Abstract
A novel parametrically efficient approach to estimating the spectra of short transient signals is proposed and evaluated, with an application to estimating material properties, including complex refractive index and absorption coefficient, in the terahertz frequency range. This technique includes uncertainty analysis of the obtained spectral estimates, allowing rigorous statistical comparison between samples. In the proposed approach, a simple few-parameter continuous-time transfer function model explains over 99.9% of the measured signal. The problem, normally solved using poorly numerically defined Fourier transform deconvolution methods, is reformulated and cast as a time-domain dynamic-system estimation problem, thus providing a true time-domain spectroscopy tool.
Highlights
The terahertz (THz) frequency range is commonly defined to lie between 0.3 and 10 THz, and corresponds to a range of fundamental material properties including: low frequency chemical bond vibrations, crystalline phonon vibrations, hydrogen-bond stretches and torsion motions [1]
To ensure that none of the reflection pulse was included in subsequent analysis, the data was truncated prior to this point resulting in 760 data points each separated by 6.7 fs
This in turn implies that using spectral estimation techniques with more complicated parametrization, such as Fast Fourier Transform (FFT) based methods, will not produce a significantly better fit, and will more likely result in increased error and poorly defined results
Summary
The terahertz (THz) frequency range is commonly defined to lie between 0.3 and 10 THz, and corresponds to a range of fundamental material properties including: low frequency chemical bond vibrations, crystalline phonon vibrations, hydrogen-bond stretches and torsion motions [1]. THz time-domain spectroscopy (THz-TDS) is becoming an established technique for substance identification and for obtaining material parameters in the form of the refractive index and absorption coefficient spectra of a broad range of samples, including small molecules [2], [3], [4], biological samples [5], [6], and semiconductors [7], [8]. THz-time domain data often takes the form of a single pulse, less than a picosecond in duration, followed by a series of attenuated pulses arising either from reflections at the interface of components within the TDS system, or from etalon reflections within the sample itself. To extract spectral estimates purporting to the sample alone, the reference signal must, be deconvolved from the second signal. The goal of spectral estimation, in this case, is to describe the distribution (over frequency) of the power contained in a signal (the power spectral density, PSD), based on a finite set of data
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