Abstract

The Cramer–Rao lower bound (CRLB) on range error is calculated for laser detection and ranging (LADAR) systems using Geiger-mode avalanche photodiodes (GMAPDs) to detect reflected laser pulses. For the cases considered, the GMAPD range error CRLB is greater than the CRLB for a photon-counting device. It is also shown that the GMAPD range error CRLB is minimized when the mean energy in the received laser pulse is finite. Given typical LADAR system parameters, a Gaussian-envelope received pulse, and a noise detection rate of less than 4MHz, the GMAPD range error CRLB is minimized when the quantum efficiency times the mean number of received laser pulse photons is between 2.2 and 2.3.

© 2010 Optical Society of America

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    [CrossRef]
  27. D. Youmans, “Avalanche photodiode detection statistics for direct detection laser radar,” Proc. SPIE 1633, 41–52 (1992).
    [CrossRef]
  28. B. Rye and R. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I. Spectral accumulation and the Cramer–Rao lower bound,” IEEE Trans. Geosci. Remote Sens. 31, 16–27 (1993).
    [CrossRef]
  29. E. Jacobsen and P. Kootsookos, “Fast, accurate frequency estimators,” IEEE Signal Process. Mag. 24, 123–125 (2007).
    [CrossRef]
  30. G. Casella and R. Berger, Statistical Inference (Duxbury, 2002).

2009

2008

2007

P. Gatt, S. Johnson, and T. Nichols, “Dead-time effects on Geiger-mode APD performance,” Proc. SPIE 6550, 65500I (2007).
[CrossRef]

E. Jacobsen and P. Kootsookos, “Fast, accurate frequency estimators,” IEEE Signal Process. Mag. 24, 123–125 (2007).
[CrossRef]

C. Gronwall, O. Steinvall, F. Gustafsson, and T. Chevalier, “Influence of laser radar sensor parameters on range-measurement and shape-fitting uncertainties,” Opt. Eng. 46, 106201 (2007).
[CrossRef]

2006

2005

R. Marino and W. Davis, “Jigsaw: A foliage-penetrating 3D imaging laser radar system,” Lincoln Lab. J. 15, 23–36(2005).

M. O’Brien and D. Fouche, “Simulation of 3D laser radar systems,” Lincoln Lab. J. 15, 37–60 (2005).

2004

S. Johnson, T. Nichols, P. Gatt, and T. Klausutis, “Range precision of direct detection laser radar systems,” Proc. SPIE 5412, 72–86 (2004).
[CrossRef]

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

2003

R. Marino, T. Stephens, R. Hatch, J. McLaughlin, J. Mooney, M. O’Brien, G. Rowe, J. Adams, L. Skelly, R. Knowlton, S. Forman, and W. Davis, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: system and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

S. Johnson, P. Gatt, and T. Nichols, “Analysis of Geiger-mode APD laser radars,” Proc. SPIE 5086, 359–368 (2003).
[CrossRef]

D. Fouche, “Detection and false-alarm probabilities for laser radars that use Geiger-mode detectors,” Appl. Opt. 42, 5388–5398 (2003).
[CrossRef] [PubMed]

2002

B. Aull, A. Loomis, D. Young, R. Heinrichs, B. Felton, P. Daniels, and D. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350(2002).

M. Albota, B. Aull, D. Fouche, R. Heinrichs, D. Kocher, R. Marino, J. Mooney, N. Newbury, M. O’Brien, B. Player, B. Willard, and J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–370 (2002).

M. Albota, R. Heinrichs, D. Kocher, D. Fouche, B. Player, M. O’Brien, B. Aull, J. Zayhowski, J. Mooney, B. Willard, and R. Carlson, “Three-dimensional imaging laser radar with a photon-counting avalanche photodiode array and microchip laser,” Appl. Opt. 41, 7671–7678 (2002).
[CrossRef]

K. McIntosh, J. Donnelly, D. Oakley, A. Napoleone, S. Calawa, L. Mahoney, K. Molvar, E. Duerr, S. Groves, and D. Shaver, “InGaAsp/InP avalanche photodiodes for photon counting at 1.06m,” Appl. Phys. Lett. 81, 2505–2507 (2002).
[CrossRef]

2001

P. Gatt and S. Henderson, “Laser radar detection statistics: A comparison of coherent and direct detection intensity receivers,” Proc. SPIE 4377, 251–262 (2001).
[CrossRef]

2000

1993

B. Rye and R. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I. Spectral accumulation and the Cramer–Rao lower bound,” IEEE Trans. Geosci. Remote Sens. 31, 16–27 (1993).
[CrossRef]

1992

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

1972

R. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: Theory,” IEEE Trans. Electron Devices 19, 703–713 (1972).
[CrossRef]

1965

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

Adams, J.

R. Marino, T. Stephens, R. Hatch, J. McLaughlin, J. Mooney, M. O’Brien, G. Rowe, J. Adams, L. Skelly, R. Knowlton, S. Forman, and W. Davis, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: system and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

Albota, M.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

M. Albota, B. Aull, D. Fouche, R. Heinrichs, D. Kocher, R. Marino, J. Mooney, N. Newbury, M. O’Brien, B. Player, B. Willard, and J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–370 (2002).

M. Albota, R. Heinrichs, D. Kocher, D. Fouche, B. Player, M. O’Brien, B. Aull, J. Zayhowski, J. Mooney, B. Willard, and R. Carlson, “Three-dimensional imaging laser radar with a photon-counting avalanche photodiode array and microchip laser,” Appl. Opt. 41, 7671–7678 (2002).
[CrossRef]

Armstrong, E.

Aull, B.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

B. Aull, A. Loomis, D. Young, R. Heinrichs, B. Felton, P. Daniels, and D. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350(2002).

M. Albota, B. Aull, D. Fouche, R. Heinrichs, D. Kocher, R. Marino, J. Mooney, N. Newbury, M. O’Brien, B. Player, B. Willard, and J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–370 (2002).

M. Albota, R. Heinrichs, D. Kocher, D. Fouche, B. Player, M. O’Brien, B. Aull, J. Zayhowski, J. Mooney, B. Willard, and R. Carlson, “Three-dimensional imaging laser radar with a photon-counting avalanche photodiode array and microchip laser,” Appl. Opt. 41, 7671–7678 (2002).
[CrossRef]

Berger, R.

G. Casella and R. Berger, Statistical Inference (Duxbury, 2002).

Cain, S.

Calawa, S.

K. McIntosh, J. Donnelly, D. Oakley, A. Napoleone, S. Calawa, L. Mahoney, K. Molvar, E. Duerr, S. Groves, and D. Shaver, “InGaAsp/InP avalanche photodiodes for photon counting at 1.06m,” Appl. Phys. Lett. 81, 2505–2507 (2002).
[CrossRef]

Carlson, R.

Casella, G.

G. Casella and R. Berger, Statistical Inference (Duxbury, 2002).

Chevalier, T.

C. Gronwall, O. Steinvall, F. Gustafsson, and T. Chevalier, “Influence of laser radar sensor parameters on range-measurement and shape-fitting uncertainties,” Opt. Eng. 46, 106201 (2007).
[CrossRef]

Daniels, P.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

B. Aull, A. Loomis, D. Young, R. Heinrichs, B. Felton, P. Daniels, and D. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350(2002).

Davis, W.

R. Marino and W. Davis, “Jigsaw: A foliage-penetrating 3D imaging laser radar system,” Lincoln Lab. J. 15, 23–36(2005).

R. Marino, T. Stephens, R. Hatch, J. McLaughlin, J. Mooney, M. O’Brien, G. Rowe, J. Adams, L. Skelly, R. Knowlton, S. Forman, and W. Davis, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: system and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

Donnelly, J.

K. McIntosh, J. Donnelly, D. Oakley, A. Napoleone, S. Calawa, L. Mahoney, K. Molvar, E. Duerr, S. Groves, and D. Shaver, “InGaAsp/InP avalanche photodiodes for photon counting at 1.06m,” Appl. Phys. Lett. 81, 2505–2507 (2002).
[CrossRef]

Duerr, E.

K. McIntosh, J. Donnelly, D. Oakley, A. Napoleone, S. Calawa, L. Mahoney, K. Molvar, E. Duerr, S. Groves, and D. Shaver, “InGaAsp/InP avalanche photodiodes for photon counting at 1.06m,” Appl. Phys. Lett. 81, 2505–2507 (2002).
[CrossRef]

Felton, B.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

B. Aull, A. Loomis, D. Young, R. Heinrichs, B. Felton, P. Daniels, and D. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350(2002).

Forman, S.

R. Marino, T. Stephens, R. Hatch, J. McLaughlin, J. Mooney, M. O’Brien, G. Rowe, J. Adams, L. Skelly, R. Knowlton, S. Forman, and W. Davis, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: system and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

Fouche, D.

M. O’Brien and D. Fouche, “Simulation of 3D laser radar systems,” Lincoln Lab. J. 15, 37–60 (2005).

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

D. Fouche, “Detection and false-alarm probabilities for laser radars that use Geiger-mode detectors,” Appl. Opt. 42, 5388–5398 (2003).
[CrossRef] [PubMed]

M. Albota, R. Heinrichs, D. Kocher, D. Fouche, B. Player, M. O’Brien, B. Aull, J. Zayhowski, J. Mooney, B. Willard, and R. Carlson, “Three-dimensional imaging laser radar with a photon-counting avalanche photodiode array and microchip laser,” Appl. Opt. 41, 7671–7678 (2002).
[CrossRef]

M. Albota, B. Aull, D. Fouche, R. Heinrichs, D. Kocher, R. Marino, J. Mooney, N. Newbury, M. O’Brien, B. Player, B. Willard, and J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–370 (2002).

Gatt, P.

P. Gatt, S. Johnson, and T. Nichols, “Geiger-mode avalanche photodiode LADAR receiver performance characteristics and detection statistics,” Appl. Opt. 48, 3261–3276 (2009).
[CrossRef] [PubMed]

P. Gatt, S. Johnson, and T. Nichols, “Dead-time effects on Geiger-mode APD performance,” Proc. SPIE 6550, 65500I (2007).
[CrossRef]

S. Johnson, T. Nichols, P. Gatt, and T. Klausutis, “Range precision of direct detection laser radar systems,” Proc. SPIE 5412, 72–86 (2004).
[CrossRef]

S. Johnson, P. Gatt, and T. Nichols, “Analysis of Geiger-mode APD laser radars,” Proc. SPIE 5086, 359–368 (2003).
[CrossRef]

P. Gatt and S. Henderson, “Laser radar detection statistics: A comparison of coherent and direct detection intensity receivers,” Proc. SPIE 4377, 251–262 (2001).
[CrossRef]

Goodman, J.

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

Gronwall, C.

C. Gronwall, O. Steinvall, F. Gustafsson, and T. Chevalier, “Influence of laser radar sensor parameters on range-measurement and shape-fitting uncertainties,” Opt. Eng. 46, 106201 (2007).
[CrossRef]

Groves, S.

K. McIntosh, J. Donnelly, D. Oakley, A. Napoleone, S. Calawa, L. Mahoney, K. Molvar, E. Duerr, S. Groves, and D. Shaver, “InGaAsp/InP avalanche photodiodes for photon counting at 1.06m,” Appl. Phys. Lett. 81, 2505–2507 (2002).
[CrossRef]

Gustafsson, F.

C. Gronwall, O. Steinvall, F. Gustafsson, and T. Chevalier, “Influence of laser radar sensor parameters on range-measurement and shape-fitting uncertainties,” Opt. Eng. 46, 106201 (2007).
[CrossRef]

Hardesty, R.

B. Rye and R. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I. Spectral accumulation and the Cramer–Rao lower bound,” IEEE Trans. Geosci. Remote Sens. 31, 16–27 (1993).
[CrossRef]

Hatch, R.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

R. Marino, T. Stephens, R. Hatch, J. McLaughlin, J. Mooney, M. O’Brien, G. Rowe, J. Adams, L. Skelly, R. Knowlton, S. Forman, and W. Davis, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: system and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

Heinrichs, R.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

B. Aull, A. Loomis, D. Young, R. Heinrichs, B. Felton, P. Daniels, and D. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350(2002).

M. Albota, B. Aull, D. Fouche, R. Heinrichs, D. Kocher, R. Marino, J. Mooney, N. Newbury, M. O’Brien, B. Player, B. Willard, and J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–370 (2002).

M. Albota, R. Heinrichs, D. Kocher, D. Fouche, B. Player, M. O’Brien, B. Aull, J. Zayhowski, J. Mooney, B. Willard, and R. Carlson, “Three-dimensional imaging laser radar with a photon-counting avalanche photodiode array and microchip laser,” Appl. Opt. 41, 7671–7678 (2002).
[CrossRef]

Henderson, S.

P. Gatt and S. Henderson, “Laser radar detection statistics: A comparison of coherent and direct detection intensity receivers,” Proc. SPIE 4377, 251–262 (2001).
[CrossRef]

Hines, E.

Huntington, A.

G. Williams and A. Huntington, “Probabilistic analysis of linear mode vs. Geiger mode APD FPAs for advanced LADAR enabled interceptors,” Proc. SPIE 6220, 622008 (2006).
[CrossRef]

Jacobsen, E.

E. Jacobsen and P. Kootsookos, “Fast, accurate frequency estimators,” IEEE Signal Process. Mag. 24, 123–125 (2007).
[CrossRef]

Jiang, L.

Johnson, S.

P. Gatt, S. Johnson, and T. Nichols, “Geiger-mode avalanche photodiode LADAR receiver performance characteristics and detection statistics,” Appl. Opt. 48, 3261–3276 (2009).
[CrossRef] [PubMed]

S. Johnson and S. Cain, “Bound on range precision for shot-noise limited LADAR systems,” Appl. Opt. 47, 5147–5154 (2008).
[CrossRef] [PubMed]

P. Gatt, S. Johnson, and T. Nichols, “Dead-time effects on Geiger-mode APD performance,” Proc. SPIE 6550, 65500I (2007).
[CrossRef]

S. Johnson, T. Nichols, P. Gatt, and T. Klausutis, “Range precision of direct detection laser radar systems,” Proc. SPIE 5412, 72–86 (2004).
[CrossRef]

S. Johnson, P. Gatt, and T. Nichols, “Analysis of Geiger-mode APD laser radars,” Proc. SPIE 5086, 359–368 (2003).
[CrossRef]

S. Johnson, “Range precision of ladar systems,” Ph.D. thesis (Air Force Institute of Technology, 2008).

Kay, S.

S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice Hall, 1993).

Klausutis, T.

S. Johnson, T. Nichols, P. Gatt, and T. Klausutis, “Range precision of direct detection laser radar systems,” Proc. SPIE 5412, 72–86 (2004).
[CrossRef]

Knowlton, R.

R. Marino, T. Stephens, R. Hatch, J. McLaughlin, J. Mooney, M. O’Brien, G. Rowe, J. Adams, L. Skelly, R. Knowlton, S. Forman, and W. Davis, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: system and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

Kocher, D.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

M. Albota, R. Heinrichs, D. Kocher, D. Fouche, B. Player, M. O’Brien, B. Aull, J. Zayhowski, J. Mooney, B. Willard, and R. Carlson, “Three-dimensional imaging laser radar with a photon-counting avalanche photodiode array and microchip laser,” Appl. Opt. 41, 7671–7678 (2002).
[CrossRef]

M. Albota, B. Aull, D. Fouche, R. Heinrichs, D. Kocher, R. Marino, J. Mooney, N. Newbury, M. O’Brien, B. Player, B. Willard, and J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–370 (2002).

Kootsookos, P.

E. Jacobsen and P. Kootsookos, “Fast, accurate frequency estimators,” IEEE Signal Process. Mag. 24, 123–125 (2007).
[CrossRef]

Landers, D.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

B. Aull, A. Loomis, D. Young, R. Heinrichs, B. Felton, P. Daniels, and D. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350(2002).

Liau, Z.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

Loomis, A.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

B. Aull, A. Loomis, D. Young, R. Heinrichs, B. Felton, P. Daniels, and D. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350(2002).

Luu, J.

Mahoney, L.

K. McIntosh, J. Donnelly, D. Oakley, A. Napoleone, S. Calawa, L. Mahoney, K. Molvar, E. Duerr, S. Groves, and D. Shaver, “InGaAsp/InP avalanche photodiodes for photon counting at 1.06m,” Appl. Phys. Lett. 81, 2505–2507 (2002).
[CrossRef]

Marino, R.

R. Marino and W. Davis, “Jigsaw: A foliage-penetrating 3D imaging laser radar system,” Lincoln Lab. J. 15, 23–36(2005).

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

R. Marino, T. Stephens, R. Hatch, J. McLaughlin, J. Mooney, M. O’Brien, G. Rowe, J. Adams, L. Skelly, R. Knowlton, S. Forman, and W. Davis, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: system and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

M. Albota, B. Aull, D. Fouche, R. Heinrichs, D. Kocher, R. Marino, J. Mooney, N. Newbury, M. O’Brien, B. Player, B. Willard, and J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–370 (2002).

McIntosh, K.

K. McIntosh, J. Donnelly, D. Oakley, A. Napoleone, S. Calawa, L. Mahoney, K. Molvar, E. Duerr, S. Groves, and D. Shaver, “InGaAsp/InP avalanche photodiodes for photon counting at 1.06m,” Appl. Phys. Lett. 81, 2505–2507 (2002).
[CrossRef]

McIntyre, R.

R. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: Theory,” IEEE Trans. Electron Devices 19, 703–713 (1972).
[CrossRef]

McLaughlin, J.

R. Marino, T. Stephens, R. Hatch, J. McLaughlin, J. Mooney, M. O’Brien, G. Rowe, J. Adams, L. Skelly, R. Knowlton, S. Forman, and W. Davis, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: system and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

Milstein, A.

Molvar, K.

K. McIntosh, J. Donnelly, D. Oakley, A. Napoleone, S. Calawa, L. Mahoney, K. Molvar, E. Duerr, S. Groves, and D. Shaver, “InGaAsp/InP avalanche photodiodes for photon counting at 1.06m,” Appl. Phys. Lett. 81, 2505–2507 (2002).
[CrossRef]

Mooney, J.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

R. Marino, T. Stephens, R. Hatch, J. McLaughlin, J. Mooney, M. O’Brien, G. Rowe, J. Adams, L. Skelly, R. Knowlton, S. Forman, and W. Davis, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: system and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

M. Albota, R. Heinrichs, D. Kocher, D. Fouche, B. Player, M. O’Brien, B. Aull, J. Zayhowski, J. Mooney, B. Willard, and R. Carlson, “Three-dimensional imaging laser radar with a photon-counting avalanche photodiode array and microchip laser,” Appl. Opt. 41, 7671–7678 (2002).
[CrossRef]

M. Albota, B. Aull, D. Fouche, R. Heinrichs, D. Kocher, R. Marino, J. Mooney, N. Newbury, M. O’Brien, B. Player, B. Willard, and J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–370 (2002).

Napoleone, A.

K. McIntosh, J. Donnelly, D. Oakley, A. Napoleone, S. Calawa, L. Mahoney, K. Molvar, E. Duerr, S. Groves, and D. Shaver, “InGaAsp/InP avalanche photodiodes for photon counting at 1.06m,” Appl. Phys. Lett. 81, 2505–2507 (2002).
[CrossRef]

Newbury, N.

M. Albota, B. Aull, D. Fouche, R. Heinrichs, D. Kocher, R. Marino, J. Mooney, N. Newbury, M. O’Brien, B. Player, B. Willard, and J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–370 (2002).

Nichols, T.

P. Gatt, S. Johnson, and T. Nichols, “Geiger-mode avalanche photodiode LADAR receiver performance characteristics and detection statistics,” Appl. Opt. 48, 3261–3276 (2009).
[CrossRef] [PubMed]

P. Gatt, S. Johnson, and T. Nichols, “Dead-time effects on Geiger-mode APD performance,” Proc. SPIE 6550, 65500I (2007).
[CrossRef]

S. Johnson, T. Nichols, P. Gatt, and T. Klausutis, “Range precision of direct detection laser radar systems,” Proc. SPIE 5412, 72–86 (2004).
[CrossRef]

S. Johnson, P. Gatt, and T. Nichols, “Analysis of Geiger-mode APD laser radars,” Proc. SPIE 5086, 359–368 (2003).
[CrossRef]

O’Brien, M.

M. O’Brien and D. Fouche, “Simulation of 3D laser radar systems,” Lincoln Lab. J. 15, 37–60 (2005).

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

R. Marino, T. Stephens, R. Hatch, J. McLaughlin, J. Mooney, M. O’Brien, G. Rowe, J. Adams, L. Skelly, R. Knowlton, S. Forman, and W. Davis, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: system and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

M. Albota, R. Heinrichs, D. Kocher, D. Fouche, B. Player, M. O’Brien, B. Aull, J. Zayhowski, J. Mooney, B. Willard, and R. Carlson, “Three-dimensional imaging laser radar with a photon-counting avalanche photodiode array and microchip laser,” Appl. Opt. 41, 7671–7678 (2002).
[CrossRef]

M. Albota, B. Aull, D. Fouche, R. Heinrichs, D. Kocher, R. Marino, J. Mooney, N. Newbury, M. O’Brien, B. Player, B. Willard, and J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–370 (2002).

Oakley, D.

K. McIntosh, J. Donnelly, D. Oakley, A. Napoleone, S. Calawa, L. Mahoney, K. Molvar, E. Duerr, S. Groves, and D. Shaver, “InGaAsp/InP avalanche photodiodes for photon counting at 1.06m,” Appl. Phys. Lett. 81, 2505–2507 (2002).
[CrossRef]

Player, B.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

M. Albota, B. Aull, D. Fouche, R. Heinrichs, D. Kocher, R. Marino, J. Mooney, N. Newbury, M. O’Brien, B. Player, B. Willard, and J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–370 (2002).

M. Albota, R. Heinrichs, D. Kocher, D. Fouche, B. Player, M. O’Brien, B. Aull, J. Zayhowski, J. Mooney, B. Willard, and R. Carlson, “Three-dimensional imaging laser radar with a photon-counting avalanche photodiode array and microchip laser,” Appl. Opt. 41, 7671–7678 (2002).
[CrossRef]

Rathman, D.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

Retherford, L.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

Richmond, R.

Rowe, G.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

R. Marino, T. Stephens, R. Hatch, J. McLaughlin, J. Mooney, M. O’Brien, G. Rowe, J. Adams, L. Skelly, R. Knowlton, S. Forman, and W. Davis, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: system and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

Rye, B.

B. Rye and R. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I. Spectral accumulation and the Cramer–Rao lower bound,” IEEE Trans. Geosci. Remote Sens. 31, 16–27 (1993).
[CrossRef]

Schultz, K.

Seal, M.

M. Seal, “Nonlinear time-variant response in an avalanche photodiode array based laser detection and ranging system,” Master’s thesis (Air Force Institute of Technology, 2007).

Shaver, D.

K. McIntosh, J. Donnelly, D. Oakley, A. Napoleone, S. Calawa, L. Mahoney, K. Molvar, E. Duerr, S. Groves, and D. Shaver, “InGaAsp/InP avalanche photodiodes for photon counting at 1.06m,” Appl. Phys. Lett. 81, 2505–2507 (2002).
[CrossRef]

Skelly, L.

R. Marino, T. Stephens, R. Hatch, J. McLaughlin, J. Mooney, M. O’Brien, G. Rowe, J. Adams, L. Skelly, R. Knowlton, S. Forman, and W. Davis, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: system and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

Steinvall, O.

C. Gronwall, O. Steinvall, F. Gustafsson, and T. Chevalier, “Influence of laser radar sensor parameters on range-measurement and shape-fitting uncertainties,” Opt. Eng. 46, 106201 (2007).
[CrossRef]

O. Steinvall, “Effects of target shape and reflection on laser radar cross sections,” Appl. Opt. 39, 4381–4391 (2000).
[CrossRef]

Stephens, T.

R. Marino, T. Stephens, R. Hatch, J. McLaughlin, J. Mooney, M. O’Brien, G. Rowe, J. Adams, L. Skelly, R. Knowlton, S. Forman, and W. Davis, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: system and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

Stern, A.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

Willard, B.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

M. Albota, R. Heinrichs, D. Kocher, D. Fouche, B. Player, M. O’Brien, B. Aull, J. Zayhowski, J. Mooney, B. Willard, and R. Carlson, “Three-dimensional imaging laser radar with a photon-counting avalanche photodiode array and microchip laser,” Appl. Opt. 41, 7671–7678 (2002).
[CrossRef]

M. Albota, B. Aull, D. Fouche, R. Heinrichs, D. Kocher, R. Marino, J. Mooney, N. Newbury, M. O’Brien, B. Player, B. Willard, and J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–370 (2002).

Williams, G.

G. Williams and A. Huntington, “Probabilistic analysis of linear mode vs. Geiger mode APD FPAs for advanced LADAR enabled interceptors,” Proc. SPIE 6220, 622008 (2006).
[CrossRef]

Youmans, D.

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

Young, D.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

B. Aull, A. Loomis, D. Young, R. Heinrichs, B. Felton, P. Daniels, and D. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350(2002).

Zayhowski, J.

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

M. Albota, B. Aull, D. Fouche, R. Heinrichs, D. Kocher, R. Marino, J. Mooney, N. Newbury, M. O’Brien, B. Player, B. Willard, and J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–370 (2002).

M. Albota, R. Heinrichs, D. Kocher, D. Fouche, B. Player, M. O’Brien, B. Aull, J. Zayhowski, J. Mooney, B. Willard, and R. Carlson, “Three-dimensional imaging laser radar with a photon-counting avalanche photodiode array and microchip laser,” Appl. Opt. 41, 7671–7678 (2002).
[CrossRef]

Appl. Opt.

D. Fouche, “Detection and false-alarm probabilities for laser radars that use Geiger-mode detectors,” Appl. Opt. 42, 5388–5398 (2003).
[CrossRef] [PubMed]

J. Luu and L. Jiang, “Saturation effects in heterodyne detection with Geiger-mode InGaAs avalanche photodiode detector arrays,” Appl. Opt. 45, 3798–3804 (2006).
[CrossRef] [PubMed]

A. Milstein, L. Jiang, J. Luu, E. Hines, and K. Schultz, “Acquisition algorithm for direct-detection LADARs with Geiger-mode avalanche photodiodes,” Appl. Opt. 47, 296–311 (2008).
[CrossRef] [PubMed]

M. Albota, R. Heinrichs, D. Kocher, D. Fouche, B. Player, M. O’Brien, B. Aull, J. Zayhowski, J. Mooney, B. Willard, and R. Carlson, “Three-dimensional imaging laser radar with a photon-counting avalanche photodiode array and microchip laser,” Appl. Opt. 41, 7671–7678 (2002).
[CrossRef]

P. Gatt, S. Johnson, and T. Nichols, “Geiger-mode avalanche photodiode LADAR receiver performance characteristics and detection statistics,” Appl. Opt. 48, 3261–3276 (2009).
[CrossRef] [PubMed]

O. Steinvall, “Effects of target shape and reflection on laser radar cross sections,” Appl. Opt. 39, 4381–4391 (2000).
[CrossRef]

S. Cain, R. Richmond, and E. Armstrong, “Flash light detection and ranging accuracy limits for returns from single opaque surfaces via Cramer–Rao bounds,” Appl. Opt. 45, 6154–6162 (2006).
[CrossRef] [PubMed]

S. Johnson and S. Cain, “Bound on range precision for shot-noise limited LADAR systems,” Appl. Opt. 47, 5147–5154 (2008).
[CrossRef] [PubMed]

Appl. Phys. Lett.

K. McIntosh, J. Donnelly, D. Oakley, A. Napoleone, S. Calawa, L. Mahoney, K. Molvar, E. Duerr, S. Groves, and D. Shaver, “InGaAsp/InP avalanche photodiodes for photon counting at 1.06m,” Appl. Phys. Lett. 81, 2505–2507 (2002).
[CrossRef]

IEEE Signal Process. Mag.

E. Jacobsen and P. Kootsookos, “Fast, accurate frequency estimators,” IEEE Signal Process. Mag. 24, 123–125 (2007).
[CrossRef]

IEEE Trans. Electron Devices

R. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: Theory,” IEEE Trans. Electron Devices 19, 703–713 (1972).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

B. Rye and R. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I. Spectral accumulation and the Cramer–Rao lower bound,” IEEE Trans. Geosci. Remote Sens. 31, 16–27 (1993).
[CrossRef]

Lincoln Lab. J.

M. O’Brien and D. Fouche, “Simulation of 3D laser radar systems,” Lincoln Lab. J. 15, 37–60 (2005).

R. Marino and W. Davis, “Jigsaw: A foliage-penetrating 3D imaging laser radar system,” Lincoln Lab. J. 15, 23–36(2005).

M. Albota, B. Aull, D. Fouche, R. Heinrichs, D. Kocher, R. Marino, J. Mooney, N. Newbury, M. O’Brien, B. Player, B. Willard, and J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–370 (2002).

B. Aull, A. Loomis, D. Young, R. Heinrichs, B. Felton, P. Daniels, and D. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350(2002).

Opt. Eng.

C. Gronwall, O. Steinvall, F. Gustafsson, and T. Chevalier, “Influence of laser radar sensor parameters on range-measurement and shape-fitting uncertainties,” Opt. Eng. 46, 106201 (2007).
[CrossRef]

Proc. IEEE

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

Proc. SPIE

P. Gatt and S. Henderson, “Laser radar detection statistics: A comparison of coherent and direct detection intensity receivers,” Proc. SPIE 4377, 251–262 (2001).
[CrossRef]

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

G. Williams and A. Huntington, “Probabilistic analysis of linear mode vs. Geiger mode APD FPAs for advanced LADAR enabled interceptors,” Proc. SPIE 6220, 622008 (2006).
[CrossRef]

P. Gatt, S. Johnson, and T. Nichols, “Dead-time effects on Geiger-mode APD performance,” Proc. SPIE 6550, 65500I (2007).
[CrossRef]

S. Johnson, T. Nichols, P. Gatt, and T. Klausutis, “Range precision of direct detection laser radar systems,” Proc. SPIE 5412, 72–86 (2004).
[CrossRef]

B. Aull, A. Loomis, D. Young, A. Stern, B. Felton, P. Daniels, D. Landers, L. Retherford, D. Rathman, R. Heinrichs, R. Marino, D. Fouche, M. Albota, R. Hatch, G. Rowe, D. Kocher, J. Mooney, M. O’Brien, B. Player, B. Willard, Z. Liau, and J. Zayhowski, “Three-dimensional imaging with arrays of Geiger-mode avalanche photodiodes,” Proc. SPIE 5353, 105–116 (2004).
[CrossRef]

S. Johnson, P. Gatt, and T. Nichols, “Analysis of Geiger-mode APD laser radars,” Proc. SPIE 5086, 359–368 (2003).
[CrossRef]

R. Marino, T. Stephens, R. Hatch, J. McLaughlin, J. Mooney, M. O’Brien, G. Rowe, J. Adams, L. Skelly, R. Knowlton, S. Forman, and W. Davis, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: system and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

Other

M. Seal, “Nonlinear time-variant response in an avalanche photodiode array based laser detection and ranging system,” Master’s thesis (Air Force Institute of Technology, 2007).

S. Johnson, “Range precision of ladar systems,” Ph.D. thesis (Air Force Institute of Technology, 2008).

G. Casella and R. Berger, Statistical Inference (Duxbury, 2002).

S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice Hall, 1993).

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Figures (9)

Fig. 1
Fig. 1

Detected photon flux functions as the mean number of detected laser pulse photons varies.

Fig. 2
Fig. 2

GMAPD signal distributions in nanoseconds. The distribution’s peak moves away from the target position as the mean number of laser pulse photons increases.

Fig. 3
Fig. 3

Range error Cramer–Rao lower bounds for GMAPDs and for photon-counting devices. The PC curves are nearly identical for background photon detection rates of 0.1 and 5 MHz .

Fig. 4
Fig. 4

GMAPD range error CRLB as pulse duration varies. The standard deviation is nearly, but not exactly, proportional to the pulse’s FWHM.

Fig. 5
Fig. 5

Range error CRLB as target position varies. The GMAPD CRLB depends on the position of the target in the acquisition window.

Fig. 6
Fig. 6

Mean number of detected laser pulse photons to minimize the GMAPD range error CRLB.

Fig. 7
Fig. 7

Simulation of range measurement using GMAPDs and photon-counting devices. Range measurement standard deviation and root mean squared error are shown.

Fig. 8
Fig. 8

Effect of pulse accumulation on range measurement with GMAPDs. The standard deviation and the RMSE differ because of measurement bias.

Fig. 9
Fig. 9

Effect of pulse accumulation on range measurement with photon-counting devices. The standard deviation and the RMSE are equal because the measurement is unbiased.

Equations (43)

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Ψ p ( t ) = A p exp [ 1 2 σ 2 ( t d ) 2 ] + B p ,
Ψ ( t ) = η Ψ p ( t ) = A exp [ 1 2 σ 2 ( t d ) 2 ] + B ,
A = η A p
B = η B p
N = A σ 2 π .
m ( t ) = 0 t Ψ ( u ) d u ,
m ( t ) = B t + N 2 [ erf ( t d 2 σ ) + erf ( d 2 σ ) ] ,
c T ( t ) = 1 exp [ m ( t ) ] .
p T ( t ) = t c T ( t ) = Ψ ( t ) exp [ m ( t ) ] .
p T ( t ) = { A exp [ 1 2 σ 2 ( t d ) 2 ] + B } × exp { B t N 2 [ erf ( t d 2 σ ) + erf ( d 2 σ ) ] } .
l 1 ( d , A , B ; t ) = ln [ Ψ ( d , A , B ; t ) ] m ( d , A , B ; t ) ,
p K ( k ) = m = 1 M p K m ( k m ) = m = 1 M 1 k m ! I m k m exp ( I m ) ,
I m = ( m 1 ) / f s m / f s Ψ ( t ) d t = A ( m 1 ) / f s m / f s exp [ 1 2 σ 2 ( t d ) 2 ] d t + B f s .
I m A f s exp [ 1 2 σ 2 ( t m d ) 2 ] + B f s ,
t m = m 1 / 2 f s
l 2 ( d , A , B ; K ) = log [ p K ( k ) ] = m = 1 M [ log ( k m ! ) + k m log ( I m ) I m ] .
J 1 = [ E [ 2 l 1 ( d , A , B ) d 2 ] E [ 2 l 1 ( d , A , B ) d A ] E [ 2 l 1 ( d , A , B ) d B ] E [ 2 l 1 ( d , A , B ) d A ] E [ 2 l 1 ( d , A , B ) A 2 ] E [ 2 l 1 ( d , A , B ) A B ] E [ 2 l 1 ( d , A , B ) d B ] E [ 2 l 1 ( d , A , B ) A B ] E [ 2 l 1 ( d , A , B ) B 2 ] ] ,
2 l 1 ( d , A , B ; t ) d 2 = 1 σ 2 Ψ ( t ) B Ψ ( t ) [ 1 B Ψ ( t ) ( t d σ ) 2 ] + A σ 2 { d exp ( 1 2 σ 2 d 2 ) + ( t d ) exp [ 1 2 σ 2 ( t d ) 2 ] } .
2 l 1 ( d , A , B ; t ) A 2 = 1 Ψ 2 ( t ) exp [ 1 σ 2 ( t d ) 2 ]
2 l 1 ( d , A , B ; t ) B 2 = 1 Ψ 2 ( t ) .
2 l 1 ( d , A , B ; t ) d A = [ 1 + B Ψ 2 ( t ) t d σ 2 ] exp [ 1 2 σ 2 ( t d ) 2 ] exp ( 1 2 σ 2 d 2 ) ,
2 l 1 ( d , A , B ; t ) d B = A Ψ 2 ( t ) t d σ 2 exp [ 1 2 σ 2 ( t d ) 2 ] ,
2 l 1 ( d , A , B ; t ) A B = 1 Ψ 2 ( t ) exp [ 1 2 σ 2 ( t d ) 2 ] .
E [ 2 l 1 ( d , A , B ; t ) d 2 ] = p T ( t ) 2 l 1 ( d , A , B ; t ) d 2 d t = 0 Ψ ( t ) exp [ m ( t ) ] 2 l 1 ( d , A , B ; t ) d 2 d t .
var [ d ^ ] [ J 1 1 ] 11 .
r = c 2 d ,
var [ r ^ ] c 2 4 [ J 1 1 ] 11 .
J 2 = [ E [ 2 l 2 ( d , A , B ) d 2 ] E [ 2 l 2 ( d , A , B ) d A ] E [ 2 l 2 ( d , A , B ) d B ] E [ 2 l 2 ( d , A , B ) d A ] E [ 2 l 2 ( d , A , B ) A 2 ] E [ 2 l 2 ( d , A , B ) A B ] E [ 2 l 2 ( d , A , B ) d B ] E [ 2 l 2 ( d , A , B ) A B ] E [ 2 l 2 ( d , A , B ) B 2 ] ] .
l 2 ( d , A , B ; K ) d = m = 1 M ( k m I m 1 ) I m d
2 l 2 ( d , A , B ; K ) d 2 = m = 1 M [ ( k m I m 1 ) 2 I m d 2 k m I m 2 ( I m d ) 2 ] .
E [ 2 l 2 ( d , A , B ; K ) d 2 ] = m = 1 M 1 I m ( I m d ) 2 .
I m d = A f s t m d σ 2 exp [ 1 2 σ 2 ( t m d ) 2 ] .
E [ 2 l 2 ( d , A , B ; K ) d 2 ] = m = 1 M { A f s exp [ 1 2 σ 2 ( t m d ) 2 ] + B f s } 1 { A f s t m d σ 2 exp [ 1 2 σ 2 ( t m d ) 2 ] } 2 .
E [ 2 l 2 ( d , A , B ; K ) d 2 ] A 2 σ u 2 exp ( u 2 ) A exp ( 1 2 u 2 ) + B d u ,
u = t m d σ .
E [ 2 l 2 ( d , A , B ) d A ] = 0 ,
E [ 2 l 2 ( d , A , B ) d B ] = 0 .
[ J 2 1 ] 11 = 1 [ J 2 ] 11 = 1 E [ 2 l 2 ( d , A , B ; K ) d 2 ] .
var [ d ^ ] σ A 2 [ u 2 exp ( u 2 ) A exp ( 1 2 u 2 ) + B d u ] 1 .
var [ r ^ ] c 2 σ 4 A 2 [ u 2 exp ( u 2 ) A exp ( 1 2 u 2 ) + B d u ] 1 .
lim B 0 A 2 σ u 2 exp ( u 2 ) A exp ( 1 2 u 2 ) + B d u = N σ 2 .
lim B 0 var [ d ^ ] σ 2 N ,
c T ( t ) = 1 exp { B t N 2 [ erf ( t d 2 σ ) + erf ( d 2 σ ) ] } .

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