OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 17, Iss. 12 — Dec. 1, 2000
  • pp: 2229–2235

Inverse Mie problem

I. K. Ludlow and J. Everitt  »View Author Affiliations


JOSA A, Vol. 17, Issue 12, pp. 2229-2235 (2000)
http://dx.doi.org/10.1364/JOSAA.17.002229


View Full Text Article

Enhanced HTML    Acrobat PDF (266 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We apply functional analysis to the scattered electromagnetic field of a particle with spherical symmetry to obtain a pair of integral transforms for converting the Mie-scattering amplitudes S(θ) and S(θ) into the Mie coefficients an and bn. In the case of a homogeneous sphere, a simple mathematical construction is derived that uniquely inverts the Mie coefficients to find the refractive index and the radius of the particle. A more general method for construction of the refractive-index profile of an arbitrary sphere is discussed that follows from the treatment of Newton and Sabatier.

© 2000 Optical Society of America

OCIS Codes
(290.3200) Scattering : Inverse scattering
(290.4020) Scattering : Mie theory

History
Original Manuscript: January 27, 2000
Revised Manuscript: July 10, 2000
Manuscript Accepted: August 7, 2000
Published: December 1, 2000

Citation
I. K. Ludlow and J. Everitt, "Inverse Mie problem," J. Opt. Soc. Am. A 17, 2229-2235 (2000)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-12-2229


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. G. Mie, “Beitrage zur Optic trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908). [CrossRef]
  2. Z. Ulanowski, I. K. Ludlow, W. M. Waites, “Water content and size of bacterial spore components determined from laser diffractometry,” FEMS Microbiol. Rev. 40, 229–232 (1987). [CrossRef]
  3. P. J. Wyatt, “Some chemical, physical, and optical properties of fly ash particles,” Appl. Opt. 19, 975–983 (1980). [CrossRef] [PubMed]
  4. C. F. Bohren, E. D. Hirleman, eds., feature on Optical Particle Sizing, Appl. Opt. 30, 4685–4987 (1991). [CrossRef]
  5. M. R. Jones, B. P. Curry, M. Quinn Brewster, K. H. Leong, “Inversion of light-scattering measurements for particle size and optical constants: theoretical study,” Appl. Opt. 33, 4025–4034 (1994). [CrossRef] [PubMed]
  6. Z. Ulanowski, Z. Wang, P. H. Kaye, I. K. Ludlow, “Application of neural networks to the inverse light scattering problem for spheres,” Appl. Opt. 37, 4027–4033 (1998). [CrossRef]
  7. K. Chadan, P. C. Sabatier, Inverse Problems in Quantum Scattering Theory (Springer-Verlag, New York, 1989).
  8. C. F. Bohren, D. R. Huffman. Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  9. L. Kai, P. Massoli, “Scattering of electromagnetic-plane waves by radially inhomogeneous spheres: a finely stratified sphere model,” Appl. Opt. 33, 501–511 (1994). [CrossRef] [PubMed]
  10. B. R. Johnson, “Exact theory of electromagnetic scattering by a hetrogeneous multilayered sphere in the infinite-layer limit: effective media approach,” J. Opt. Soc. Am. A 16, 845–852 (1999). [CrossRef]
  11. R. G. Newton, Scattering Theory of Waves and Particles (Springer-Verlag, New York, 1982).
  12. R. G. Newton, “Construction of potentials from the phase shifts at fixed energy,” J. Math. Phys. 3, 75–82 (1962). [CrossRef]
  13. R. G. Newton, “Connection between complex angular momenta and the inverse scattering problem at fixed energy,” J. Math. Phys. 8, 1566–1570 (1967). [CrossRef]
  14. P. C. Sabatier, “Asymptotic properties of potentials in the inverse-scattering problem at fixed energy,” J. Math. Phys. 7, 1515–1531 (1966). [CrossRef]
  15. P. C. Sabatier, “Analytic properties of a class of potentials and the corresponding Jost function,” J. Math. Phys. 7, 2079–2091 (1966). [CrossRef]
  16. P. C. Sabatier, “General method for the inverse scattering problem of fixed energy,” J. Math. Phys. 8, 905–918 (1967). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited