Abstract

For a direct-detection laser radar that uses a Geiger-mode detector, theory shows that the single-pulse detection probability is reduced by a factor exp(-K), where K is the mean number of primary electrons created by noise in the interval t between detector turn-on and arrival of laser photons reflected from the target. The corresponding false-alarm probability is at least 1 - exp(-K). For fixed-rate noise, one can improve the detection and false-alarm probabilities by reducing t. Moreover, when background-light noise is significant and dominates dark-current noise and when the laser signal is of the order of ten photoelectrons or more, the probabilities can be improved by reducing the amount of light falling on the detector, even if the laser signal is reduced by the same factor as the background light is. Additional analytical calculations show that identifying coincidences in data from as few as three pulses can reduce the false-alarm probability by orders of magnitude and, for some conditions, can also improve the detection probability.

© 2003 Optical Society of America

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References

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  1. B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).
  2. M. A. Albota, R. M. Heinrichs, D. G. Kocher, D. G. Fouche, B. E. Player, M. E. O’Brien, B. F. Aull, J. J. Zayhowski, J. J. Mooney, B. C. Willard, R. R. Carlson, “Three-dimensional imaging laser radar with a photon-counting avalanche photodiode array and microchip laser,” Appl. Opt. 41, 7671–7678 (2002).
    [CrossRef]
  3. R. H. Kingston, Detection of Optical and Infrared Radiation (Springer-Verlag, Berlin, 1978).
    [CrossRef]
  4. D. G. Youmans, “Avalanche photodiode detection statistics for direct detection laser radar,” in Laser Radar VII: Advanced Technology for Applications, R. J. Becherer, ed., Proc. SPIE1633, 41–53 (1992).
  5. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  6. K. A. McIntosh, J. P. Donnelly, D. C. Oakley, A. Napoleone, S. D. Calawa, L. J. Mahoney, K. M. Molvar, E. K. Duerr, S. H. Groves, D. C. Shaver, “InGaAsP/InP avalanche photodiodes for photon counting at 1.06 µm,” Appl. Phys. Lett. 81, 2505–2507 (2002).
    [CrossRef]

2002

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

M. A. Albota, R. M. Heinrichs, D. G. Kocher, D. G. Fouche, B. E. Player, M. E. O’Brien, B. F. Aull, J. J. Zayhowski, J. J. Mooney, B. C. Willard, R. 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. A. McIntosh, J. P. Donnelly, D. C. Oakley, A. Napoleone, S. D. Calawa, L. J. Mahoney, K. M. Molvar, E. K. Duerr, S. H. Groves, D. C. Shaver, “InGaAsP/InP avalanche photodiodes for photon counting at 1.06 µm,” Appl. Phys. Lett. 81, 2505–2507 (2002).
[CrossRef]

Albota, M. A.

Aull, B. F.

Calawa, S. D.

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

Carlson, R. R.

Daniels, P. J.

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

Donnelly, J. P.

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

Duerr, E. K.

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

Felton, B. J.

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

Fouche, D. G.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Groves, S. H.

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

Heinrichs, R. M.

Kingston, R. H.

R. H. Kingston, Detection of Optical and Infrared Radiation (Springer-Verlag, Berlin, 1978).
[CrossRef]

Kocher, D. G.

Landers, D. J.

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

Loomis, A. H.

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

Mahoney, L. J.

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

McIntosh, K. A.

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

Molvar, K. M.

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

Mooney, J. J.

Napoleone, A.

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

O’Brien, M. E.

Oakley, D. C.

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

Player, B. E.

Shaver, D. C.

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

Willard, B. C.

Youmans, D. G.

D. G. Youmans, “Avalanche photodiode detection statistics for direct detection laser radar,” in Laser Radar VII: Advanced Technology for Applications, R. J. Becherer, ed., Proc. SPIE1633, 41–53 (1992).

Young, D. J.

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

Zayhowski, J. J.

Appl. Opt.

Appl. Phys. Lett.

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

Lincoln Lab. J.

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

Other

R. H. Kingston, Detection of Optical and Infrared Radiation (Springer-Verlag, Berlin, 1978).
[CrossRef]

D. G. Youmans, “Avalanche photodiode detection statistics for direct detection laser radar,” in Laser Radar VII: Advanced Technology for Applications, R. J. Becherer, ed., Proc. SPIE1633, 41–53 (1992).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

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Figures (5)

Fig. 1
Fig. 1

Single-pulse probabilities of detection (solid curves) and false alarm (dashed curves) versus mean signal level S. The curves are differentiated by, and labeled with, the mean noise level N, in units of primary electrons per gate interval (interval that the detector is on). From top to bottom, the target return arrives at the beginning, middle, and end of the gate. For this and the following figures, there are 200 time bins within the gate, and the target return falls in one bin.

Fig. 2
Fig. 2

Another presentation of the single-pulse results. Here the abscissa is N, and the ordinate is S. The curves are those for constant probabilities of detection (solid) and false alarm (dashed). Again, from top to bottom, the target return arrives at the beginning, middle, and end of the gate.

Fig. 3
Fig. 3

Same as Fig. 1, except here the curves are differentiated by, and labeled with, contrast (S/ N).

Fig. 4
Fig. 4

Multiple-pulse and single-pulse probabilities of detection (two upper graphs) and false alarm (two lower graphs). The two left graphs are for N = 0.1 primary electron/gate interval, and the two right are for N = 1. The curves are labeled with the number of pulses (pul) and, if more than one pulse, the processing algorithm [either the threshold algorithm with a threshold (thr) of 2 or the maximum-firings algorithm (max)]. The abscissa is the per-pulse value of S. In all cases, the target is in the middle of the gate.

Fig. 5
Fig. 5

Same as Fig. 4, except here the two left graphs are for a contrast (S/ N) of 10 and the two right are for a contrast of 1.

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

Pm; t1, t2=1m!Mt1, t2m exp-Mt1, t2,
Mt1, t2=t1t2 rtdt
Pj=i=1j-1 Pm=0; iPm1; j=exp-i=1j-1 Mi1-exp-Mj.
PTGT=exp-fN1-exp-S-n.
Pg; S, d=Γg+dΓg+1Γd1+dS-g1+Sd-d.
Pw=m+g; n, S, d =g=0wexp-nnw-gw-g!Γg+dΓg+1Γd×1+dS-g1+Sd-d.
Pw=0; n, S, d=exp-n1+Sd-d.
PTGTNB=exp-fN1-exp-n1+Sd-d.
SOPT=bCbC+1ln1+Cf+1fb.
xj=exp-j-1n1-exp-n  1jfb
xj=exp-S-nj1-exp-n  fb+1jb-1
PD=1-i=0T-1u!i!u-i! yi1-yu-i,
PFA=j=1b-11-i=0T-1u!i!u-i! xji1-xju-i.
QDu, T=j=1b-1u!T!T!yTxjT,
QFAu, T=QDu, T+u!T!T!j=1b-1xjTkj xkT.
QDu, T=j=1b-1u!T!T!yTxjT1-y-xj+yT+1+xjT+1,
QFAu, T=QDu, T+u!T!T!×j=1b-1xjTkj xkT1-xj-xk+xj+xkT+1.
QDu, T=j=1b-1u!T!T!yTxjT1-y-xj22+y2+xj2T+1T+2+1-y-xjy+xjT+1+yxjT+12,QFAu, T=QDu, T+u!T!T!j=1b-1xjTkj xkT1-xj-xk22+xj2+xk2T+1T+2+1-xj-xkxj+xkT+1+xjxkT+12.
PD=y2+2yz, PFA=j=1b-1 xj2+2zj=1b-1 xj.
PD=y3+3y21-y+3yz2, PFA=j=1b-1 xj3+3y+zj=1b-1 xj2+3j=1b-1xj2kj xk+3z2j=1b-1 xj.
S=E λhc TxmitTatm2ρLAR2 Trecη,
Nsun=Isunλhc Tatmψθ2ρSTatmATrecηtgβ.

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