Abstract

Light detection and ranging (lidar) systems use binary hypothesis tests to detect the presence of a target in a range interval. For systems that count photon detections, hypothesis test thresholds are normally set so that a target detection is declared if the number of detections exceeds a particular number. When this method is employed, the false alarm probability can not be selected arbitrarily. In this paper, a hypothesis test that uses randomized thresholds is described. This randomized method of thresholding allows lidar operation at any false alarm probability. When there is a maximum allowable false alarm probability, the hypothesis test that uses randomized thresholds generally produces higher target detection probabilities than the conventional (nonrandom) hypothesis test.

© 2012 Optical Society of America

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References

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  1. G. Flint, “Analysis and optimization of laser ranging techniques,” IEEE Trans. Mil. Electron. 8, 22–28 (1964).
    [CrossRef]
  2. J. Goodman, “Some effects of target-induced scintillation on optical radar performance,” Proc. IEEE 53, 1688–1700 (1965).
    [CrossRef]
  3. 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]
  4. G. Osche, Optical Detection Theory (Wiley-Interscience, 2002).
  5. 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]
  6. R. Richmond and S. Cain, Direct-Detection LADAR Systems (SPIE Optical Engineering Press, 2010).
  7. H. Poor, An Introduction to Signal Detection and Estimation (Springer, 1994).
  8. L. Scharf, Statistical Signal Processing (Addison-Wesley, 1991).
  9. J. Goodman, Statistical Optics (Wiley-Interscience, 1985).
  10. 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]
  11. 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]
  12. S. Johnson and S. Cain, “Bound on range precision for shot-noise limited ladar systems,” Appl. Opt. 47, 5147–5154 (2008).
    [CrossRef]
  13. S. Johnson, “Cramer-Rao lower bound on range error for LADARs with Geiger-mode avalanche photodiodes,” Appl. Opt. 49, 4581–4590 (2010).
    [CrossRef]
  14. M. Oh, H. Kong, and T. Kim, “Systematic experiments for proof of Poisson statistics on direct-detection laser radar using Geiger mode avalanche photodiode,” Curr. Appl. Phys. 10, 1041–1045 (2010).
    [CrossRef]
  15. S. Johnson, “Range precision of ladar systems,” Ph.D. thesis, Air Force Institute of Technology (2008).
  16. R. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: theory,” IEEE Trans. Electron Devices 19, 703–713 (1972).
    [CrossRef]
  17. D. Youmans, “Avalanche photodiode detection statistics for direct detection laser radar,” Proc. SPIE 1633, 41–52 (1992).
    [CrossRef]
  18. 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]
  19. D. Youmans and G. Hart, “Numerical evaluation of the M parameter for direct detection ladar,” Proc. SPIE 3380, 176–187 (1998).
    [CrossRef]
  20. D. Youmans, “Receiver-operating characteristic for several multiple hypothesis range-rate filter algorithms,” Proc. SPIE 7684, 768412 (2010).
    [CrossRef]
  21. M. O’Brien and D. Fouche, “Simulation of 3d laser radar systems,” Lincoln Lab. J. 15, 37–60 (2005).
  22. R. Younger, K. McIntosh, J. Chludzinski, D. Oakley, L. Mahoney, J. Funk, J. Donnelly, and S. Verghese, “Crosstalk analysis of integrated Geiger-mode avalanche photodiode focal plane arrays,” Proc. SPIE 7320, 73200Q (2009).
    [CrossRef]
  23. G. Osche, “Single- and multiple-pulse noncoherent detection statistics associated with partially developed speckle,” Appl. Opt. 39, 4255–4262 (2000).
    [CrossRef]
  24. H. Dautet, P. Deschamps, B. Dion, A. MacGregor, D. MacSween, R. McIntyre, C. Trottier, and P. Webb, “Photon counting techniques with silicon avalanche photodiodes,” Appl. Opt. 32, 3894–3900 (1993).
    [CrossRef]
  25. P. Owens, J. Rarity, P. Tapster, D. Knight, and P. Townsend, “Photon counting with passively quenched germanium avalanche,” Appl. Opt. 33, 6895–6901 (1994).
    [CrossRef]
  26. S. Johnson, P. Gatt, and T. Nichols, “Analysis of Geiger-mode APD laser radars,” Proc. SPIE 5086, 359–368 (2003).
    [CrossRef]
  27. M. Henriksson, “Detection probabilities for photon-counting avalanche photodiodes applied to a laser radar system,” Appl. Opt. 44, 5140–5147 (2005).
    [CrossRef]
  28. P. Gatt, S. Johnson, and T. Nichols, “Dead-time effects on Geiger-mode APD performance,” Proc. SPIE 6550, 65500I (2007).
    [CrossRef]
  29. P. Gatt, T. Nichols, and S. Johnson, “Finite dead-time Geiger-mode APD performance,” in 14th Coherent Laser Radar Conference (2007).
  30. D. Fouche, “Detection and false-alarm probabilities for laser radars that use Geiger-mode detectors,” Appl. Opt. 42, 5388–5398 (2003).
    [CrossRef]

2010 (3)

M. Oh, H. Kong, and T. Kim, “Systematic experiments for proof of Poisson statistics on direct-detection laser radar using Geiger mode avalanche photodiode,” Curr. Appl. Phys. 10, 1041–1045 (2010).
[CrossRef]

D. Youmans, “Receiver-operating characteristic for several multiple hypothesis range-rate filter algorithms,” Proc. SPIE 7684, 768412 (2010).
[CrossRef]

S. Johnson, “Cramer-Rao lower bound on range error for LADARs with Geiger-mode avalanche photodiodes,” Appl. Opt. 49, 4581–4590 (2010).
[CrossRef]

2009 (2)

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]

R. Younger, K. McIntosh, J. Chludzinski, D. Oakley, L. Mahoney, J. Funk, J. Donnelly, and S. Verghese, “Crosstalk analysis of integrated Geiger-mode avalanche photodiode focal plane arrays,” Proc. SPIE 7320, 73200Q (2009).
[CrossRef]

2008 (1)

2007 (1)

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

2006 (2)

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]

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]

2005 (2)

M. Henriksson, “Detection probabilities for photon-counting avalanche photodiodes applied to a laser radar system,” Appl. Opt. 44, 5140–5147 (2005).
[CrossRef]

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

2003 (2)

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]

2001 (1)

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 (1)

1998 (1)

D. Youmans and G. Hart, “Numerical evaluation of the M parameter for direct detection ladar,” Proc. SPIE 3380, 176–187 (1998).
[CrossRef]

1994 (1)

1993 (2)

H. Dautet, P. Deschamps, B. Dion, A. MacGregor, D. MacSween, R. McIntyre, C. Trottier, and P. Webb, “Photon counting techniques with silicon avalanche photodiodes,” Appl. Opt. 32, 3894–3900 (1993).
[CrossRef]

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 (1)

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

1972 (1)

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

1965 (1)

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

1964 (1)

G. Flint, “Analysis and optimization of laser ranging techniques,” IEEE Trans. Mil. Electron. 8, 22–28 (1964).
[CrossRef]

Armstrong, E.

Cain, S.

Chludzinski, J.

R. Younger, K. McIntosh, J. Chludzinski, D. Oakley, L. Mahoney, J. Funk, J. Donnelly, and S. Verghese, “Crosstalk analysis of integrated Geiger-mode avalanche photodiode focal plane arrays,” Proc. SPIE 7320, 73200Q (2009).
[CrossRef]

Dautet, H.

Deschamps, P.

Dion, B.

Donnelly, J.

R. Younger, K. McIntosh, J. Chludzinski, D. Oakley, L. Mahoney, J. Funk, J. Donnelly, and S. Verghese, “Crosstalk analysis of integrated Geiger-mode avalanche photodiode focal plane arrays,” Proc. SPIE 7320, 73200Q (2009).
[CrossRef]

Flint, G.

G. Flint, “Analysis and optimization of laser ranging techniques,” IEEE Trans. Mil. Electron. 8, 22–28 (1964).
[CrossRef]

Fouche, D.

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

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

Funk, J.

R. Younger, K. McIntosh, J. Chludzinski, D. Oakley, L. Mahoney, J. Funk, J. Donnelly, and S. Verghese, “Crosstalk analysis of integrated Geiger-mode avalanche photodiode focal plane arrays,” Proc. SPIE 7320, 73200Q (2009).
[CrossRef]

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]

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

P. Gatt, T. Nichols, and S. Johnson, “Finite dead-time Geiger-mode APD performance,” in 14th Coherent Laser Radar Conference (2007).

Goodman, J.

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

J. Goodman, Statistical Optics (Wiley-Interscience, 1985).

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]

Hart, G.

D. Youmans and G. Hart, “Numerical evaluation of the M parameter for direct detection ladar,” Proc. SPIE 3380, 176–187 (1998).
[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]

Henriksson, M.

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]

Johnson, S.

S. Johnson, “Cramer-Rao lower bound on range error for LADARs with Geiger-mode avalanche photodiodes,” Appl. Opt. 49, 4581–4590 (2010).
[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]

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

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

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

P. Gatt, T. Nichols, and S. Johnson, “Finite dead-time Geiger-mode APD performance,” in 14th Coherent Laser Radar Conference (2007).

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

Kim, T.

M. Oh, H. Kong, and T. Kim, “Systematic experiments for proof of Poisson statistics on direct-detection laser radar using Geiger mode avalanche photodiode,” Curr. Appl. Phys. 10, 1041–1045 (2010).
[CrossRef]

Knight, D.

Kong, H.

M. Oh, H. Kong, and T. Kim, “Systematic experiments for proof of Poisson statistics on direct-detection laser radar using Geiger mode avalanche photodiode,” Curr. Appl. Phys. 10, 1041–1045 (2010).
[CrossRef]

MacGregor, A.

MacSween, D.

Mahoney, L.

R. Younger, K. McIntosh, J. Chludzinski, D. Oakley, L. Mahoney, J. Funk, J. Donnelly, and S. Verghese, “Crosstalk analysis of integrated Geiger-mode avalanche photodiode focal plane arrays,” Proc. SPIE 7320, 73200Q (2009).
[CrossRef]

McIntosh, K.

R. Younger, K. McIntosh, J. Chludzinski, D. Oakley, L. Mahoney, J. Funk, J. Donnelly, and S. Verghese, “Crosstalk analysis of integrated Geiger-mode avalanche photodiode focal plane arrays,” Proc. SPIE 7320, 73200Q (2009).
[CrossRef]

McIntyre, R.

H. Dautet, P. Deschamps, B. Dion, A. MacGregor, D. MacSween, R. McIntyre, C. Trottier, and P. Webb, “Photon counting techniques with silicon avalanche photodiodes,” Appl. Opt. 32, 3894–3900 (1993).
[CrossRef]

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

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]

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

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

P. Gatt, T. Nichols, and S. Johnson, “Finite dead-time Geiger-mode APD performance,” in 14th Coherent Laser Radar Conference (2007).

O’Brien, M.

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

Oakley, D.

R. Younger, K. McIntosh, J. Chludzinski, D. Oakley, L. Mahoney, J. Funk, J. Donnelly, and S. Verghese, “Crosstalk analysis of integrated Geiger-mode avalanche photodiode focal plane arrays,” Proc. SPIE 7320, 73200Q (2009).
[CrossRef]

Oh, M.

M. Oh, H. Kong, and T. Kim, “Systematic experiments for proof of Poisson statistics on direct-detection laser radar using Geiger mode avalanche photodiode,” Curr. Appl. Phys. 10, 1041–1045 (2010).
[CrossRef]

Osche, G.

Owens, P.

Poor, H.

H. Poor, An Introduction to Signal Detection and Estimation (Springer, 1994).

Rarity, J.

Richmond, R.

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]

Scharf, L.

L. Scharf, Statistical Signal Processing (Addison-Wesley, 1991).

Tapster, P.

Townsend, P.

Trottier, C.

Verghese, S.

R. Younger, K. McIntosh, J. Chludzinski, D. Oakley, L. Mahoney, J. Funk, J. Donnelly, and S. Verghese, “Crosstalk analysis of integrated Geiger-mode avalanche photodiode focal plane arrays,” Proc. SPIE 7320, 73200Q (2009).
[CrossRef]

Webb, P.

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, “Receiver-operating characteristic for several multiple hypothesis range-rate filter algorithms,” Proc. SPIE 7684, 768412 (2010).
[CrossRef]

D. Youmans and G. Hart, “Numerical evaluation of the M parameter for direct detection ladar,” Proc. SPIE 3380, 176–187 (1998).
[CrossRef]

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

Younger, R.

R. Younger, K. McIntosh, J. Chludzinski, D. Oakley, L. Mahoney, J. Funk, J. Donnelly, and S. Verghese, “Crosstalk analysis of integrated Geiger-mode avalanche photodiode focal plane arrays,” Proc. SPIE 7320, 73200Q (2009).
[CrossRef]

Appl. Opt. (9)

H. Dautet, P. Deschamps, B. Dion, A. MacGregor, D. MacSween, R. McIntyre, C. Trottier, and P. Webb, “Photon counting techniques with silicon avalanche photodiodes,” Appl. Opt. 32, 3894–3900 (1993).
[CrossRef]

P. Owens, J. Rarity, P. Tapster, D. Knight, and P. Townsend, “Photon counting with passively quenched germanium avalanche,” Appl. Opt. 33, 6895–6901 (1994).
[CrossRef]

G. Osche, “Single- and multiple-pulse noncoherent detection statistics associated with partially developed speckle,” Appl. Opt. 39, 4255–4262 (2000).
[CrossRef]

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

M. Henriksson, “Detection probabilities for photon-counting avalanche photodiodes applied to a laser radar system,” Appl. Opt. 44, 5140–5147 (2005).
[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]

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

S. Johnson, “Cramer-Rao lower bound on range error for LADARs with Geiger-mode avalanche photodiodes,” Appl. Opt. 49, 4581–4590 (2010).
[CrossRef]

Curr. Appl. Phys. (1)

M. Oh, H. Kong, and T. Kim, “Systematic experiments for proof of Poisson statistics on direct-detection laser radar using Geiger mode avalanche photodiode,” Curr. Appl. Phys. 10, 1041–1045 (2010).
[CrossRef]

IEEE Trans. Electron Devices (1)

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. (1)

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]

IEEE Trans. Mil. Electron. (1)

G. Flint, “Analysis and optimization of laser ranging techniques,” IEEE Trans. Mil. Electron. 8, 22–28 (1964).
[CrossRef]

Lincoln Lab. J. (1)

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

Proc. IEEE (1)

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

Proc. SPIE (8)

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]

R. Younger, K. McIntosh, J. Chludzinski, D. Oakley, L. Mahoney, J. Funk, J. Donnelly, and S. Verghese, “Crosstalk analysis of integrated Geiger-mode avalanche photodiode focal plane arrays,” Proc. SPIE 7320, 73200Q (2009).
[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]

D. Youmans and G. Hart, “Numerical evaluation of the M parameter for direct detection ladar,” Proc. SPIE 3380, 176–187 (1998).
[CrossRef]

D. Youmans, “Receiver-operating characteristic for several multiple hypothesis range-rate filter algorithms,” Proc. SPIE 7684, 768412 (2010).
[CrossRef]

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

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

Other (7)

P. Gatt, T. Nichols, and S. Johnson, “Finite dead-time Geiger-mode APD performance,” in 14th Coherent Laser Radar Conference (2007).

R. Richmond and S. Cain, Direct-Detection LADAR Systems (SPIE Optical Engineering Press, 2010).

H. Poor, An Introduction to Signal Detection and Estimation (Springer, 1994).

L. Scharf, Statistical Signal Processing (Addison-Wesley, 1991).

J. Goodman, Statistical Optics (Wiley-Interscience, 1985).

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

G. Osche, Optical Detection Theory (Wiley-Interscience, 2002).

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Figures (12)

Fig. 1.
Fig. 1.

The CDF of Poisson random variable with mean Kn=2.5 is illustrated. For a false alarm probability of Pfa=0.15, the threshold is η=4 and the randomized decision rule uses the value q=0.3082. If k=4, the randomized decision rule accepts the alternate hypothesis with probability q.

Fig. 2.
Fig. 2.

Poisson PMFs are illustrated. Under the null hypothesis, the mean is Kn=2, and under the alternate hypothesis, the mean is Kn+Ks=5 (i.e., Ks=3).

Fig. 3.
Fig. 3.

Receiver operating characteristic curves for Poisson signals. The null hypothesis mean is Kn=2, and the signal mean varies from zero to four. The Ks=3 case is produced by the distributions shown in Fig. 2.

Fig. 4.
Fig. 4.

Receiver operating characteristic curves for Poisson signals. The randomized decision rule improves performance because the false alarm probability is exactly Pfa=106. The simple decision rule results shown here also appear in Fig. 2 of [2] and Figs. 4–11 of [4].

Fig. 5.
Fig. 5.

Poisson and Goodman PMFs are illustrated. The null hypothesis distribution is Poisson with a mean of Kn=2. Under the alternate hypothesis, the distribution is Goodman with parameters Kn=2, Ks=3, and M=2.

Fig. 6.
Fig. 6.

ROC curves for Poisson and Goodman distributions are shown. The parameters Kn=2 and Ks=3 are common to all cases. The alternate hypothesis diversity varies between 0.5 and 8. The M=2 case corresponds to the PMFs shown in Fig. 5.

Fig. 7.
Fig. 7.

Binomial PMFs. The null hypothesis distribution has parameters N=12 and q0=0.2. The alternate hypothesis distribution parameters are N=12 and q1=0.5.

Fig. 8.
Fig. 8.

ROC curves for binomial signals. Under the null hypothesis, the binomial distribution parameters are N=12 and q0=0.2. The alternate hypothesis parameters vary between q1=0.2 and q1=0.6. The case where q1=0.5 corresponds to the PMFs shown in Fig. 7.

Fig. 9.
Fig. 9.

Required number of photoelectrons to achieve a false alarm rate of Pfa0.001 and a detection rate of Pd=0.9. The accumulated target-present photoelectron count has a Poisson distribution with mean NKn+Ks. The simple decision rule results shown here also appear in Fig. 7 of [3].

Fig. 10.
Fig. 10.

Required number of photoelectrons to achieve a false alarm rate of Pfa0.001 and a detection rate of Pd=0.9. The accumulated target-present photoelectron count has a Goodman distribution with parameters NKn, Ks, and NM. The simple decision rule results shown here also appear in Fig. 7 of [3].

Fig. 11.
Fig. 11.

Required number of photoelectrons to achieve a false alarm rate of Pfa105 and a detection rate of Pd=0.95 for a Geiger-mode APD receiver. For each pulse, the target-present photoelectron count has a Poisson distribution with mean Kn+Ks/N. The simple decision rule results shown here also appear in Fig. 10b of [5].

Fig. 12.
Fig. 12.

Required number of photoelectrons to achieve a false alarm rate of Pfa105 and a detection rate of Pd=0.95 for a Geiger-mode APD receiver. For each pulse, the target-present photoelectron count has a Goodman distribution with parameters Kn, Ks/N, and M. The simple decision rule results shown here also appear in Fig. 10a of [5].

Tables (3)

Tables Icon

Table 1. Target Detection in a Poisson Backgrounda

Tables Icon

Table 2. Required Mean Number of Target Photoelectrons for a GMAPD Lidar Observing a Specular Target

Tables Icon

Table 3. Required Mean Number of Target Photoelectrons for a GMAPD Lidar Observing a Diffuse Target

Equations (27)

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c0(k)=n=0kp0(n).
c1(k)=n=0kp1(n).
δ(k)={1whenk>η0whenkη.
Pfa=n=η+1p0(n)=1c0(η),
Pd=n=η+1p1(n)=1c1(η).
η=argmaxη{1c0(η):1c0(η)Pfa}.
δ(k)={1whenk>ηqwhenk=η0whenk<η,
Pfa=qp0(η)+k=η+1p0(k)=1c0(η)+qp0(η),
Pd=1c1(η)+qp1(η).
q=Pfa+c0(η)1p0(η)=Pd+c1(η)1p1(η).
p0(k)={exp(Kn)k!Knkwhenk{0,1,,}0otherwise.
p1(k)={exp(KnKs)k!(Kn+Ks)kwhenk{0,1,,}0otherwise,
pt(k)={Γ(k+M)k!Γ(M)(KsKs+M)k(MKs+M)Mwhenk{0,1,,}0otherwise.
p1(k)=(p0*pt)(k)=j=0kp0(j)pt(kj).
p1(k)={exp(Kn)Γ(M)(MM+Ks)Mj=0kΓ(k+Mj)j!(kj)!Knj(KsM+Ks)kjwhenk{0,1,,}0otherwise.
p0(k)={(Nk)q0k(1q0)Nkwhenk{0,1,,N}0otherwise.
p1(k)={(Nk)q0k(1q0)Nkwhenk{0,1,,N}0otherwise.
p0(k)={exp(NKn)k!(NKn)kwhenk{0,1,,}0otherwise.
p1(k)={exp(NKnKs)k!(NKn+Ks)kwhenk{0,1,,}0otherwise.
p1(k)={exp(NKn)Γ(NM)(NMNM+Ks)NMj=0kΓ(k+NMj)j!(kj)!Knj(KsNM+Ks)kjwhenk{0,1,,}0otherwise.
Pa=11+KnNb.
Pr(K>0)=1exp(Kn).
q0=PaPr(K>0)=1exp(Kn)1+KnNb.
Pr(K>0)=1exp(KnKs/N).
q1=PaPr(K>0)=1exp(KnKs/N)1+KnNb.
Pr(K>0)=1exp(Kn)(MM+Ks/N)M.
q1=PaPr(K>0)=11+KnNb[1exp(Kn)(MM+Ks/N)M].

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