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An algorithm is presented for the calculation of the Kramers-Kronig transform of a spectrum via a piecewise Laurent polynomial method. This algorithm is demonstrated to be highly accurate, while also being computationally efficient. The algorithm places no requirements on data point spacing and is capable of integrating across the full spectrum (i.e. from zero to infinity). Further, we present a computer application designed to aid in calculating the Kramers-Kronig transform on near-edge experimental X-ray absorption spectra (extended with atomic scattering factor data) in order to produce the dispersive part of the X-ray refractive index, including near-edge features.

Calculation of the Kramers-Kronig transform of X-ray spectra by a piecewise Laurent polynomial method