Laser intensity modulation method (limm): Experimental techniques, theory and solution of the integral equation

The Laser Intensity Modulation Method (LIMM) was developed for the determination of the spatial distribution of polarization or space charge through the thickness of a dielectric sample. It has been used in measurements on a number of ferroelectric ceramics and polymers, single crystals and pyroelectric glass-ceramics. Its applications have included poling studies, determination of crystallite orientation in glass-ceramics and influence of surface treatments on polarization of ceramics. The experimental technique and the theory are reviewed, and modifications for increase of accuracy are discussed. A major difficulty 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. A technique was developed for solving this class of equations by a modification of the constrained regularization method. The method was verified by experimental measurements on a lead-zirconate-titanate ceramic (PZT), polyvinylidene fluoride (PVF2), a glass-ceramic and multilayer samples composed of two or three sheets of PVF2, poled in either a positive or a negative direction or unpoled.