A Comparison of Different Mathematical Treatments for Solving the Inverse Problem in Focused Laser Intensity Modulation Method

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Focused laser intensity modulation method (FLIMM) is a non-destructive technique for determining the polarization and/or space charge profiles in thin dielectric polymers. However, this requires to solve a Fredholm integral equation of the first kind which is an “ill-posed” problem. The aim of this paper is to evaluate different mathematical methods and to choose the one most adapted to our experimental needs. After a brief introduction to the FLIMM, various mathematical methods are described and compared. These procedures were used to calculate the polarization profiles in multilayered samples of polyvinylidene fluoride (PVDF). Thus we can make a comparison between well-known theoretical profiles and the results obtained using the different implemented methods. Due to the computation particularities and in order to obtain a good spatial resolution, two methods were preferred. The approximation method has been chosen for the study of a zone close to the surface sample. For a more in-depth analysis, Tikhonov procedure will be used.
2004-05-15