A technique to assess the reliability of the second-order susceptibility determination of thin films

We present a detailed description of a new, statistical technique to determine the second-order susceptibility tensor of thin films [M. Siltanen, S. Cattaneo, E. Vuorimaa, H. Lemmetyinen, T.J. Katz, K.E.S. Phillips, M. Kauranen, J. Chem. Phys. 121 (2004) 1]. The technique is based on combining the results of several independent non-linear measurements with a theoretical model describing the sample. By increasing the number of measurements well beyond the minimum required, we obtain an over-determined group of equations and solve it using the statistical total least squares method. The procedure yields indicators that allow the validity of theoretical models of different level of detail to be assessed, the symmetry group of the sample to be verified, and the accuracy of the determined tensor components to be estimated. The technique thus increases the reliability of any subsequent conclusions regarding the properties of the sample and facilitates the detection of invalid or inaccurate results.