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.

Document Type

Peer-Reviewed Article

Publication Date


Permanent URL


Optical Society of America




Ira A. Fulton College of Engineering and Technology


Mechanical Engineering