Optical particle sizing, inverse problems
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 Publication Citation
Matthew R. Jones, Keng H. Leong, M. Quinn Brewster, and Bill P. Currry. "Inversion of Light Scattering Measurements for Particle Size and Optical Constants: Theoretical Study." Applied Optics, 33(18), 20 June 1994. 4025-4034.
BYU ScholarsArchive Citation
Jones, Matthew R.; Curry, Bill P.; Brewster, M. Quinn; and Leong, Keng H., "Inversion of Light Scattering Measurements for Particle Size and Optical Constants: Theoretical Study" (1994). All Faculty Publications. 1344.
Optical Society of America
Ira A. Fulton College of Engineering and Technology
© 1994 Optical Society of America. This paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/view_article.cfm?gotourl=http%3A%2F%2Fwww%2Eopticsinfobase%2Eorg%2FDirectPDFAccess%2F67E2AE48-C909-59BD-91591D480212ACC2_41594%2Fao-33-18-4025%2Epdf%3Fda%3D1%26id%3D41594%26seq%3D0%26mobile%3Dno&org=Brigham%20Young%20University. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.
Copyright Use Information