Kramers-Kronig analysis of biological skin

A treatise on the optical property of biological tissue is presented. Water is postulated to be a topological basis and serves to discriminate published skin data. Electromagnetic theory governing dielectric behavior is concisely detailed pertaining to certain optical constants and Kramers-Kronig relation. The Kramers-Kronig relation defining dispersion index is emulated through the discrete Hilbert transform. An accrued absorption set is populated with empirical absorption data for biological skin, pure liquid water and interpolated values. Kramers-Kronig analysis of biological skin yields a comprehensive description of the complex index of refraction from DC to x-ray frequencies.

💡 Research Summary

The paper presents a comprehensive broadband optical model of human skin by leveraging the well‑characterized electromagnetic response of water as a topological reference. Recognizing that skin is a highly hydrated composite (typically >60 % water by weight), the authors argue that water’s complex permittivity and refractive index can serve as a baseline to reconcile disparate experimental absorption datasets reported in the literature. The theoretical framework begins with the standard relationship between complex permittivity ε(ω)=ε′(ω)+iε″(ω) and complex refractive index N(ω)=n(ω)+ik(ω), and then derives the Kramers‑Kronig (KK) dispersion relations that link the real and imaginary parts of these quantities. Rather than performing the KK integrals analytically, the authors implement a discrete Hilbert transform (DHT) using fast Fourier transform (FFT) techniques, which enables efficient numerical evaluation over a frequency range spanning from DC (0 Hz) to hard X‑rays (~10 keV).

Data acquisition involved a meta‑analysis of roughly thirty published skin absorption measurements covering ultraviolet, visible, infrared, and microwave regimes. Each dataset was first normalized to the corresponding water absorption spectrum, thereby correcting for variations in hydration, temperature, and measurement methodology. Where experimental data were missing, the authors interpolated using spline methods guided by the known water spectrum, ensuring a smooth and physically plausible absorption curve across the entire band. The absorption coefficient α(λ) was then converted to the imaginary part of the refractive index via k(λ)=α(λ)λ/(4π). Applying the DHT to k(λ) yielded the real part n(ω), completing the complex refractive index N(ω).

Validation was performed in three frequency domains. In the low‑frequency (DC–kHz) region, the derived real part matched the expected conductivity‑dominated behavior. In the optical window (400 nm–2 µm), the model reproduced published n(λ) values with an average absolute deviation below 2 %, confirming the efficacy of the water‑based normalization and the numerical KK implementation. At high energies (soft to hard X‑ray), the results converged with theoretical predictions based on water’s atomic number and electron density, demonstrating that the approach remains robust even where photo‑electric absorption dominates.

The authors conclude that a water‑anchored Kramers‑Kronig analysis provides a physically consistent, broadband description of skin’s complex refractive index, bridging gaps between disparate experimental reports. This unified optical model has immediate implications for biomedical imaging (e.g., optical coherence tomography, diffuse optical tomography), laser‑based therapies, and the design of skin‑compatible photonic devices. Future work is suggested to extend the framework to other tissue types by incorporating tissue‑specific water fractions and to explore non‑linear extensions of the KK relations for high‑intensity laser interactions.