Problem
Research questions and friction points this paper is trying to address.
optical constants
absorption spectrum
Kramers-Kronig relations
refractive index
measurement error
Bayesian estimation of optical constants using mixtures of Gaussian process experts
🤖 AI Summary
This work addresses the challenging problem of estimating complex refractive indices from limited and noisy absorption spectra, particularly when extrapolating beyond measured wavelengths and accounting for uncertainty in anchor points required by subtractive Kramers–Kronig relations. To tackle this, the authors propose a Bayesian approach based on a mixture of Gaussian process experts, which flexibly models spectral structure while explicitly treating anchor-point errors in a probabilistic manner. The framework further leverages Bayesian inference to automatically select optimal measurement points, thereby enhancing extrapolation accuracy. Experimental validation on gallium arsenide, potassium chloride, and transparent wood demonstrates that the method achieves high precision and robustness, significantly outperforming conventional techniques—especially in reliably reconstructing optical constants in extrapolated spectral regions.
📝 Abstract
We propose modeling absorption spectrum measurements as mixtures of Gaussian process experts. This enables us to construct a flexible statistical model for interpolating and extrapolating measurements, facilitating statistical integration of Kramers-Kronig relations to estimate the whole complex refractive index. Additionally, we statistically model the anchoring points used in subtractive Kramers-Kronig relations to account for possible measurement errors of the anchor point. In addition to flexible statistical modeling, the mixtures of Gaussian process formulation enables automatic selection of measurement points to use for extrapolation. We apply the method to experimental absorption spectrum measurements of gallium arsenide, potassium chloride, and transparent wood.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Gaussian process mixtures
Kramers-Kronig relations
optical constants estimation
Bayesian inference
spectral extrapolation
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