An analysis of the integral equation of the surface laser intensity modulation method using the constrained regularization method

The SLIMM (surface laser intensity modulation method) is used for the determination of polarization distributions near the surfaces of ferroelectric samples. The experimental data measured are pyroelectric currents as functions of frequency. The data analysis requires the solution of a Fredholm integral equation of the 1st kind. This is an ill-posed problem which has multiple and very different solutions. The constrained regularization method can be used to solve this problem. However, the choice of the proper regularization parameter is normally somewhat arbitrary and this can affect the solution drastically. In the technique used here, an optimal regularization parameter is found using a set of simulated data. These data are based on a polarization distribution constructed from a simple frequency-to-space transformation. It is shown that the conventional minimization of the deviations between experimental data and the predicted values according to the principles of least-squares gives meaningless results in an ill-posed problem of this type. Experimental data on lanthanum-doped lead-zirconate-titanate ceramics and LiNbO₃ are analyzed.