@article {Ohta:1988-08-01T00:00:00:0003-7028:952,
author = "Ohta, Koji and Ishida, Hatsuo",
title = "Comparison Among Several Numerical Integration Methods for Kramers-Kronig Transformation",
journal = "Applied Spectroscopy",
volume = "42",
number = "6",
year = "1988-08-01T00:00:00",
abstract = "Several numerical integration methods are compared in order to search out the most effective method for the Kramers-Kronig transformation, using the analytical formula of the Kramers-Kronig transformation of a Lorentzian function as a reference. The methods to be compared involve the
use of (1) Maclaurin's formula, (2) trapezium formula, (3) Simpson's formula, and (4) successive double Fourier transform methods. It is found that Maclaurin's formula, in which no special approximation is necessary for the pole part of the integration, gives the most accurate results, and
also that its computation time is short. Successive Fourier transform is less accurate than the other methods, but it takes the least time when used without zero-filling. These results have important relevance for programs used to obtain optical constant spectra and to analyze spectral data.",
pages = "952-957",
url = "http://www.ingentaconnect.com/content/sas/sas/1988/00000042/00000006/art00003",
doi = "doi:10.1366/0003702884430380",
keyword = "Optical constant spectra, Kramers-Kronig transformation, Numerical integration"
}