Determination of Noise-Free Optical Constants in the Infrared by Kramers—Kronig Transformation of the Reflectance Ratio in s- and p-Polarization

Abstract

A method for Kramers-Kronig transformation of the reflectance ratio of s- and p-polarized light is discussed. The method is well suited for the determination of the optical constants of isotropic samples such as pellets prepared from powders. An algorithm is given that performs the transformation, including extrapolation at the data margins and an automated data fitting routine, that can handle very complex spectra of, e.g., biomacromolecules such as cellulose to obtain noise free spectra. Criteria for evaluation of the quality of the obtained data are given, and experimental data for cellulose II and xylane are presented.

Thickness Dependence of Reflection−Absorption Infrared Spectra of Supported Thin Polymer Films

“…Below 100 nm the spectroscopic approach does not seem to be sufficiently sensitive for thickness determination. This is due partly to the aforementioned noise and partly to unknown optical constants of the cellulose film in the infrared region, which are approximated from a Kramers−Kroning transformation of a cellulose sample. There is a constant overestimation of the film thickness by the spectral fit.…”

Simple method for the quantitative analysis of thin copolymer films on substrates by infrared spectroscopy using direct calibration

“…The central quantity which characterizes the properties of waves in or at the interface of materials is the complex index of refraction, which is wavenumber dependent. The Kramers–Kronig relation relates the real part to the imaginary part and vice versa , but requires the knowledge of one part at all frequencies 29. It is straightforward to calculate the transmission function of a free-standing layer at normal incidence with perfectly smooth surfaces given the complex and wavenumber dependent index of refraction and the thickness.…”