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Inverse Mie problem.

I K Ludlow1, J Everitt

  • 1Department of Physical Sciences, University of Hertfordshire, Hatfield, United Kingdom.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|January 5, 2001
PubMed
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This study introduces integral transforms to convert Mie-scattering amplitudes into Mie coefficients. For homogeneous spheres, this method uniquely determines the refractive index and radius, enabling detailed particle analysis.

Area of Science:

  • Electromagnetism
  • Optical Physics
  • Applied Mathematics

Background:

  • Mie theory describes light scattering by spherical particles.
  • Scattering amplitudes (S perpendicular and S parallel) are experimentally measurable.
  • Mie coefficients (an and bn) characterize particle properties but are not directly observed.

Purpose of the Study:

  • To develop a method for deriving Mie coefficients from scattering amplitudes.
  • To enable unique determination of homogeneous sphere properties (refractive index, radius).
  • To extend the method for reconstructing refractive index profiles of arbitrary spheres.

Main Methods:

  • Application of functional analysis to the scattered electromagnetic field.
  • Derivation of integral transforms to link scattering amplitudes and Mie coefficients.

Related Experiment Videos

  • Mathematical construction for inverting Mie coefficients for homogeneous spheres.

    • Main Results:

    • A pair of integral transforms was obtained to convert Mie-scattering amplitudes to Mie coefficients.
    • A unique inversion method was derived for homogeneous spheres, determining refractive index and radius.
    • A generalized approach for arbitrary sphere refractive index profiling was discussed.

    Conclusions:

    • The developed integral transforms provide a novel pathway from scattering data to particle characteristics.
    • The method offers a direct route to determine key parameters of homogeneous spheres.
    • The work extends Mie theory applications to complex, non-uniform spherical particles.