Maximum-likelihood parameter estimation in terahertz time-domain spectroscopy

TL;DR

This paper introduces a maximum-likelihood approach for more accurate parameter estimation in terahertz time-domain spectroscopy, improving reliability and fit assessment over existing methods.

Contribution

It develops a novel maximum-likelihood estimation technique tailored for terahertz spectroscopy, including a simple noise model and application to material characterization.

Findings

Estimates are more accurate than traditional methods.

Provides a reliable goodness-of-fit measure.

Demonstrates effectiveness in material characterization.

Abstract

We present a maximum-likelihood method for parameter estimation in terahertz time-domain spectroscopy. We derive the likelihood function for a parameterized frequency response function, given a pair of time-domain waveforms with known time-dependent noise amplitudes. The method provides parameter estimates that are superior to other commonly-used methods, and provides a reliable measure of the goodness of fit. We also develop a simple noise model that is parameterized by three dominant sources, and derive the likelihood function for their amplitudes in terms of a set of repeated waveform measurements. We demonstrate the method with applications to material characterization.