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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 47, Iss. 28 — Oct. 1, 2008
  • pp: 5147–5154

Bound on range precision for shot-noise limited ladar systems

Steven Johnson and Stephen Cain  »View Author Affiliations


Applied Optics, Vol. 47, Issue 28, pp. 5147-5154 (2008)
http://dx.doi.org/10.1364/AO.47.005147


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Abstract

The precision of ladar range measurements is limited by noise. The fundamental source of noise in a laser signal is the random time between photon arrivals. This phenomenon, called shot noise, is modeled as a Poisson random process. Other noise sources in the system are also modeled as Poisson processes. Under the Poisson-noise assumption, the Cramer–Rao lower bound (CRLB) on range measurements is derived. This bound on the variance of any unbiased range estimate is greater than the CRLB derived by assuming Gaussian noise of equal variance. Finally, it is shown that, for a ladar capable of dividing a fixed amount of energy into multiple laser pulses, the range precision is maximized when all energy is transmitted in a single pulse.

© 2008 Optical Society of America

OCIS Codes
(270.5290) Quantum optics : Photon statistics
(280.3400) Remote sensing and sensors : Laser range finder

ToC Category:
Quantum Optics

History
Original Manuscript: June 16, 2008
Manuscript Accepted: August 1, 2008
Published: September 25, 2008

Citation
Steven Johnson and Stephen Cain, "Bound on range precision for shot-noise limited ladar systems," Appl. Opt. 47, 5147-5154 (2008)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-28-5147


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References

  1. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  2. J. Goodman, “Some effects of target-induced scintillation on optical radar performance,” Proc. IEEE 53, 1688-1700 (1965). [CrossRef]
  3. U. Fano, “Ionization yield of radiations. II. The fluctuations of the number of ions,” Phys. Rev. 72, 26-29 (1947). [CrossRef]
  4. A. Jelalian, Laser Radar Systems (Artech House, 1992).
  5. G. Osche, Optical Detection Theory (Wiley-Interscience, 2002).
  6. 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]
  7. B. Rye and R. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I. Spectral accumulation and the Cramer-Rao lowerbound,” IEEE Trans. Geosci. Remote Sens. 31, 16-27 (1993). [CrossRef]
  8. S. Johnson, T. Nichols, P. Gatt, and T. Klausutis, “Range precision of direct detection laser radar systems,” Proc. SPIE 5412, 72-86 (2004). [CrossRef]
  9. O. Steinvall, “Effects of target shape and reflection on laser radar cross sections,” Appl. Opt. 39, 4381-4391 (2000). [CrossRef]
  10. 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]
  11. K. Winick, “Cramer-Rao lower bounds on the performance of charge-coupled device optical position estimators,” J. Opt. Soc. Am. A 3, 1809-1815 (1986). [CrossRef]
  12. A. Siegman, Lasers (University Science Books, 1986).
  13. S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice Hall, 1993).
  14. I. Gradshteyn and I. Ryzhik, Table of Integrals, Series, and Products (Academic, 2000).
  15. 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]
  16. N. Hagen, M. Kupinski, and E. Dereniak, “Gaussian profile estimation in one dimension,” Appl. Opt. 46, 5374-5383 (2007). [CrossRef] [PubMed]
  17. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, 1965).
  18. G. Casella and R. Berger, Statistical Inference (Duxbury, 2002).
  19. J. Shapiro, B. Capron, and R. Harney, “Imaging and target detection with a heterodyne-reception optical radar,” Appl. Opt. 20, 3292-3313 (1981). [CrossRef] [PubMed]

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