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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 17 — Jun. 10, 2011
  • pp: 2559–2571

Range separation performance and optimal pulse-width prediction of a three-dimensional flash laser detection and ranging using the Cramer–Rao bound

Jason McMahon, Richard K. Martin, and Stephen C. Cain  »View Author Affiliations

Applied Optics, Vol. 50, Issue 17, pp. 2559-2571 (2011)

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This paper derives the Cramer–Rao bound (CRB) on range separation estimation of two point sources interrogated by a three-dimensional flash laser detection and ranging (LADAR) system. An unbiased range separation estimator is also derived to compare against the bound. Additionally, the CRB can be expressed as a function of two LADAR design parameters (range sampling and transmitted pulse width), which can be selected in order to optimize the expected range resolution between two point sources. Given several range sampling capabilities, the CRB and simulation show agreement that there is an optimal pulse width where a shorter pulse width would increase estimation variance due to undersampling of the pulse and a longer pulse width would degrade the resolving capability. Finally, the optimal pulse-width concept is extended to more complex targets and a normalized pulse definition.

© 2011 Optical Society of America

OCIS Codes
(280.3640) Remote sensing and sensors : Lidar
(350.5730) Other areas of optics : Resolution

ToC Category:
Remote Sensing and Sensors

Original Manuscript: January 18, 2011
Manuscript Accepted: February 11, 2011
Published: June 1, 2011

Jason McMahon, Richard K. Martin, and Stephen C. Cain, "Range separation performance and optimal pulse-width prediction of a three-dimensional flash laser detection and ranging using the Cramer–Rao bound," Appl. Opt. 50, 2559-2571 (2011)

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  1. R. Richmond, R. Stettner, and H. Bailey, “Laser radar focal plane array for three-dimensional imaging (update),” Proc. SPIE 3380, 138–143 (1998). [CrossRef]
  2. H. L. van Trees, Detection, Estimation, and Modulation Theory (Wiley, 2001).
  3. M. I. Skolnik, Introduction to RADAR Systems, 3rd ed. (McGraw-Hill, 2002).
  4. A. Weiner, Ultrafast Optics (Wiley, 2009). [CrossRef]
  5. J. C. Dries, B. Miles, and R. Stettner., “A 32×32 pixel flash laser radar system incorporating InGaAs PIN and APD detectors,” Proc. SPIE 5412, 250–256 (2004). [CrossRef]
  6. S. C. Cain, R. Richmond, and E. Armstrong, “Flash light detection and ranging range accuracy limits for returns from single opaque surfaces via Cramer–Rao bounds,” Appl. Opt. 45, 6154–6162 (2006). [CrossRef] [PubMed]
  7. S. Johnson and S. C. Cain, “Bound on range precision for shot-noise limited ladar systems,” Appl. Opt. 47, 5147–5154(2008). [CrossRef] [PubMed]
  8. J. Khoury, C. Woods, J. Lorenzo, J. Kierstead, D. Pyburn, and S. Sengupta, “Resolution limits in imaging LADAR systems,” Appl. Opt. 45, 697–704 (2006). [CrossRef] [PubMed]
  9. N. Hagen, M. Kupinski, and E. L. Dereniak, “Gaussian profile estimation in one dimension,” Appl. Opt. 46, 5374–5383(2007). [CrossRef] [PubMed]
  10. 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]
  11. J. Eriksson and M. Viberg, “On Cramer–Rao bounds and optimal beamspace transformation in radar array processing,” in IEEE International Symposium on Phased Array Systems and Technology, 1996, (IEEE, 1996), pp. 301–306. [CrossRef]
  12. D. J. van der Laan, M. C. Maas, D. R. Schaart, P. Bruyndonckx, S. Leonard, and C. W. E. van Eijk, “Using Cramer–Rao theory combined with Monte Carlo simulations for the optimization of monolithic scintillator PET detectors,” IEEE Trans. Nucl. Sci. 53, 1063–1070 (2006). [CrossRef]
  13. J. Li, L. Xu, P. Stoica, K. Forsythe, and D. Bliss, “Range compression and waveform optimization for MIMO radar: a Cramer–Rao bound based study,” IEEE Trans. Signal Process. 56, 218–232 (2008). [CrossRef]
  14. R. Linnehan, D. Brady, J. Schindler, L. Perlovsky, and M. Rangaswamy, “On the design of SAR apertures using the Cramer–Rao bound,” IEEE Trans. Aerosp. Electron. Syst. 43, 344–355 (2007). [CrossRef]
  15. B. J. Rye and R. M. 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]
  16. J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).
  17. A. K. Jain, Fundamentals of Digital Image Processing(Prentice-Hall, 1989).
  18. J. W. Goodman, Statistical Optics (McGraw-Hill, 1985).
  19. A. Papoulis and S. Pillai, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 2002).
  20. C. R. Burris, “An estimation theory approach to detection and ranging of obscured targets in 3-D LADAR data,” Master’s thesis (Air Force Institute of Technology, 2006), http://handle.dtic.mil/100.2/ADA449928.
  21. R. Richmond and S. Cain, Direct-Detection LADAR Systems (SPIE, 2010).

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