Measurement comparison among time-domain, FTIR and VNA-based spectrometers in the THz frequency range

Abstract

In this paper we present the outcome of the first international comparison in the terahertz frequency range among three different kinds of spectrometers. A Fourier-Transform infrared spectrometer, a Vector Network Analyzer and a Time-Domain Spectrometer have been employed for measuring the complex refractive index of three travelling standards made of selected dielectric materials in order to offer a wide enough range of parameters to be measured. The three spectrometers have been compared in terms of measurement capability and uncertainty.

Metrology of complex refractive index for solids in the terahertz regime using frequency domain spectroscopy

“…We start by modelling these experimental limitations using simple extensions to our model data presented in previous sections, and thereafter apply the algorithms to real experimental data for a practical comparison. By doing so, we gain an insight into the real limitations on refractive index extraction in contemporary settings comparable to travelling standard analysis [10].…”

Metrology of complex refractive index for solids in the terahertz regime using frequency domain spectroscopy

“…The simplest set of methods by which we may extract ̂ relate the frequencies ± of local maxima ( + ) or minima ( − ) to the refractive index, from which a family of algorithms arises which we denote "fringe" methods [10] [21]. By inspection of the periodic term in the denominator of Eqn.…”

“…1, it is straightforward to show that + and − satisfy; The integer = 0,1,2 … is called the order of the fringe, and these relations imply that the real part of the refractive index at any point ± may be deduced if is known absolutely, and is known or negligible. If the absolute order is unknown, it may be determined by linearly extrapolating a section of a graph of ( ) to = 0 ("extrapolation" methods) [10], or may be eliminated by taking the difference between successive peaks ("peak-difference" methods) [21]. These techniques inherently assume that is a constant, at least locally, which results in strong systematic errors.…”

“…Different experimental equipment can address different spectral regions, with vector-or scalar-network analysis appropriate for the ~100 GHz range [7], Time Domain Spectroscopy (TDS) for the ~3 THz range [5], and ellipsometry across the spectrum (especially close to ~100 THz [8] [9]) all being independently studied, where differing considerations and terminologies apply. In addition, recent experiments in terahertz travelling standards and instrumental intercomparisons [10] have highlighted the utility of Fourier Transform Infrared spectroscopy (FTIR) techniques as a calibration cross-check with sufficient bandwidth to be an effective comparison for all other methodologies. Continual improvement of the metrology surrounding FTIR techniques is therefore of direct relevance to the general effort of optical parameter characterization in the terahertz regime.…”

“…Historical literature for extracting optical constants from the Fabry Perot interference in FDS (FP-FDS) is plentiful [15] [24], but has ignored many of the systematic errors implicit in extraction techniques. Indeed, even comprehensive recent studies [10] [22] leave the sensitivity of their methods uncharacterized. Additionally, the reliance upon physical artefacts for intercomparison purposes leaves us comparatively ignorant about deviations of our measurements from the actual physical constants, either due to noise or systematic errors.…”