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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 23, Iss. 24 — Dec. 15, 1984
  • pp: 4499–4508

Anomalous diffraction model for inversion of multispectral extinction data including absorption effects

James D. Klett  »View Author Affiliations


Applied Optics, Vol. 23, Issue 24, pp. 4499-4508 (1984)
http://dx.doi.org/10.1364/AO.23.004499


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Abstract

An analytical solution to the problem of inverting multispectral extinction measurements including absorption effects is constructed, via Laplace transform theory, under the assumption that the particulate extinction efficiency is given by the anomalous diffraction model of van de Hulst. A solution representation in terms of a finite series of generalized Laquerre polynomials is carried out to provide a framework for coping with the problem of limited extinction information. The solution is stabilized by means of the technique of constrained linear inversion.

© 1984 Optical Society of America

History
Original Manuscript: November 23, 1983
Published: December 15, 1984

Citation
James D. Klett, "Anomalous diffraction model for inversion of multispectral extinction data including absorption effects," Appl. Opt. 23, 4499-4508 (1984)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-23-24-4499


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References

  1. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  2. K. S. Shifrin, A. Y. Perelman, “Determination of the Particle Spectrum of a Dispersed System from Data on its Transparency,” Opt. Spectrosc. 15, 285 (1963).
  3. K. S. Shifrin, A. Y. Perelman, “Calculation of Particle Distribution by the Data on Spectral Transparency,” PAGEOPH 58, 208 (1964). [CrossRef]
  4. M. A. Box, B. H. J. McKellar, “Analytic Inversion of Multispectral Extinction Data in the Anomalous Diffraction Approximation,” Opt. Lett. 3, 91, (1978). [CrossRef] [PubMed]
  5. A. L. Fymat, “Analytical Inversions in Remote Sensing of Particle Size Distributions. 1: Multispectral Extinctions in the Anomalous Diffraction Approximation,” Appl. Opt. 17, 1675 (1978).
  6. V. A. Punina, A. Y. Perelman, “Uber die Berechnung der Grössenverteilung von den Absorbierenden Kugelförmigen,” PAGEOPH 74, 92 (1969). [CrossRef]
  7. D. L. Phillips, “A Technique for the Numerical Solution of Certain Integral Equations of the First Kind,” J. Assoc. Comput. Mach. 9, 84 (1962). [CrossRef]
  8. S. Twomey, “On the Numerical Solution of Fredholm Integral Equations of the First Kind by the Inversion of the Linear System Produced by Quadrature,” J. Assoc. Comput. Mach. 10, 97 (1963). [CrossRef]
  9. P. T. Walters, “Practical Applications of Inverting Spectral Turbidity Data to Provide Aerosol Size Distributions,” Appl. Opt. 19, 2353 (1980. [PubMed]
  10. P. M. Morse, H. Feshbach, Methods of Theoretical Physics, Vol. 1 (McGraw-Hill, New York, 1953).
  11. A. L. Fymat, C. B. Smith, “Analytical Inversions in Remote Sensing of Particle Size Distributions. 4: Comparison of Fymat and Box-McKeller Solutions in the Anomalous Diffraction Approximation,” Appl. Opt. 18, 3595 (1979). [CrossRef] [PubMed]
  12. R. Piessens, M. Branders, “Numerical Inversion of the Laplace Transform Using Generalized Laguerre Polynomials,” Proc. Inst. Electr. Eng. 118, 1517 (1971). [CrossRef]
  13. Y. L. Luke, The Special Functions and Their Approximations, Vol. 2 (Academic, New York, 1969).
  14. S. Twomey, Introduction to the Mathematics of Inversion in Remove Sensing and Indirect Measurements (Elsevier, New York, 1977).
  15. G. Yamamoto, M. Tanaka, “Determination of Aerosol Size Distributions from Spectral Attenuation Measurements,” Appl. Opt. 8, 447 (1969 [CrossRef] [PubMed]

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