Accuracy and Optimization of the Two Prism Technique for Calculating the Optical Constants from ATR Data

Abstract

An ATR technique for calculating the optical constants has been developed that uses two reflectivities taken with different prisms at preset angles. These reflectivities can be solved exactly for the optical constants by a simple algebraic expression. The technique is the sole extant method that will give accurate optical constants for media of arbitrary anisotropy without any approximations. Thus n_x, n_y, n_z, and k_x, k_y, k_z, can all be determined separately for the same sample. The accuracy of the method is high and comparable to the two-angle technique under optimum conditions. The variation of accuracy with prism index, incidence angle, and the type of error in the measurement is studied for various ranges of samples n and k. Under optimal conditions the relative accuracy in k approaches the relative accuracy of the energy loss in reflection, which may be much better than 1%. Another unique feature of the method is that it works at constant penetration, thus allowing work with samples showing some extent of depth inhomogeneity. In some cases the variation of both constants with depth can be obtained with reduced precision.