Low-bias macroscopic analysis of polydispersity.

where s(z), which characterizes the ‘polydispersity’, is to be estimated. In addition to actual size polydispersity, the distribution s(z) may describe additional processes, such as non-translational motions. At most, the covariance matrix of the noise components, ej1 is approximately known. The kernel, K(1; t), is assumed to be known and typically contains a scattering form factor, a weighting factor for the particular type of distribution function in the variable z, and an exponentially decaying factor, e.g. exp( zt), as in quasi-elastic light scattering, where the 3 are measurements of the electric-field autocorrelation function magnitude at delay times $. However, the methods described here can handle other K(z, t). This is now widely recognized as an ill-posed problem, where there is an infinite set, &, of possible solutions, all of which fit the data to within experimental error. Even worse, the errors are unbounded. Thus, for most physically reasonable K(2; t) and true s(z), and an arbitrarily large error amplitude (A), there always exists a large enough o such that [3]: