Multiply subtractive Kramers-Kronig analysis of optical data

We describe a new, multiply subtractive Kramers-Kronig (MSKK) method to find the optical constants of a material from a single transmittance or reflectance spectrum covering a small frequency domain. The MSKK method incorporates independent measurements of n and k at one or more reference wavenumber values to minimize errors due to extrapolations of the data. An unexpected connection between the MSKK equations and the interpolation theory allows us to derive the equations from an interpolation theorem. We found that the locations of the reference points affect the accuracy of the values determined for the optical constants and that the optimal spacing of N reference data points is related to the zeros of a suitably transformed Chebychev polynomial of order N. We discuss our efforts to optimize both the number and the spacing of these reference points and apply our method to some test spectra. (C) 1998 Optical Society of America.