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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 2 — Jan. 10, 2012
  • pp: 139–147

Maximum-likelihood reconstruction of photon returns from simultaneous analog and photon-counting lidar measurements

Darko Veberič  »View Author Affiliations


Applied Optics, Vol. 51, Issue 2, pp. 139-147 (2012)
http://dx.doi.org/10.1364/AO.51.000139


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Abstract

We present a novel method for combining the analog and photon-counting measurements of lidar transient recorders into reconstructed photon returns. The method takes into account the statistical properties of the two measurement modes and estimates the most likely number of arriving photons and the most likely values of acquisition parameters describing the two measurement modes. It extends and improves the standard combining (“gluing”) methods and does not rely on any ad hoc definitions of the overlap region nor on any background subtraction methods.

© 2012 Optical Society of America

OCIS Codes
(010.3640) Atmospheric and oceanic optics : Lidar
(030.5260) Coherence and statistical optics : Photon counting
(040.5250) Detectors : Photomultipliers

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: July 5, 2011
Manuscript Accepted: August 29, 2011
Published: January 6, 2012

Citation
Darko Veberič, "Maximum-likelihood reconstruction of photon returns from simultaneous analog and photon-counting lidar measurements," Appl. Opt. 51, 139-147 (2012)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-2-139


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References

  1. V. A. Kovalev and W. E. Eichinger, Elastic Lidar (Wiley, 2004), pp. 136–141.
  2. D. P. Donovan, J. A. Whiteway, and A. I. Carswell, “Correction for nonlinear photon-counting effects in lidar systems,” Appl. Opt. 32, 6742–6753 (1993). [CrossRef] [PubMed]
  3. Z. Liu, Z. Li, B. Liu, and R. Li, “Analysis of saturation signal correction of the troposphere lidar,” Chin. Opt. Lett. 7, 1051–1054 (2009). [CrossRef]
  4. R. K. Newsom, D. D. Turner, B. Mielke, M. Clayton, R. Ferrare, and C. Sivaraman, “Simultaneous analog and photon counting detection for Raman lidar,” Appl. Opt. 48, 3903–3914 (2009). [CrossRef] [PubMed]
  5. D. N. Whiteman, B. Demoz, P. Di Girolamo, J. Comer, I. Veselovskii, K. Evans, Z. Wang, M. Cadirola, K. Rush, G. Schwemmer, B. Gentry, S. H. Melfi, B. Mielke, D. Venable, and T. Van Hove, “Raman lidar measurements during the international H2O project. part I: instrumentation and analysis techniques,” J. Atmos. Oceanic Technol. 23, 157–169 (2006). [CrossRef]
  6. B. Mielke, “Analog + photon counting,” http://www.licel.com/analogpc.pdf.
  7. The procedure given here can be naturally adapted also for the extending (or paralyzable) type of photon counters by replacing Eq.  with C(p)=pexp⁡(δp) and its associated variance .
  8. http://www.licel.com/Transientrecorder.pdf; http://www.licel.com/TRInstallation.pdf.
  9. With the specific requirement that 0×ln⁡0≡0.
  10. The minimization in Eq.  is thus embedded inside the outer minimization.
  11. F. James, “Minuit, function minimization and error analysis,” CERN long writeup D506 (1998); and the implementation in http://root.cern.ch.
  12. Uncertainties are in fact not so large, considering that the parameters are obtained on a single trace with Ns=20summation only.
  13. For example, the maximum-likelihood combination of two normally distributed measurements with errors σ1 and σ2 gives a new estimate with a smaller error σ1σ2/σ12+σ22.
  14. At the time of writing, it takes 0.2 s per 16 k trace on a normal desktop computer.
  15. E. J. Axton and T. B. Ryves, “Dead-time corrections in the measurement of short-lived radionuclides,” Int. J. Appl. Radiat. Isotopes 14, 159–161 (1963). [CrossRef]
  16. J. W. Müller, “Some formulae for a dead-time-distorted Poisson process,” Nucl. Instr. Methods 117, 401–404 (1974). [CrossRef]
  17. C. Walck, “Hand-book on statistical distributions for experimentalists,” Stockholms Universitet, Internal report SUF-PFY/96-01, 10 September 2007, pp. 159–160.

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