A General-Purpose Constrained Regularization Method for Inverting Photon Correlation Data

Abstract

In photon correlation spectroscopy (PCS), there are relatively few cases where there is prior knowledge that the scattered field autocorrelation function contains only one component. Even in these favorable cases, every data analysis procedure should have the capability of accounting for extra unexpected components, e.g., due to instrumentation problems, aggregation, strongly scattering impurities, or even an important undiscovered effect. Often the main purpose of the experiment is to study polydispersity anyway. The first-order correlation function can often be approximated as a linear superposition of apparently independent contributions, yielding a Freaholm integral equation of the first kind,

$${y_j} = \int\limits_a^b {s(\lambda )} K(\lambda ,{t_j})d\lambda + {\varepsilon _j},\;j = 1, \ldots {N_{y,}}$$

((1))

where K(λ, t_j) is known [e.g., exp(-λt_j)], and s(λ) (e.g., a velocity or particle radius distribution) is to be estimated from the data γ_j, containing unknown noise components ε_j.