Finite element based Kerr electro-optic reconstructions of space charge

Abstract

Recent advances in Kerr electro-optic measurement theory resulted in various promising algorithms that can reconstruct the electric field and/or space charge density from optical data. In particular the finite element based Kerr electro-optic reconstruction algorithm (FEBKER) calculates the space charge density directly to avoid the numerical problems associated with taking the gradient of the electric field, uses single parameter intensity measurements to enable transient analysis which otherwise is difficult since multiple parameter intensity measurements is slow due to the rotation of polarizers, and is capable of reconstruction even when the number of measurements are limited by the window size of the experimental set-up. In this paper we apply FEBKER to synthetic Kerr electro-optic data obtained for a point/plane electrode geometry in transformer oil with a specified space charge density distribution. The performance of the algorithm is tested. The impact of experimental error is analyzed by incorporating random error to the synthetic data. Regularization techniques that decrease the impact of experimental noise are applied.