Using the Kramers—Kronig Method to Determine Optical Constants and Evaluating its Suitability as a Linear Transform for Near-Normal Front-Surface Reflectance Spectra

Abstract

In this paper, the suitability of using the Kramers-Kronig transform to routinely extract optical constants from near-normal incidence reflectance spectra of solids and liquids is demonstrated. In addition, the possibility of utilizing the Kramers-Kronig transform as a linearizing transform for near-normal incidence reflectance spectra is investigated. Also, several commercial Kramers-Kronig software packages were utilized in determining the optical constants from the near-normal incidence reflectance of Plexiglas. Unexpectedly, the results produced by the various packages differed significantly. The near-normal reflectance of water was measured, the Kramers-Kronig transform was applied to extract the optical constants of water, and the result was compared to values found in the literature. Furthermore, the Kramers-Kronig transforms of near-normal incidence reflectance spectra of various concentrations of sugar in water were calculated to evaluate its use as a linearizing transform for quantitative applications.

Water Structure at the Air−Aqueous Interface of Divalent Cation and Nitrate Solutions

“…Figure b,c presents the real ( n ) and imaginary ( k ) refractive index spectra extracted from the IRRAS spectra by using the Kramers−Kronig tranformation. Both n and k spectra of neat water obtained through our IRRAS experiments and Kramers−Kronig tranformation are higher than values found in the literature. , (The refractive index values obtained from the literature rather than from our IRRAS experiments are employed in the determination of Fresnel factors and the normalization of VSFG spectra.) However, n and k spectra of neat water shown in Figure b,c follow the same shape as the refractive index spectra obtained by other groups. , (We are interested in the spectral features rather than the absolute values of n and k , and therefore, the y -axis values of n and k spectra have been removed in Figures f and b,c.)…”

Infrared Refraction Spectroscopy

“…This is the reason why complex methods are needed to invert Eq. 1 like those based on the Kramers–Kronig relations, which are very error-prone 10,11 or dispersion analysis, which is complex and not user-friendly, to solve this inverse problem. 9…”

“…This is the reason why complex methods are needed to invert Eq. 1 like those based on the Kramers-Kronig relations, which are very error-prone 10,11 or dispersion analysis, which is complex and not user-friendly, to solve this inverse problem. 9 On the other hand, absorbance is based on the negligence of the influence of the refractive index if it is calculated as -log 10 T or -log 10 (R/R 0 ).…”

Apparatus for High-Precision Angle-Resolved Reflection Spectroscopy in the Mid-Infrared Region

“…Reflection measurement allows us to study optically thick and highly absorbing samples whose transmission spectra are difficult to obtain. Nevertheless, a rigorous Kramers-Kronig analysis of specular reflection spectra provides both the real and imaginary refractive indices of materials, [3][4][5] the same information gained by transmission measurements of carefully prepared optically thin samples. Moreover, attenuated total reflection (ATR) techniques are used to measure the spectra of small amounts of samples.…”