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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 24 — Aug. 20, 2010
  • pp: 4581–4590

Cramer–Rao lower bound on range error for LADARs with Geiger-mode avalanche photodiodes

Steven E. Johnson  »View Author Affiliations

Applied Optics, Vol. 49, Issue 24, pp. 4581-4590 (2010)

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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 4 MHz , 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

OCIS Codes
(010.3640) Atmospheric and oceanic optics : Lidar
(030.5260) Coherence and statistical optics : Photon counting
(280.3400) Remote sensing and sensors : Laser range finder
(040.1345) Detectors : Avalanche photodiodes (APDs)

ToC Category:
Atmospheric and Oceanic Optics

Original Manuscript: May 18, 2010
Revised Manuscript: June 25, 2010
Manuscript Accepted: July 23, 2010
Published: August 16, 2010

Steven E. Johnson, "Cramer–Rao lower bound on range error for LADARs with Geiger-mode avalanche photodiodes," Appl. Opt. 49, 4581-4590 (2010)

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  1. S. Johnson, P. Gatt, and T. Nichols, “Analysis of Geiger-mode APD laser radars,” Proc. SPIE 5086, 359–368 (2003). [CrossRef]
  2. D. Fouche, “Detection and false-alarm probabilities for laser radars that use Geiger-mode detectors,” Appl. Opt. 42, 5388–5398 (2003). [CrossRef] [PubMed]
  3. 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]
  4. 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]
  5. 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).
  6. 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]
  7. 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).
  8. S. Johnson, “Range precision of ladar systems,” Ph.D. thesis (Air Force Institute of Technology, 2008).
  9. 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).
  10. 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]
  11. 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]
  12. R. Marino and W. Davis, “Jigsaw: A foliage-penetrating 3D imaging laser radar system,” Lincoln Lab. J. 15, 23–36(2005).
  13. 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]
  14. P. Gatt, S. Johnson, and T. Nichols, “Dead-time effects on Geiger-mode APD performance,” Proc. SPIE 6550, 65500I (2007). [CrossRef]
  15. 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]
  16. 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]
  17. M. O’Brien and D. Fouche, “Simulation of 3D laser radar systems,” Lincoln Lab. J. 15, 37–60 (2005).
  18. S. Johnson, T. Nichols, P. Gatt, and T. Klausutis, “Range precision of direct detection laser radar systems,” Proc. SPIE 5412, 72–86 (2004). [CrossRef]
  19. O. Steinvall, “Effects of target shape and reflection on laser radar cross sections,” Appl. Opt. 39, 4381–4391 (2000). [CrossRef]
  20. 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]
  21. 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]
  22. S. Johnson and S. Cain, “Bound on range precision for shot-noise limited LADAR systems,” Appl. Opt. 47, 5147–5154 (2008). [CrossRef] [PubMed]
  23. S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice Hall, 1993).
  24. J. Goodman, “Some effects of target-induced scintillation on optical radar performance,” Proc. IEEE 53, 1688–1700 (1965). [CrossRef]
  25. 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]
  26. R. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: Theory,” IEEE Trans. Electron Devices 19, 703–713 (1972). [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).

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