A procedure is presented for the use of the Kramers-Kronig dispersion relations in treatment of normal-incidence infrared reflection spectra to yield optical constants of crystals. The crux of the practical problem, treatment of unobserved wing regions in the integrations, is discussed in detail. Definitive methods of picking optimum upper and lower limits for integration over actual data and for fitting artificial wings are discussed.
The method is tested on a reflection spectrum generated by a model involving several damped harmonic oscillators. It is shown how a region involving a single band (but flanked by "unobserved" bands) can be treated, and how accurately the method reproduces the theoretically known optical indices. It appears feasible to obtain the indices of absorption and of refraction to ±0.005 and ±0.002, respectively, given accurate data on reflectance. Integrated band intensities are reproduced to within a few percent.
G. ANDERMANN, A. CARON, and DAVID A. Dows, "Kramers-Kronig Dispersion Analysis of Infrared Reflectance Bands," J. Opt. Soc. Am. 55, 1210-1212 (1965)