A study on the accuracy of surface charge measurement

Abstract

The measurement of accumulated surface charge for thick specimens requires multipoint probe outputs to establish the inverse calculation for the determination of an unknown charge distribution. Until now, studies on the various errors associated with the measurement have been conducted only for simplified arrangements mainly in axisymmetric geometry where the charged surface is parallel to the ground. We have numerically analyzed a model measurement setup more comparable to practical conditions by a highly effcient surface charge method. We have studied the effect of probe position, the induction from charge existing not directly beneath the (prohe) sensor and the difference in matrix components computed hy two numerical methods. In particular, we have studied the accuracy of the reconstructed charge distributions by numerical simulations of the inverse calculation. It has been shown that the assumed measurement errors make much larger differences in the reconstructed charge distributions, although the influence depends considerably on the assumed charge distribution. Reducing the condition number of the matrix improves the accuracy of the inverse calculation for uniform and linearly changing charge distributions.

Solving regularized least squares with qualitatively controlled adaptive cross‐approximated matrices

“…As an example of inverse calculation problem, we consider here the estimation of the accumulated charge distribution on the surface of a bulk solid insulator using multi-point measurement data acquired by a scanning electrostatic probe [4]. With x denoting the charge distribution, spatially discretized in n unknowns, and b denoting the probe data (measured in m points), the problem reduces to the inverse calculation for solving the governing equation Ax = b.…”

“…The measurement model is reported in Ref. 4, and here we address only the basic issues. The number of probe measurement points is m = 19,188, and the number of triangular charged areas is n = 10,140.…”

“…The authors applied ACA to the coefficient matrix of the inverse calculation problem using regularized least squares, and attempted to accelerate the conjugate gradient (CG) algorithm and other solvers by faster calculation of matrixvector products and transposed matrix-vector products [2,3]. In this study, we consider numerical simulation of the inverse problem of accumulated charge estimation [4]. Assuming that the coefficient matrix A org is known, we propose the fast generation of the approximated matrix A ACA , approximation quality representation using matrix norms, and approximation quality selection according to the S/N level of the signal.…”

Estimation of charge distribution on a bulky solid dielectric using regularization technique

“…Aiming at a practical measurement method, the authors have studied the measurement of accumulated charges [1][2][3][4][5][6], and other reports have also been published recently in this field [7][8][9][10].…”

“…As regards point (1), the authors applied a surface charge method [14] based on a fast multipole method [13] and achieved high accuracy with reduced computing time [5]. In the present study, we focus on point (2). In particular, we examine the estimation accuracy of inverse calculation, and apply the results to charge measurement of a test spacer.…”