Kramers-kronig type analysis of short spectral range reflection spectra

Abstract

Abstract This paper describes a new development in the use of the Kramers-Kronig method for the analysis of infrared reflection spectra. It is shown that precise and useful data can be obtained from even a small region of the reflection spectrum when appropriate boundary conditions are carefully applied. In particular it is shown how the use of boundary conditions which reduce to a minimum the calculated phase change on reflection of the radiation at relatively low absorption regions at the high and low energy limits of the studied region, adds significantly to the reliability of the calculations. Infrared reflectivity data for ammonium chloride and bromide in the spectral range 1000 to 1700 cm −1 are used to illustrate the method. A frequency precision of v ± 0.15 cm −1 is obtained for band-center frequencies of equivalent absorption spectra calculated from the observed reflection spectra. This has allowed a detailed study of the small but significant changes that take place in this internal mode frequency as the crystal is made to pass through its λ-transition. It has also shown how a short section of an IR reflection spectrum from a sample held within a hostile environment (e.g. within a high pressure enclosure,) can be used to derive precise data on the properties of such a sample.