THE CALCULATION OF A DISTRIBUTION OF RELAXATION-TIMES FROM THE FREQUENCY-DEPENDENCE OF THE REAL PERMITTIVITY WITH THE INVERSE FOURIER TRANSFORMATION

A deconvolution method for the determination of the distribution of re laxation times directly from the frequency dependence of the real part of the complex permittivity is presented. The method involves the mul tiplication of the real part of the complex permittivity by a function of the type A omega(beta), Fourier transformation of the product, div ision by the Fourier transform of e((beta-1)x) sech x and the inverse Fourier transformation back into the time domain. The method is shown to be able to reveal local relaxation processes visible neither in the frequency dependence of the real part of the complex permittivity nor in the loss factor. The factors influencing the resolution are discus sed; with simulated noise-free data, the method is able to resolve two relaxation processes with tau(01)/tau(02) = 2, provided a substantial part of the relaxation lies within the experimental window.