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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 39, Iss. 24 — Aug. 20, 2000
  • pp: 4214–4231

Determination of the aerosol size distribution by analytic inversion of the extinction spectrum in the complex anomalous diffraction approximation

Ghislain Franssens, Martine De Mazière, and Dominique Fonteyn  »View Author Affiliations


Applied Optics, Vol. 39, Issue 24, pp. 4214-4231 (2000)
http://dx.doi.org/10.1364/AO.39.004214


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Abstract

A new derivation is presented for the analytical inversion of aerosol spectral extinction data to size distributions. It is based on the complex analytic extension of the anomalous diffraction approximation (ADA). We derive inverse formulas that are applicable to homogeneous nonabsorbing and absorbing spherical particles. Our method simplifies, generalizes, and unifies a number of results obtained previously in the literature. In particular, we clarify the connection between the ADA transform and the Fourier and Laplace transforms. Also, the effect of the particle refractive-index dispersion on the inversion is examined. It is shown that, when Lorentz’s model is used for this dispersion, the continuous ADA inverse transform is mathematically well posed, whereas with a constant refractive index it is ill posed. Further, a condition is given, in terms of Lorentz parameters, for which the continuous inverse operator does not amplify the error.

© 2000 Optical Society of America

OCIS Codes
(010.1110) Atmospheric and oceanic optics : Aerosols
(010.1310) Atmospheric and oceanic optics : Atmospheric scattering
(290.2200) Scattering : Extinction
(290.3200) Scattering : Inverse scattering

History
Original Manuscript: October 5, 1999
Revised Manuscript: March 31, 2000
Published: August 20, 2000

Citation
Ghislain Franssens, Martine De Mazière, and Dominique Fonteyn, "Determination of the aerosol size distribution by analytic inversion of the extinction spectrum in the complex anomalous diffraction approximation," Appl. Opt. 39, 4214-4231 (2000)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-24-4214

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