Dresden 2026 – scientific programme
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DS: Fachverband Dünne Schichten
DS 20: Poster
DS 20.35: Poster
Thursday, March 12, 2026, 18:30–20:30, P2
A Kramers-Kronig Consistent, Parameter Free, Probabilistic Dielectric Function Model — •Noah Stiehm1, 2, Stefan Krischok1, Rüdiger Schmidt-Grund1, and Jana de Wiljes2 — 1Technische Physik I, TU Ilmenau, Germany — 2Mathematics of Data Science, TU Ilmenau, Germany
Utilizing a Bayesian probabilistic modeling approach to approximate the full posterior probability density p(θ | y) of a model’s parameters θ given data y can provide greater insight into the model’s performance and parameter uncertainties than point estimates provided by classic, deterministic optimization algorithms.
Here we present a parameter free dielectric function model, that might be used in a Bayesian modeling context as a substitute for the well known B-spline models. Our approach is based on Gaussian processes (GP), which are a flexible class of random functions, that enable numerical sampling in an efficient manner. We utilize a GP to model the time-domain response function χ(t − t′) as a latent function, from which the dielectric function ε(ω) is constructed via a discrete Fourier transform. The resulting dielectric function is therefor Kramers-Kronig consistent by construction. We implement approximate and exact (depending on available compute resources) sampling strategies to include our model in different Bayesian modeling frameworks which utilize either Markov Chain Monte Carlo (MCMC) or particle filter methods. We demonstrate our model’s performance in scenarios with significant uncertainties: a sample with a concentration gradient of a AgAl alloy, and pump-probe transient ellipsometry data.
Keywords: ellipsometry; Bayesian; modeling; probabilistic; software