OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 39, Iss. 33 — Nov. 20, 2000
  • pp: 6049–6057

Statistics of the slope-method estimator

Francesc Rocadenbosch, Adolfo Comerón, and Lorena Albiol  »View Author Affiliations

Applied Optics, Vol. 39, Issue 33, pp. 6049-6057 (2000)

View Full Text Article

Enhanced HTML    Acrobat PDF (169 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The slope method has customarily been used and is still used for inversion of atmospheric optical parameters, extinction, and backscatter in homogeneous atmospheres from lidar returns. Our aim is to study the underlying statistics of the old slope method and ultimately to compare its inversion performance with that of the present-day nonlinear least-squares solution (the so-called exponential-curve fitting). The contents are twofold: First, an analytical study is conducted to characterize the bias and the mean-square-estimation error of the regression operator, which permits estimation of the optical parameters from the logarithm of the range-compensated lidar return. Second, universal plots for most short- and far-range tropospheric backscatter lidars are presented as a rule of thumb for obtaining the optimum regression interval length that yields unbiased estimates. As a result, the simple graphic basis of the slope method is still maintained, and its inversion performance improves up to that of the present-day computer-oriented exponential-curve fitting, which ends the controversy between these two algorithms.

© 2000 Optical Society of America

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(010.3640) Atmospheric and oceanic optics : Lidar

Original Manuscript: October 5, 1999
Published: November 20, 2000

Francesc Rocadenbosch, Adolfo Comerón, and Lorena Albiol, "Statistics of the slope-method estimator," Appl. Opt. 39, 6049-6057 (2000)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. T. H. Collis, “Lidar: a new atmospheric probe,” Q. J. R. Meteorol. Soc. 92, 220–230 (1966). [CrossRef]
  2. R. T. H. Collis, P. B. Russell, “Lidar measurement of particles and gases by elastic backscattering and differential absorption,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed. (Springer-Verlag, New York, 1976), Chap. 4, pp. 71–102. [CrossRef]
  3. J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981). [CrossRef] [PubMed]
  4. G. J. Kunz, “Probing of the atmosphere with lidar,” in Proceedings of the Remote Sensing of the Propagation Environment Conference, AGARD-CP-502, (AGARD, Neuilly sur Seine, France, 1992), Vol. 23, pp. 1–11.
  5. J. D. Klett, “Lidar calibration and extinction coefficients,” Appl. Opt. 22, 514–515 (1983). [CrossRef] [PubMed]
  6. R. T. Brown, “A new lidar for meteorological application,” J. Appl. Meteorol. 12, 698–708 (1973). [CrossRef]
  7. G. J. Kunz, G. de Leeuw, “Inversion of lidar signals with the slope method,” Appl. Opt. 32, 3249–3256 (1993). [CrossRef] [PubMed]
  8. F. Rocadenbosch, A. Comerón, D. Pineda, “Assessment of lidar inversion errors for homogeneous atmospheres,” Appl. Opt. 37, 2199–2206 (1998). [CrossRef]
  9. J. J. More, “The Levenberg–Marquardt algorithm: implementation and theory,” in Numerical Analysis, Vol. 630 of Springer-Verlag Lecture Notes in Mathematics Series, G. A. Watson, ed. (Springer-Verlag, New York, 1977), pp. 105–116.
  10. R. Velotta, B. Bartoli, R. Capobianco, L. Fiorani, N. Spinelli, “Analysis of the receiver response in lidar measurements,” Appl. Opt. 37, 6999–7007 (1998). [CrossRef]
  11. G. J. Kunz, “Effects of detector bandwidth reduction on lidar signal processing,” (Physics and Electronics Laboratory, TNO-FEL, The Hague, 1977).
  12. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1991), pp. 345–354.
  13. A. B. Carlson, “Signal transmission and filtering,” in Communication Systems, 3rd ed. (McGraw-Hill, Singapore, 1986), Chap. 3, pp. 177–178.
  14. H. Koschmieder, “Theorie der Horizontalen Sichtweite,” Beitr. Phys. Freien Atmos. 12, 33–53 (1924).
  15. P. W. Kruse, L. D. McGlauchlin, R. B. McQuiston, Elements of Infrared Technology: Generation, Transmission and Detection (Wiley, New York, 1962).
  16. R. J. Barlow, “Least squares,” in Statistics: A Guide To The Use Of Statistical Methods In The Physical Sciences, F. Mandl, R. J. Ellison, D. J. Sandiford, eds. (Wiley, New York, 1989), Chap. 6.
  17. W. B. Jones, Introduction to Optical Fiber Communication Systems (Holt, Rinehart & Winston, New York, 1988), Chaps. 7 and 8.
  18. R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Krieger, Malabar, Fla., 1992), Chap. 4, pp. 138–145.
  19. R. J. McIntyre, “Multiplication noise in uniform avalanche photodiodes,” IEEE Trans. Electron Devices ED-13, 164–168 (1966). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited