Inversion of light-scattering measurements for particle size and optical constants: Theoretical study

Matthew R. Jones, Bill P. Curry, M. Quinn Brewster, Keng H. Leong

Research output: Contribution to journalArticlepeer-review

Abstract

We invert the Fredholm equation representing the light scattered by a single spherical particle or a distribution of spherical particles to obtain the particle size distribution function and refractive index. We obtain the solution by expanding the distribution function as a linear combination of a set of orthonormal basis functions. The set of orthonormal basis functions is composed of Schmidt-Hilbert eigenfunctions and a set of supplemental basis functions, which have been orthogonalized with respect to the Schmidt-Hilbert eigenfunctions by using the Gram-Schmidt orthogonalization procedure. We use the orthogonality properties of the basis functions and of the eigenvectors of the kernel covariance matrix to obtain the solution that minimizes the residual errors subject to a trial function constraint. The inversion process is described, and results from the inversion of several simulated data sets are presented.

Original languageEnglish (US)
Pages (from-to)4025-4034
Number of pages10
JournalApplied Optics
Volume33
Issue number18
DOIs
StatePublished - Jun 20 1994

Keywords

  • Inverse proble
  • Optical particle sizing

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Engineering (miscellaneous)
  • Electrical and Electronic Engineering

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