The recently developed Laser Intensity Modulation Method (LIMM) has proven to be a very useful technique for determining the thickness spatial distribution of polarization or space charge in ferroelectric materials. A major drawback in the analysis of LIMM measurements is the necessity of solving a Fredholm integral equation of the 1st kind using experimental data. This is an ill-posed problem which can inherently yield a number of solutions, each of which satisfies the measured data to within experimental accuracy. In this paper, several assumptions in the original theory are eliminated to give a modified and more precise analysis of the problem. Application of the regularization method and imposition of physical constraints and the principle of parsimony then lead to the optimal solution.