A Comparison of Three Techniques for Solving the Fredholm Integral Equation of the Laser Intensity Modulation Method (LIMM)

The Laser Intensity Modulation Method (LIMM) is widely used for the determination of the spatial distribution of polarization in polar ceramics and polymers, and space charge in non-polar polymers. The analysis of experimental data requires a solution of a Fredholm integral equation of the 1st kind. This is an ill-posed problem that has multiple and very different solutions. A number of methods have been used to solve this problem. In this paper, a comparison is made among three different techniques: the Scale Transformation Method, the Polynomial Regularization L-Curve Method and the Monte Carlo Method. The accuracy and ease of use of the three techniques are compared using both simulated and experimental data.