Concurrent Determination of Optical Constants and the Kramers-Kronig Integration Constant (Anchor Point) Using Variable-Angle ATR/FT-IR Spectroscopy

Abstract

Attenuated total reflection Fourier transform infrared (ATR/FT-IR) spectroscopy has been used to determine optical constants in the infrared region of the spectrum for a variety of materials. Usually, the Kramers-Kronig transform is used to obtain optical constants from spectra, given that the baseline refractive index (anchor point) is known or can be determined. This determination often involves performing a separate experiment in which the refractive index of the sample is measured in a nonabsorbing region of the visible part of the spectrum, and the result extrapolated to the infrared. However, this is not feasible for opaque samples or for ones that contain domains large enough to scatter visible light. In this paper, we present a method for concurrently determining the anchor point and the optical constants using only variable-angle ATR/FT-IR spectroscopy and the subtractive form of the Kramers–Kronig transform. The method for determining the anchor point involves ratioing pATR (the negative log of the intensity of the ATR spectrum) values from weak absorption bands from spectra recorded at different angles of incidence. The anchor point can then be determined by computer. The only requirements are that the ATR system use unpolarized radiation and that the sample be thicker than the sampling depth of the IR radiation.