, the proposed ranging performance model by Professor Song Li and her colleagues can be used to effectively, accurately and preciously predict the ranging of a photon-counting lidar. Additionally, it will correct the range walk errors by optimizing the system parameters during the design and development of photon-counting lidars.

Ranging performance models based on negative-binomial (NB) distribution for photon-counting lidars - Advances in Engineering

About the author

Prof. Dr. Song Li is a professor and the associate dean in School of Electronic Information, Wuhan University. She received the B.S. degree in Optical Device from Wuhan Technical University of Surveying and Mapping in 1986 and the Ph.D. degree in Geodesy and Survey Engineering from Wuhan University in 2002. She is now the team leader of the opto-electronic detection and laser remote sensing lab and her research interests include optical design, weak signal detection, and laser remote sensing.

Email: [email protected]

About the author

Zhiyu Zhang is a Ph.D. candidate in electronic in School of Electronic Information, Wuhan University. He received the B.S. degree from Wuhan University in 2015. His research interest includes laser remote sensing and photon-counting lidars. He is currently doing research on the detection theory of lidars with single photon detectors.

Email: [email protected]

About the author

A/Prof. Dr. Yue Ma received the B.S. degree in electronic information engineering from Wuhan University of Technology in 2008 and the Ph.D. degree in space detection and signal processing from Wuhan University in 2014. He is currently with the School of Electronic Information, Wuhan University, China and with the School of Science, University of New South Wales, Australia. His current research interests include satellite laser altimeter/lidar signal processing, systematic error calibration, and data application.

Email: [email protected]


Li, S., Zhang, Z., Ma, Y., Zeng, H., Zhao, P., & Zhang, W. (2019). Ranging performance models based on negative-binomial (NB) distribution for photon-counting lidars. Optics Express, 27(12), A861.

Go To Optics Express

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