Accuracy of extracted optical conductivity by Kramer-Kronig analysis from reflectivity spectrum

Kramers-Kronig (KK) analysis has been widely used to extract the optical conductivity spectrum from a broad range of reflectance spectrum obtained from far-infrared to ultraviolet frequency ranges. In this study, we present how measurement uncertainty in the reflectivity spectrum affects the extracted optical conductivity spectrum obtained through KK analysis. We consider realistic uncertainties that can easily occur in reflectance measurement environments: (1) a rigid shift of the absolute reflectance in the whole measurement frequency window, and (2) a linear decrement of reflectance with increasing frequency. Our investigation reveals that the reliability of the extracted optical conductivity spectrum, especially in the lower-frequency range, should be carefully addressed, particularly when the reflectance is above approximately 95 %.