Abstract

Two commonly used correction algorithms that were originally developed by Bertie and Dignam and their co-workers for quantitative analysis of ATR spectra are examined. It is shown that the Dignam theory is more suitable for strong ATR bands, whereas the Bertie algorithm is more applicable for weak bands. On the basis of analysis of possible deviation sources determined in the Bertie and Dignam theories, a new ATR algorithm is developed and analyzed. With this approach, the initial estimate of the absorption index spectrum is obtained by KK correlation of the intensity and the phase of the complex Fresnel reflection coefficient. An iterative process that minimizes the difference between the true and calculated reflectivity spectra while maintaining the KK relation between refractive and absorption indices is used in conjunction with the Maclaurin numerical KKT method. Such an approach appears to improve accuracies for both weak and strong ATR bands.

Kramers–Kronig analysis of infrared reflection spectra with perpendicular polarization

Kiyoshi Yamamoto, Akio Masui, and Hatsuo Ishida
Appl. Opt. 33(27) 6285-6293 (1994)

Validity of the Kramers-Kronig transformation used in reflection spectroscopy

Ralph H. Young
J. Opt. Soc. Am. 67(4) 520-523 (1977)

Kramers-Kronig Analysis of Relative Reflectance Spectra Measured at an Oblique Angle

George M. Hale, Wayne E. Holland, and Marvin R. Querry
Appl. Opt. 12(1) 48-51 (1973)

Kramers-Kronig Analysis of Ratio Reflectance Spectra Measured at an Oblique Angle

Marvin R. Querry and Wayne E. Holland
Appl. Opt. 13(3) 595-598 (1974)

Numerical evaluation of truncated Kramers-Kronig transforms

Frederick W. King
J. Opt. Soc. Am. B 24(7) 1589-1595 (2007)