Maximum Entropy Analysis of Dynamic Light Scattering Signals

Abstract

Glass transition temperatures of thin polymer coatings (similar to the coating of a magnetic storage disc) on alumina substrates have been evaluated with dynamic light scattering methods. At this temperature the correlation time of the thermodynamical fluctuations in the polymer increases and so the spectrum of the dynamic light scattering signal changes accordingly. In practise only partial knowledge of the autocorrelation function exists, usually based on a finite series of data samples taken in a finite intervall. In the common analysis the autocorrelation function is set zero for all lags for which no estimate exists or the missing data is replaced by the already measured data of the intervall. Both procedures of course can not lead to correct autocorrelation functions or spectra. Maximum entropy methods can give the most unbiased estimates of the missing data and so lead to the "best possible" autocorrelation function/power spectra obtainable from such a limited data set.