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.
Highlights
At the heart of most applications of terahertz time-domain spectroscopy (THz-TDS) is a mathematical procedure that relates raw THz-TDS waveform measurements to parameters of scientific and technological interest [1,2,3]. This analysis is formulated in the frequency domain, since it provides the most natural description of any linear, time-invariant system of interest
As we found with the idealized Monte Carlo simulations, the residuals of the empirical transfer function estimate (ETFE) fit in the frequency domain are much more structured than the residuals of the TLS fit to the same data in the time domain
By adding only two additional fit parameters, we reduce SETFE by 33, which erroneously suggests that the added complexity of Eq (45) captures a real physical effect
Summary
At the heart of most applications of terahertz time-domain spectroscopy (THz-TDS) is a mathematical procedure that relates raw THz-TDS waveform measurements to parameters of scientific and technological interest [1,2,3]. We describe a maximum-likelihood approach to THz-TDS analysis in which both the signal and the noise are treated explicitly in the time domain, together with a frequency-domain constraint between the input and the output signal. We show that this approach produces superior results to existing analysis methods
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