Calculation of integral singularities in Kramers-Kronig relations

When Kramers-Kronig relation is applied to solve absorption coefficient and real refractive index of materials, how to deal with integral singularity exerts great influence on the accuracy of these two optical parameters. We proposed a nonlinear interpolation method to deal with singularity of the integral, and compared it with commonly used average value method and L’Hôpital’s rule method. It was found that the average value method and L’Hôpital’s rule method were suitable for slow changes in optical parameters, while non-linear interpolation method was applicable both for slow and rapid changes. Water vaporcal culations showed that the maximum error in real refractive index by average and L’Hôpital’s rule methods was 5%, while the error by nonlinear interpolation method was less than 1.5%.