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

Journal Article · Mon Jun 20 04:00:00 EDT 1994 · Applied Optics; (United States)

DOI:https://doi.org/10.1364/AO.33.004025· OSTI ID:7284160

Brewster, M Q ^[1]; Leong, K H ^[2]

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1. Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 140 Mechanical Engineering Building, 1206 West Green Street, Urbana, Illinois 61801 (United States)
2. Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439 (United States)

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.

• OSTI ID: 7284160
• Journal Information: Applied Optics; (United States), Journal Name: Applied Optics; (United States) Vol. 33:18; ISSN APOPAI; ISSN 0003-6935
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANGULAR DISTRIBUTION
CROSS SECTIONS
DISTRIBUTION
DISTRIBUTION FUNCTIONS
EQUATIONS
FREDHOLM EQUATION
FUNCTIONS
INTEGRAL EQUATIONS
INVERSE SCATTERING PROBLEM
LIGHT SCATTERING
OPTICAL PROPERTIES
PARTICLE SIZE
PARTICLES
PHYSICAL PROPERTIES
REFRACTIVE INDEX
SCATTERING
SIZE