Singular Function Techniques for Photon Correlation Data Reduction

Abstract

The photon correlation technique has a special feature relating to the accuracy achieved in typical experiments on the data points. With modern sources and detectors experiments are virtually noiseless except for the discrete photon nature of the light itself. This fact has given rise to a special study of the information content of such data, particularly in the case of photon correlation spectroscopy (or PCS) (1) in which light scattering from diffusing macromolecules produces an exponential photon correlation function if a single species or size of particle is present, and a superposition of exponentials or Laplace transform of a distribution of such radii or sizes. In this case it very quickly became apparent that the "information content" of the photon correlation function, even with very high accuracy in the data points themselves, was very low and that inversion of such data rarely provided more than about three independent data points on the distribution function required. Equivalently only the first three central moments of the distribution could be reasonably recovered.