Skip to main content

Size Distributions of Particles Obtained by Inversion of Spectral Extinction and Scattering Measurements

  • Chapter
Optics of Cosmic Dust

Part of the book series: NATO Science Series ((NAII,volume 79))

Abstract

Suspended particles attenuate and scatter light. Both the attenuation and the scattering is influenced by the particle’s size and optical constants of the material. The angular scattering and the wavelength dependent extinction provides a means of obtaining information on the size distribution of the particles. The relation between optical properties and size is given by integral equations which are not easy to solve, since no unique solution exists.

It is possible to predict the accuracy of any inversion procedure through mathematical operations. The information parameter is close to one if the inverted size distribution data have little ambiguity and goes to zero if the inverted size distribution is meaningless. For spectral extinction measurements (in the visible) the range of meaningful size distributions obtained through inversions is between particle radii of 0.1 to 1 µm. For inversion of angular scattering data, the range is between 0.05 and 1.5 µm if scattering angles between 20 and 160° are used. The upper size limit increases if the scattering is also measured at smaller angles.

Simultaneous measurements of the horizontal attenuation, the sky radiation and the size distribution of the aerosol with an impactor has shown that inversions give meaningful results within the range, where the information parameter is high. The usual features of the atmospheric aerosol are also detected by the inversion of the angular scattering obtained from sky radiation measurements.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G.E. Backus, and J.F. Gilbert, Uniqueness of the inversion of gross earth data, Philos. Trans. R. Soc. London A bf 266, 123–192, (1970).

    Article  MathSciNet  ADS  Google Scholar 

  2. P. W. Barber, S. C. Hill, Light scattering by particles: Computational methods. World Scientific, Singapore (1990).

    Google Scholar 

  3. C. F. Bohren, and D. R. Huffman, Absorption and scattering of light by small particles. Wiley Interscience, New York (1983).

    Google Scholar 

  4. M. A. Box, and S. Lo, Approximate determination of aerosol size distributions. J. Appl. Meteor. 15, 1068–1976, (1976)

    Article  ADS  Google Scholar 

  5. C. D. Capps, R. L. Henning, and G. M. Hess, Analytic inversion of remote sensing data. Appl. Opt. 34, 3581–87, (1982).

    Article  ADS  Google Scholar 

  6. C. Dellago, and H. Horvath, On the accuracy of size distribution information obtained from light extinction and scattering measurements-I. basic considerations and models. J. Aerosol Sci. 24, 129–141, (1993).

    Article  Google Scholar 

  7. J. Heintzenberg, H. Muller, H. Quenzel, and E. Thomalla, Information content of optical data with respect to aerosol properties: numerical studies with a randomized minimization-search-technique inversion algorithm. Appl. Optics 20, 1308–1315, (1981).

    Article  ADS  Google Scholar 

  8. H. Horvath, The University of Vienna Telephotometer, Atmospheric Environment 15, 2537–2546, (1981).

    Article  Google Scholar 

  9. M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, Aerosol size distributions obtained by inversion of spectral optical depth measurements. J. Atmos. Sci. 2153–2167, (1978).

    Google Scholar 

  10. L. Landweber, An interactive formula for Fredholm integral equations of the first kind Am. J. Math. 73, 615–624, (1951).

    Article  MathSciNet  MATH  Google Scholar 

  11. J. M. Livingstone, and P. B. Russel, Retrieval of aerosol size distribution moments from multiwavelength particulate extinction measurements. J. Geophysical Research 94, 8425–8433, (1989).

    Article  ADS  Google Scholar 

  12. G. Mie, Beiträge zur Optik trüber Medien, speziell kolloidaler Goldlosungen. Ann. Phys. 25, 377–455, (1908).

    Article  MATH  Google Scholar 

  13. T. Nakajima, G. Tonna, R. Rao, P. Boi, Y. Kaufman, and B. Holben, Use of sky brightness measurements from ground for remote sensing of particulate dispersion. Appl. Opt. 35, 2672–2686. (1996).

    Article  ADS  Google Scholar 

  14. G. E. Shaw, Inversion of optical scattering and spectral extinction measurements to recover aerosol size spectra. Applied Optics 18, 988–993, (1979).

    Article  ADS  Google Scholar 

  15. Twomey S., Introduction to the mathematics of inversions in remote sensing and indirect measurements. Elsevier, New York. (1977)

    Google Scholar 

  16. K. T. Whitby, The physical characteristics of Sulfur aerosol. Atmospheric Environment 12, 135–159, (1978).

    Article  Google Scholar 

  17. Yamamoto G., and M. Tanaka, Determination of the aerosol size distribution from spectral attenuation measurements. Appl. Optics bf 8 447–453, (1969)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Horvath, H. et al. (2002). Size Distributions of Particles Obtained by Inversion of Spectral Extinction and Scattering Measurements. In: Videen, G., Kocifaj, M. (eds) Optics of Cosmic Dust. NATO Science Series, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0628-6_9

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-0628-6_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-0820-7

  • Online ISBN: 978-94-010-0628-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics