Novel method to analyse and reconstruct optical constants of biological substances with application of Kramers–Kronig relations

Spectroscopic measurements of dielectric characteristics of biomolecules and tissues is a basis of many modern methods of medical diagnostics, research, and engineering. This requires accurate knowledge about the refraction index, n , and the extinction coefficient, k , at various frequencies, which are usually not available from the literature. Moreover, spectral data often need to be analysed, compared, or verified, especially if obtained for different samples and experimental conditions. The above problems can be tackled with the help of Kramers–Kronigrelations, which are based on fundamental physical principles and can be generally used for arbitrary substances, including complex biological molecules and tissues. However, their direct application for analysis and reconstruction of the optical constants from experiment is hindered by the restricted frequency range of data, the presence of experimental errors, and the prevalence of qualitative rather than quantitative spectra. Our work focuses on the calibration of measured data and the reconstruction of missing spectra. We developed robust reconstruction techniques designed for cases, when disjoint intervals of absorbance data are available, commonly given in IR or/and UV ranges. The techniques hinge on a reference refractive index, given within a certain frequency window and preferably situated in proximity to the absorbance data. The proposed methods are applied to reconstruct the dielectric functions of the protein bovine serum albumine (BSA) and glucose across the entire frequency range. The acquired data are further employed to assess the feasibility of constructing a protein-based coating for implanted antennas. By incorporating spectral characteristics from different frequency ranges into one consistent picture, our methods supply the full information about dielectric response, which is associated with concentration, structure and environment of biomolecules. This provides a mathematical background for combined applications of spectroscopic instruments operating in different frequency ranges that will support fundamental research and stimulate the development of medical technologies. • Methods, based on Kramers–Kronigrelations are developed to reconstruct, calibrate and analyze spectroscopic data. • Methods are applied for disjoint intervals of absorbance data, given in IR or/and UV ranges. • Dielectric functions of the protein bovine serum albumine and glucose are obtained across the entire frequency range. • Our techniques provide a solid mathematical foundation for the combined application of spectroscopic instruments operating in different ranges.