Quantitative analysis of optical parameters using THz-TDS

Terahertz Time Domain Spectroscopy gained much popularity in recent decades due to its broadband range and high signal to noise ratio. Researchers have already started working rigorously on all aspects of this domain from developing spectroscopy for getting high-resolution signal to extracting other indispensable information out of gas molecules and biological samples. In this study, I have emphasize the use of this powerful THZ-TDS technique to extract information in a quantitative approach. We have shown that the sensitivity of our spectroscopy can be estimated by measuring the concentration of a sample. This has been demonstrated through a physical model applied on both solid samples as well as on gas sample. In addition, knowing that several convolutional mathematical physical modelling are being exploited in order to acquire better precision but less work has been done on measuring the uncertainty on the parameters extracted from these mathematical modelling. In this study, I have also attempted to visualise uncertainties on optical parameters of lactose sample extracted through Lorentz model of electronic dispersion. This is achieved by numerically evaluating Hessian matrix, which is a second order partial derivatives of the function at optimised parameters. Subsequently, the standard deviation is computed by taking diagonal elements of inverse of this Hessian matrix. This uncertainties are shown using error bars on real and imaginary part of refractive index of lactose sample.