Deep Learning for Scattering Robust TeraHertz Time Domain Spectroscopy

The complex frequency-dependent electromagnetic physics on rough samples is prohibitive for analytical and even numerical minimization based material extraction methods for THz time-domain spectrometers. To deal with such nonlinear complexity, we resort to machine learning (Gated Recurrent Unit, GRU) alongside 3D printing and automatic THz time-domain imaging to demonstrate the ability to extract the complex refractive index of materials from transmission measurements without prior knowledge of the sample's thickness or the surface roughness properties, even in regimes where perturbation theory is not valid. The machine learning methodology is first validated with smooth samples of varying thicknesses from five types of indoor materials (wood, engineered wood, plastic, stone, and glass); mean squared error for these smooth samples is in the range of 10<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{-5}$</tex-math></inline-formula> to 10<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{-6}$</tex-math></inline-formula>, which is at least one order of magnitude lower than that of convolutional neural network and linear models trained with the same number of epochs. Then, three different 3D printable materials are used to construct 12 rough samples with spatial correlation length of 0.2mm (drawn from Gaussian or exponential distribution) and root mean square surface roughness varying from 0.2 to 0.4mm. While a numerical minimization based extraction algorithm fails to provide good results, the GRU successfully retrieves the material properties of the sample with mean squared errors for these rough samples still in the range of 10<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{-5}$</tex-math></inline-formula> to 10<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{-6}$</tex-math></inline-formula>, again outperforming convolutional neural network and linear models proposed in the literature.