The Inversion Method for Determining the Particle Size Distribution from the Scattered Light Intensity Pattern in a Laser Droplet Sizer

Abstract

The purpose of this paper is to present a new method for determining the particle size distribution from angulary scattered light intensity pattern. By the present method arbitrarily shaped particle size distribution can be obtained.
This method is a constrained inversion method of equation (1) under the following conditions: (1) n(D) is smooth and (2) n(D) is non-negative.
logI(θ)=log[∫i(D, θ)n(D)dD] (1)
I(θ): scattered light intensity pattern.
n(D): particle size distribution
i(D, θ): Mie scattering function Equation (1) is approximated by linear equations (I=G·n). The least square solution of its equations is obtained using Lagrange's method of indeterminate coefficients and KuhnTucker's theorem. In Lagrange's method Lagrangian multiplier γ must be selected. It is shown that geometrical mean value of G*G's eigenvalues is suitable for Lagrangian multiplier γ.
Numerical experiments are performed to verify the effectiveness of constraint conditions and the validity of γ selection. Several particle size distributions are inverted from measured light intensity patterns scattering by Polystyrene particles whose diameters are known to verify the applicability of the present method.