However, in terahertz time-domain spectroscopy (THz-TDS), the data are in the time domain while the models remain in the frequency domain. Therefore, the multiplication by the transfer function becomes a convolution. As a corollary, the noise becomes correlated. E.g. for a slab sample, the model transforms the reference pulse into several Fabry-Perot echoes, each of them getting the same, consequently correlated, noise. Thus, the weighting function does not apply anymore.
The authors propose here to use so-called maximum-likelihood parameter estimation where the normalization is done using the noise correlation matrix, providing a statistically valid technique to fit THz-TDS data. Furthermore, they derive the Akaike information criterion, which enables the comparison of different models with various numbers of parameters. This will increase the quality of the THz-TDS spectroscopy results, both in terms of the validity of the models and the precision of the parameters.
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