Bayesian estimation of optical constants using mixtures of Gaussian process experts

TL;DR

This paper introduces a flexible Bayesian modeling approach using mixtures of Gaussian process experts to estimate optical constants from absorption spectra, accounting for measurement errors and enabling automatic extrapolation.

Contribution

It presents a novel Bayesian Gaussian process mixture model for optical constant estimation that handles measurement errors and automates measurement point selection.

Findings

Successfully applied to gallium arsenide, potassium chloride, and transparent wood spectra.

Improves interpolation and extrapolation accuracy of optical constants.

Accounts for measurement errors in anchor points used in Kramers-Kronig relations.

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.