Abstract

For photon-counting lidars, the current ranging performance models are based on Poisson statistics that are a special case of a negative-binomial (NB) distribution. In this paper, a new ranging performance model that considers the effect of a target’s speckle, the noise, and the dead-time of photon-counting detectors is derived from the NB distribution. The derived ranging performance model is verified by both an experiment based on a Geiger mode avalanche photodiode (GM-APD) lidar and a simulation using the recursive method. The ranging performance model is then used to analyze the effect of target speckle for two typical photon-counting ranging systems aimed at different types of target: the space-borne Ice, Cloud and land Elevation Satellite-2 (ICESat-2) for detecting the Earth’s surface, and the ground-based laser ranging system at Shanghai Astronomical Observatory (SHAO) station for detecting space debris. The results indicate that for space-borne or airborne lidar, the ranging performance model can be approximated to the classic models based on Poisson statistics, but for a ground-based laser ranging system, the approximation model introduces differences of ~1 cm in ranging bias and 4.8 cm in ranging precision from the theoretical model of the NB distribution. In addition, the new model is universal because it is compatible with the classic model of a Poisson distribution, i.e., when the speckle diversity is greater than 100, the result calculated from the new model is identical to the classic model.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (3)

2017 (3)

L. Xu, Y. Zhang, Y. Zhang, L. Wu, C. Yang, X. Yang, Z. Zhang, and Y. Zhao, “Signal restoration method for restraining the range walk error of Geiger-mode avalanche photodiode lidar in acquiring a merged three-dimensional image,” Appl. Opt. 56(11), 3059–3063 (2017).
[Crossref] [PubMed]

Z. Li, J. Lai, C. Wang, W. Yan, and Z. Li, “Influence of dead-time on detection efficiency and range performance of photon-counting laser radar that uses a Geiger-mode avalanche photodiode,” Appl. Opt. 56(23), 6680–6687 (2017).
[Crossref] [PubMed]

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

2016 (1)

K. M. Brunt, T. A. Neumann, J. M. Amundson, J. L. Kavanaugh, M. S. Moussavi, K. M. Walsh, W. B. Cook, and T. Markus, “MABEL photon-counting laser altimetry data in Alaska for ICESat-2simulations and development,” Cryosphere 10(4), 1707–1719 (2016).
[Crossref]

2013 (1)

W. He, B. Sima, Y. Chen, H. Dai, Q. Chen, and G. Gu, “A correction method for range walk error in photon counting 3D imaging LIDAR,” Opt. Commun. 308, 211–217 (2013).
[Crossref]

2012 (1)

Z. Zhang, F. Yang, H. Zhang, Z. Wu, J. Chen, P. Li, and W. Meng, “The use of laser ranging to measure space debris,” Res. Astron. Astrophys. 12(2), 212–218 (2012).
[Crossref]

2010 (1)

M. S. Oh, H. J. Kong, T. H. Kim, K. H. Hong, and B. W. Kim, “Reduction of range walk error in direct detection laser radar using a Geiger mode avalanche photodiode,” Opt. Commun. 283(2), 304–308 (2010).
[Crossref]

2009 (1)

2007 (1)

J. W. Goodman, “Speckle phenomena in optics: theory and applications,” J. Stat. Phys. 130(2), 413–414 (2007).
[Crossref]

2005 (1)

2003 (1)

2002 (1)

J. J. Degnan, “Photon-counting multikilohertz microlaser altimeters for airborne and spaceborne topographic measurements,” J. Geodyn. 34(3-4), 503–549 (2002).
[Crossref]

1992 (2)

C. S. Gardner, “Ranging performance of satellite laser altimeters,” IEEE Trans. Geosci. Remote Sens. 30(5), 1061–1072 (1992).
[Crossref]

D. G. Youmans, “Avalanche photodiode detection statistics for direct detection laser radar,” Proc. SPIE 1633, 41–52 (1992).
[Crossref]

1966 (1)

J. W. Goodman, “Comparative performance of optical-radar detection techniques,” IEEE T. Aero. Elec. Sys. AES-2(5), 526–535 (1966).
[Crossref]

1965 (1)

J. W. Goodman, “Some effects of target-induced scintillation on optical radar performance,” Proc. IEEE 53(11), 1688–1700 (1965).
[Crossref]

1924 (1)

S. N. Bose, “Plancks Gesetz und Lichtquantenhypothese,” Z. Phys. 26(1), 178–181 (1924).
[Crossref]

Abdalati, W.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Amundson, J. M.

K. M. Brunt, T. A. Neumann, J. M. Amundson, J. L. Kavanaugh, M. S. Moussavi, K. M. Walsh, W. B. Cook, and T. Markus, “MABEL photon-counting laser altimetry data in Alaska for ICESat-2simulations and development,” Cryosphere 10(4), 1707–1719 (2016).
[Crossref]

Bose, S. N.

S. N. Bose, “Plancks Gesetz und Lichtquantenhypothese,” Z. Phys. 26(1), 178–181 (1924).
[Crossref]

Brunt, K.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Brunt, K. M.

K. M. Brunt, T. A. Neumann, J. M. Amundson, J. L. Kavanaugh, M. S. Moussavi, K. M. Walsh, W. B. Cook, and T. Markus, “MABEL photon-counting laser altimetry data in Alaska for ICESat-2simulations and development,” Cryosphere 10(4), 1707–1719 (2016).
[Crossref]

Chen, J.

Z. Zhang, F. Yang, H. Zhang, Z. Wu, J. Chen, P. Li, and W. Meng, “The use of laser ranging to measure space debris,” Res. Astron. Astrophys. 12(2), 212–218 (2012).
[Crossref]

Chen, Q.

L. Ye, G. Gu, W. He, H. Dai, and Q. Chen, “A real-time restraint method for range walk error in 3-D imaging lidar via dual detection,” IEEE Photonics J. 10(2), 1 (2018).
[Crossref]

W. He, B. Sima, Y. Chen, H. Dai, Q. Chen, and G. Gu, “A correction method for range walk error in photon counting 3D imaging LIDAR,” Opt. Commun. 308, 211–217 (2013).
[Crossref]

Chen, Y.

W. He, B. Sima, Y. Chen, H. Dai, Q. Chen, and G. Gu, “A correction method for range walk error in photon counting 3D imaging LIDAR,” Opt. Commun. 308, 211–217 (2013).
[Crossref]

Cook, W. B.

K. M. Brunt, T. A. Neumann, J. M. Amundson, J. L. Kavanaugh, M. S. Moussavi, K. M. Walsh, W. B. Cook, and T. Markus, “MABEL photon-counting laser altimetry data in Alaska for ICESat-2simulations and development,” Cryosphere 10(4), 1707–1719 (2016).
[Crossref]

Csatho, B.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Dai, H.

L. Ye, G. Gu, W. He, H. Dai, and Q. Chen, “A real-time restraint method for range walk error in 3-D imaging lidar via dual detection,” IEEE Photonics J. 10(2), 1 (2018).
[Crossref]

W. He, B. Sima, Y. Chen, H. Dai, Q. Chen, and G. Gu, “A correction method for range walk error in photon counting 3D imaging LIDAR,” Opt. Commun. 308, 211–217 (2013).
[Crossref]

Degnan, J.

J. Degnan, “Impact of receiver deadtime on photon-counting SLR and altimetry during daylight operations,” Proc. International Workshop on Laser Ranging (2008).

Degnan, J. J.

J. J. Degnan, “Photon-counting multikilohertz microlaser altimeters for airborne and spaceborne topographic measurements,” J. Geodyn. 34(3-4), 503–549 (2002).
[Crossref]

Farrell, S.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Fouche, D. G.

Fricker, H.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Fu, H.

Gardner, A.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Gardner, C. S.

C. S. Gardner, “Ranging performance of satellite laser altimeters,” IEEE Trans. Geosci. Remote Sens. 30(5), 1061–1072 (1992).
[Crossref]

Gatt, P.

Goodman, J. W.

J. W. Goodman, “Speckle phenomena in optics: theory and applications,” J. Stat. Phys. 130(2), 413–414 (2007).
[Crossref]

J. W. Goodman, “Comparative performance of optical-radar detection techniques,” IEEE T. Aero. Elec. Sys. AES-2(5), 526–535 (1966).
[Crossref]

J. W. Goodman, “Some effects of target-induced scintillation on optical radar performance,” Proc. IEEE 53(11), 1688–1700 (1965).
[Crossref]

Gu, G.

L. Ye, G. Gu, W. He, H. Dai, and Q. Chen, “A real-time restraint method for range walk error in 3-D imaging lidar via dual detection,” IEEE Photonics J. 10(2), 1 (2018).
[Crossref]

W. He, B. Sima, Y. Chen, H. Dai, Q. Chen, and G. Gu, “A correction method for range walk error in photon counting 3D imaging LIDAR,” Opt. Commun. 308, 211–217 (2013).
[Crossref]

Harding, D.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

He, W.

L. Ye, G. Gu, W. He, H. Dai, and Q. Chen, “A real-time restraint method for range walk error in 3-D imaging lidar via dual detection,” IEEE Photonics J. 10(2), 1 (2018).
[Crossref]

W. He, B. Sima, Y. Chen, H. Dai, Q. Chen, and G. Gu, “A correction method for range walk error in photon counting 3D imaging LIDAR,” Opt. Commun. 308, 211–217 (2013).
[Crossref]

Henriksson, M.

Hong, K. H.

M. S. Oh, H. J. Kong, T. H. Kim, K. H. Hong, and B. W. Kim, “Reduction of range walk error in direct detection laser radar using a Geiger mode avalanche photodiode,” Opt. Commun. 283(2), 304–308 (2010).
[Crossref]

Jasinski, M.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Johnson, S.

Kavanaugh, J. L.

K. M. Brunt, T. A. Neumann, J. M. Amundson, J. L. Kavanaugh, M. S. Moussavi, K. M. Walsh, W. B. Cook, and T. Markus, “MABEL photon-counting laser altimetry data in Alaska for ICESat-2simulations and development,” Cryosphere 10(4), 1707–1719 (2016).
[Crossref]

Kim, B. W.

M. S. Oh, H. J. Kong, T. H. Kim, K. H. Hong, and B. W. Kim, “Reduction of range walk error in direct detection laser radar using a Geiger mode avalanche photodiode,” Opt. Commun. 283(2), 304–308 (2010).
[Crossref]

Kim, T. H.

M. S. Oh, H. J. Kong, T. H. Kim, K. H. Hong, and B. W. Kim, “Reduction of range walk error in direct detection laser radar using a Geiger mode avalanche photodiode,” Opt. Commun. 283(2), 304–308 (2010).
[Crossref]

Kong, H. J.

M. S. Oh, H. J. Kong, T. H. Kim, K. H. Hong, and B. W. Kim, “Reduction of range walk error in direct detection laser radar using a Geiger mode avalanche photodiode,” Opt. Commun. 283(2), 304–308 (2010).
[Crossref]

Kwok, R.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Lai, J.

Li, P.

Z. Zhang, F. Yang, H. Zhang, Z. Wu, J. Chen, P. Li, and W. Meng, “The use of laser ranging to measure space debris,” Res. Astron. Astrophys. 12(2), 212–218 (2012).
[Crossref]

Li, R.

Li, S.

Li, Y.

Li, Z.

Liu, R.

Lubin, D.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Luthcke, S.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Ma, Y.

Magruder, L.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Markus, T.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

K. M. Brunt, T. A. Neumann, J. M. Amundson, J. L. Kavanaugh, M. S. Moussavi, K. M. Walsh, W. B. Cook, and T. Markus, “MABEL photon-counting laser altimetry data in Alaska for ICESat-2simulations and development,” Cryosphere 10(4), 1707–1719 (2016).
[Crossref]

Martino, A.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Meng, W.

Z. Zhang, F. Yang, H. Zhang, Z. Wu, J. Chen, P. Li, and W. Meng, “The use of laser ranging to measure space debris,” Res. Astron. Astrophys. 12(2), 212–218 (2012).
[Crossref]

Morison, J.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Moussavi, M. S.

K. M. Brunt, T. A. Neumann, J. M. Amundson, J. L. Kavanaugh, M. S. Moussavi, K. M. Walsh, W. B. Cook, and T. Markus, “MABEL photon-counting laser altimetry data in Alaska for ICESat-2simulations and development,” Cryosphere 10(4), 1707–1719 (2016).
[Crossref]

Nelson, R.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Neuenschwander, A.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Neumann, T.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Neumann, T. A.

K. M. Brunt, T. A. Neumann, J. M. Amundson, J. L. Kavanaugh, M. S. Moussavi, K. M. Walsh, W. B. Cook, and T. Markus, “MABEL photon-counting laser altimetry data in Alaska for ICESat-2simulations and development,” Cryosphere 10(4), 1707–1719 (2016).
[Crossref]

Nichols, T.

Oh, M. S.

M. S. Oh, H. J. Kong, T. H. Kim, K. H. Hong, and B. W. Kim, “Reduction of range walk error in direct detection laser radar using a Geiger mode avalanche photodiode,” Opt. Commun. 283(2), 304–308 (2010).
[Crossref]

Palm, S.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Pi, X.

Popescu, S.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Schutz, B. E.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Shum, C. K.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Sima, B.

W. He, B. Sima, Y. Chen, H. Dai, Q. Chen, and G. Gu, “A correction method for range walk error in photon counting 3D imaging LIDAR,” Opt. Commun. 308, 211–217 (2013).
[Crossref]

Smith, B.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Su, X.

Tang, R.

Walsh, K. M.

K. M. Brunt, T. A. Neumann, J. M. Amundson, J. L. Kavanaugh, M. S. Moussavi, K. M. Walsh, W. B. Cook, and T. Markus, “MABEL photon-counting laser altimetry data in Alaska for ICESat-2simulations and development,” Cryosphere 10(4), 1707–1719 (2016).
[Crossref]

Wang, C.

Wang, X. H.

Wu, L.

Wu, Z.

Z. Zhang, F. Yang, H. Zhang, Z. Wu, J. Chen, P. Li, and W. Meng, “The use of laser ranging to measure space debris,” Res. Astron. Astrophys. 12(2), 212–218 (2012).
[Crossref]

Xu, L.

Yan, W.

Yang, C.

Yang, F.

Z. Zhang, F. Yang, H. Zhang, Z. Wu, J. Chen, P. Li, and W. Meng, “The use of laser ranging to measure space debris,” Res. Astron. Astrophys. 12(2), 212–218 (2012).
[Crossref]

Yang, X.

Yang, Y.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Ye, L.

L. Ye, G. Gu, W. He, H. Dai, and Q. Chen, “A real-time restraint method for range walk error in 3-D imaging lidar via dual detection,” IEEE Photonics J. 10(2), 1 (2018).
[Crossref]

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D. G. Youmans, “Avalanche photodiode detection statistics for direct detection laser radar,” Proc. SPIE 1633, 41–52 (1992).
[Crossref]

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Zhang, H.

R. Tang, Z. Li, Y. Li, X. Pi, X. Su, R. Li, H. Zhang, D. Zhai, and H. Fu, “Light curve measurements with a superconducting nanowire single-photon detector,” Opt. Lett. 43(21), 5488–5491 (2018).
[Crossref] [PubMed]

Z. Zhang, F. Yang, H. Zhang, Z. Wu, J. Chen, P. Li, and W. Meng, “The use of laser ranging to measure space debris,” Res. Astron. Astrophys. 12(2), 212–218 (2012).
[Crossref]

Zhang, W.

Zhang, Y.

Zhang, Z.

Zhao, Y.

Zwally, J.

T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Appl. Opt. (5)

Cryosphere (1)

K. M. Brunt, T. A. Neumann, J. M. Amundson, J. L. Kavanaugh, M. S. Moussavi, K. M. Walsh, W. B. Cook, and T. Markus, “MABEL photon-counting laser altimetry data in Alaska for ICESat-2simulations and development,” Cryosphere 10(4), 1707–1719 (2016).
[Crossref]

IEEE Photonics J. (1)

L. Ye, G. Gu, W. He, H. Dai, and Q. Chen, “A real-time restraint method for range walk error in 3-D imaging lidar via dual detection,” IEEE Photonics J. 10(2), 1 (2018).
[Crossref]

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J. W. Goodman, “Speckle phenomena in optics: theory and applications,” J. Stat. Phys. 130(2), 413–414 (2007).
[Crossref]

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M. S. Oh, H. J. Kong, T. H. Kim, K. H. Hong, and B. W. Kim, “Reduction of range walk error in direct detection laser radar using a Geiger mode avalanche photodiode,” Opt. Commun. 283(2), 304–308 (2010).
[Crossref]

W. He, B. Sima, Y. Chen, H. Dai, Q. Chen, and G. Gu, “A correction method for range walk error in photon counting 3D imaging LIDAR,” Opt. Commun. 308, 211–217 (2013).
[Crossref]

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[Crossref]

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D. G. Youmans, “Avalanche photodiode detection statistics for direct detection laser radar,” Proc. SPIE 1633, 41–52 (1992).
[Crossref]

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T. Markus, T. Neumann, A. Martino, W. Abdalati, K. Brunt, B. Csatho, S. Farrell, H. Fricker, A. Gardner, D. Harding, M. Jasinski, R. Kwok, L. Magruder, D. Lubin, S. Luthcke, J. Morison, R. Nelson, A. Neuenschwander, S. Palm, S. Popescu, C. K. Shum, B. E. Schutz, B. Smith, Y. Yang, and J. Zwally, “The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): science requirements, concept, and implementation,” Remote Sens. Environ. 190, 260–273 (2017).
[Crossref]

Res. Astron. Astrophys. (1)

Z. Zhang, F. Yang, H. Zhang, Z. Wu, J. Chen, P. Li, and W. Meng, “The use of laser ranging to measure space debris,” Res. Astron. Astrophys. 12(2), 212–218 (2012).
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A. W. Yu, A. Betin, M. Krainak, D. Hendry, B. Hendry, and C. Sotelo, “Highly efficient Yb:YAG master oscillator power amplifier laser transmitter for lidar applications,” Proc. OSA - Conference on Lasers and Electro-Optics, JTh1I.6 (2012).
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Figures (5)

Fig. 1
Fig. 1 (a) Schematic of the photon-counting lidar; (b) a photograph of the photon-counting lidar; and (c) an infrared photograph of the target and the laser beam. The photon-counting lidar consists of a semiconductor laser, a power supply, transmitting and receiving optics, as well as a GM-APD detector and its TDC. The transmitted laser beam first illuminates the target, a circular paper of 52 mm diameter, then penetrates a glass door, and finally hits a wall.
Fig. 2
Fig. 2 (a) Cumulative histograms of the PEs in eight groups with different average signal photon counts. (b) The measured range walk error Ra_mea in the experiments (using red circles), the curve calculated by the theoretical model (using blue curve), and the bias between Ra_mea and Ra_the (using yellow filled circles).
Fig. 3
Fig. 3 (a) Comparison between the range walk errors simulated by the theoretical model (the dashed red curve) and the recursive method (the solid blue curve), when the speckle diversity is M = 5. (b) Comparison between the ranging precisions simulated by the theoretical model (the dashed red curve) and the recursive method (the solid blue curve), when the speckle diversity is M = 5. (c) Comparison of the range walk errors when the speckle diversity is M = 100. (d) Comparison of the ranging precisions when the speckle diversity is M = 100. The yellow filled circles in all sub figures correspond to the bias between the results simulated by the theoretical model and the recursive method. The RMS pulse width is 0.65 ns, the noise rate is 5 MHz, and the dead-time is 3.2 ns.
Fig. 4
Fig. 4 Theoretical relationship between the detection probability and the average signal photon counts when the average noise count Nn is equal to 1. (a) Detection probability of the NB distribution. The solid, dashed and dashed dotted curves correspond to a speckle diversity of M = 1, 5, and 100, respectively. (b) Detection probabilities of the Poisson distribution and the Bose-Einstein distribution. The solid red curve corresponds to the Poisson distribution and the dashed yellow curve corresponds to the Bose-Einstein distribution.
Fig. 5
Fig. 5 (a) Range walk error comparison between the results simulated by the NB distribution model (the curves show the speckle diversities of 1, 5, and 100) and the Poisson distribution (using dots); (b) the bias between the results simulated by the NB and the Poisson distribution models; (c) ranging precision comparison between the results simulated by the NB distribution model (the curves show the speckle diversities of 1, 5, and 100) and the Poisson distribution (using dots); and (d) the bias between the results simulated by the NB and Poisson distribution models.

Tables (1)

Tables Icon

Table 1 Experimental results including the used optical attenuators, attenuation rates, average signal photons, cumulative numbers (times of repetition), the measured range walk errors Ra_mea, and the theoretical range walk errors Ra_the with eight groups of specific attenuation rates.

Equations (33)

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P( K s )= N s K s K s ! e N s ,
N s = η q hf W= η q hf r t t+ τ r I( x,y;t ) dtdxdy,
P( K s )= 0 P( K s |W )p( W )dW ,
p( W )= ( M W ¯ ) M W M1 e M W W ¯ Γ( M ) ,
P( K s )= Γ( K s +M ) Γ( K s +1 )Γ( M ) ( N s N s +M ) K s ( M N s +M ) M .
NB( K s ; N s ,M )= ( K s +M1 )! K s !( M1 )! p K s ( 1p ) M =( K s +M1 K s ) p K s ( 1p ) M .
P( K )= q=0 K N n Kq ( Kq )! e N n ( q+M1 )! q!( M1 )! ( N s N s +M ) q ( M N s +M ) M
P d ( t,t+τ )= P nd ( t t d ,t )P( t,t+τ;K>0 )= P nd ( t t d ,t )[ 1 e f n τ ( M n s ( t,t+τ )+M ) M ].
n s ( t,t+τ )= t t+τ N s 2π σ s e ( t t s ) 2 2 σ s 2 dt ,
P nd ( t t d ,t )=1P( t t d ,t,K>0 )= e f n t d ( M n s ( t t d ,t )+M ) M .
P d ( t )= e f n t d ( 1 e f n τ );
P d ( t )= e f n t d ( M t t d t N s 2π σ s e ( t t s ) 2 2 σ s 2 dt+M ) M ×[ 1 e f n τ ( M t t+τ N s 2π σ s e ( t t s ) 2 2 σ s 2 dt+M ) M ];
P d ( t )= e f n t d ( M N s +M ) M ( 1 e f n τ ).
t ¯ = t s 3 σ s t s +3 σ s t f s (t)dt t s 3 σ s t s +3 σ s f s (t)dt
Var= t s 3 σ s t s +3 σ s (t t ¯ ) 2 f s (t)dt t s 3 σ s t s +3 σ s f s (t)dt = t s 3 σ s t s +3 σ s t 2 f s (t)dt t s 3 σ s t s +3 σ s f s (t)dt t ¯ 2
f s ( t )= lim τ0 P d ( t ) τ =( N s 2π σ s e ( t t s ) 2 2 σ s 2 + f n )× e f n t d ( M t t d t N s 2π σ s e ( t t s ) 2 2 σ s 2 dt +M ) M
R a = c 2 .( t s 3 σ s t s +3 σ s t[ N s 2π σ s e ( t t s ) 2 2 σ s 2 + η q f n ] e f n t d ( M N s 2 [ 1+erf( t t s 2 σ s ) ]+M ) M dt e f n t d [ 1 e 6 f n σ s ( M N s +M ) M ] t s )
R p = c 2 . t s 3 σ s t s +3 σ s t 2 [ N s 2π σ s e ( t t s ) 2 2 σ s 2 + f n ] e f n t d ( M N s 2 [ 1+erf( t t s 2 σ s ) ]+M ) M dt e f n t d [ 1 e 6 f n σ s ( M N s +M ) M ] 4 R a c 2 2
t t d t N s 2π σ s e ( t t s ) 2 2 σ s 2 dt t N s 2π σ s e ( t t s ) 2 2 σ s 2 dt 1 2 N s [ 1+erf( t t s 2 σ s ) ]
P dr ( t 1 )=1P( t 0 , t 0 +τ;K>0 )=1exp( f n τ ) ( M n s ( t 0 , t 0 +τ )+M ) M ,
P dr ( t 2 )=[ 1 P dr ( t 1 ) ]P( t 1 , t 1 +τ;K>0 )=[ 1 P dr ( t 1 ) ]( 1exp( f n τ ) ( M n s ( t 1 , t 1 +τ )+M ) M ),
P dr ( t i )={ [ 1 j=i( n dn 1 ) i1 P dr ( t j ) ] P( t i1 , t i1 +τ;K>0 ) ( i> n dn ) [ 1 j=1 i1 P dr ( t j ) ]P( t i1 , t i1 +τ;K>0 ) ( i n dn ) .
M= [ 1 A D 2 K D ( Δx,Δy ) | μ A ( Δx,Δy ) | 2 dΔxdΔy ] -1 ,
A D = D( x r , y r )dxdy ,
K D ( Δx,Δy )= D( x r , y r )D( x r Δx, y r Δy ) d x r d y r .
μ A ( Δx,Δy )= I( u,v ) e j 2π λz [ uΔx+vΔy ] dudv I( u,v )dudv ,
μ A ( Δx,Δy )= circ( 2 u 2 + v 2 D target ) e j 2π λz ( uΔx+vΔy ) dαdβ - circ( 2 u 2 + v 2 D target )dαdβ = 2π 0 D target /2 ρ J 0 ( 2π r λz ρ )dρ π D target 2 /4 =2 J 1 ( π D target λz r ) π D target λz r ,
K D ( Δx,Δy )= circ( x r , y r )circ( x r Δx, y r Δy ) dxdy = A r ( 2 π ) [ arccos( r D r ) r D r 1 ( r D r ) 2 ],
M= [ 16 π 0 1 γ( arccosγγ 1 γ 2 )| 2 J 1 ( πβγ ) πβγ |dγ ] -1 ,
I( u,v )= 1 λ 2 z 2 | FT[ E( x t , y t ) D t ( x t , y t ) ] | 2 ,
μ A ( Δx,Δy )= I( u,v ) e j 2π λz [ uΔx+vΔy ] dudv I( u,v )dudv = FT{ FT[ | E( x t , y t ) D t ( x t , y t ) | 2 ] } 2π | E( x t , y t ) D t ( x t , y t ) | 2 d x t d y t = FT{ FT[ E( x t , y t ) D t ( x t , y t ) ] FT * [ E( x t , y t ) D t ( x t , y t ) ] } 2π | E( x t , y t ) D t ( x t , y t ) | 2 d x t d y t = [ E( x t , y t ) D t ( x t , y t ) ][ E * ( x t , y t ) D t * ( x t , y t ) ] 2π | E( x t , y t ) D t ( x t , y t ) | 2 d x t d y t .
μ A ( Δx,Δy )= Σ t E( x t , y t ) E * ( x t Δx, y t Δy )d x t d y t 2π Σ t | E( x t , y t ) | 2 d x t d y t ,
M= [ 2 π A r Σ r [ arccos( ξ )ξ 1 ξ 2 ] | μ A | 2 dΔxdΔy ] -1 ,

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