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Quantitative, FFT-Based, Kramers-Kronig Analysis for Reflectance Data

Volume 43, Number 8 (Dec. 1989) Page 1498-1501

Bortz, M.L.; French, R.H.


Kramers-Krönig analysis (KK) has been used for many years by spectroscopists to relate dissipative and dispersive processes. Traditionally, the equations have been numerically integrated according to Simpson's or Maclaurin's method, with suitable series approximations for integrating around the poles and extrapolations added to the experimentally limited data set. This implementation is usually performed on a mini or mainframe computer due to the length of the calculation, which scales as the square of the number of data points. However, the advent of 25-MHz 80386 microprocessors and Fast Fourier Transform (FFT) algorithms implemented in powerful array processing languages now allow the KK analysis to be easily performed on personal computers. The application of FFTs to KK analysis is vastly superior in computational efficiency to numerical integration, but quantitative KK analysis incorporates several subtleties, and its implementation is not straightforward. This paper discusses our implementation of quantitatively accurate FFT-based KK analysis on a 80386 processor with a 1-min run time and its performance when applied to a test function consisting of a set of Lorentz oscillators.