Single-angle reflectance spectroscopy to determine the optical constants n and k: considerations in the far-infrared...

Single-angle infrared (IR) reflectance spectroscopy is a proven and effective method for determining the complex optical constants n and k of condensed matter. The modern method uses a Fourier transform IR spectrometer to record the quantitative reflectance R(ν) spectra followed by application of the Kramers-Kronig transform (KKT) to obtain the complex optical constants. In order to carry out the KKT, it is essential to measure the reflectance spectra to as high and low a frequency (wavenumber) as possible. Traditionally, the reflectance spectra of solid specimens consist of large (typically>10  mm diameter) polished single-crystal faces free of defects or voids. The requirement of a large polished face, however, is not a realistic expectation for many synthetic, geologic, or rare specimens where the size is usually small and the morphology can vary. In this paper we discuss several improvements and considerations to both the hardware and far-IR measurement protocols that lead to more accurate R(ν) values and thus to more accurate n/k values, especially for small (millimeter-sized) specimens where the R(ν) spectrum is concatenated from multiple independent R(ν) spectra from overlapping hardware/spectral domains. Specifically, the improved hardware and analyses introduced here include the following: (1) providing a set of far-IR calibration standards; (2) custom-designing and manufacturing low reflectivity, stray-light reducing sample masks for small specimens; (3) minimizing stray light interaction between the sample mask, the interferometer Jacquinot stop, and the detector; (4) optimizing the methods to "splice" together the spectra from independent domains; (5) discussing what methods one can use to obtain or calculate the important R(0  cm^-1) value; (6) using a quartic relationship to extrapolate from the measured R data to R(0); and (7) accounting for the limiting effects of diffraction for the spot size at the sample mask and detector for millimeter-sized specimens, especially at the very long wavelengths. These seven considerations are all highly interconnected and are discussed in turn, as well as their strong interdependencies. This paper presents a holistic approach for determining reliable n/k values of millimeter-sized samples using single-angle reflectance in the mid- and far-IR.