Patent ID: 6930777

Claim:
A method for determining at least one of parameters describing a non-interacting suspension, the parameters consisting of a particle size distribution and a volume fraction, comprising: measuring an experimental scattering coefficient at a selected number of wavelengths of a radiation passing through the suspension; formulating an integral equation for a calculated scattering coefficient, the integral equation having an integrand including a product, p(x), of the particle size distribution and the volume fraction, a form factor and a structure factor; expressing p(x) as a summation of B-spline functions; calculating the form factor from Mie scattering theory; calculating an inverse of the integral equation using least squares optimization to equate the experimental scattering coefficient and the calculated scattering coefficient, stabilizing the inverse using Tikhonov regularization having a regularization parameter and a non-negativity constraint on p(x) to determine a value of p(x); separating particle size distribution and volume fraction by a normalized distribution constraint; and using input physical data and selected upper and lower bounds of particle size, calculating volume fraction.