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Particle Size Distributions from Fraunhofer Diffraction

  • M. Bertero
  • P. Boccacci
  • C. De Mol
  • E. R. Pike

Abstract

It is well known1 that the mean intensity per steradian diffracted by a random distribution of N opaque particles is given, in the Fraunhofer region, by
$$I(s)=I_o\sum_{i=1}^{N}\frac{a_{i}^{2}J_{1}^{2}(ka_is)}{s^2}$$
(1)
where a i is the radius of the particle i, k is the wave-vector of the radiation and s is the scattering angle. In the absence of noise an annular detector or segment of an annulus will respond with a current g(s) proportional to sI(s).

Keywords

Singular System Impulse Response Function Fredholm Integral Equation Resolution Ratio Singular Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    L.P. Bayvel and A.R. Jones, “Electromagnetic Scattering and its Applications”, Applied Science Publishers, London (1981)CrossRefGoogle Scholar
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    J.G. McWhirter and E.R. Pike, On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind, J. Phys. A, 11:1729 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
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    M. Bertero, and E.R. Pike, Particle size distributions from Fraunhofer diffraction: I. An analytic eigenfunction approach, Opt. Acta, 30:1043 (1983)CrossRefGoogle Scholar
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    M. Bertero, P. Boccacci, and E.R. Pike, Particle size distributions from Fraunhofer diffraction: II. The singular value spectrum, Inverse Problems, 1:111 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
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    M. Bertero, P. Boccacci, C. De Mol, and E.R. Pike, Extraction of polydispersity information in photon correlation spectroscopy, published in these Proceedings.Google Scholar
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    M. Bertero, P. Brianzi, C. De Mol, and E.R. Pike, Positive regularized solutions in electromagnetic inverse scattering, in “Proc. Int. URSI Symp. on Electromagnetic Theory”, Budapest (1986).Google Scholar

Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • M. Bertero
    • 1
  • P. Boccacci
    • 1
  • C. De Mol
    • 2
  • E. R. Pike
    • 3
    • 4
  1. 1.Dipartimento di FisicaUniversità di Genova and Istituto nazionale di Fisica NucleareGenovaItaly
  2. 2.Département de MathématiqueUniversité Libre de BruxellesBruxellesBelgium
  3. 3.Dept. of PhysicsKing’s CollegeLondonEngland
  4. 4.RSREGreat MalvernEngland

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