Artificial neural networks for material parameter extraction in terahertz time-domain spectroscopy

Abstract

Terahertz time-domain spectroscopy (THz-TDS) is a proven technique whereby the complex refractive indices of materials can be obtained without requiring the use of the Kramers-Kronig relations, as phase and amplitude information can be extracted from the measurement. However, manual pre-processing of the data is still required and the material parameters require iterative fitting, resulting in complexity, loss of accuracy and inconsistencies between measurements. Alternatively approximations can be used to enable analytical extraction but with a considerable sacrifice of accuracy. We investigate the use of machine learning techniques for interpreting spectroscopic THz-TDS data by training with large data sets of simulated light-matter interactions, resulting in a computationally efficient artificial neural network for material parameter extraction. The trained model improves on the accuracy of analytical methods that need approximations while being easier to implement and faster to run than iterative root-finding methods. We envisage neural networks can alleviate many of the common hurdles involved in analyzing THz-TDS data such as phase unwrapping, time domain windowing, slow computation times, and extraction accuracy at the low frequency range.

A General Neural Network Model for Complex Refractive Index Extraction of Low-Loss Materials in the Transmission-Mode THz-TDS

“…The dataset is randomly generated beforehand by varying the three variables ( n , k , and ω ) in suitable ranges. For common materials in THz frequencies, the refractive index n is normally smaller than 5 and the extinction coefficient k for low-loss THz materials is normally hundreds of times smaller than n [ 34 ]. Therefore, the range of n and k in the dataset is chosen as (1, 5) and (0, 0.1) in the first step of data generation, respectively.…”

“…A U-net structure neural network was constructed to extract the thickness, refractive index, and absorption coefficient of SiO 2 thin film from the Fourier transform infrared spectroscopy (FTIR) measurement [ 33 ], but it is only suitable for a few semiconductor materials. The artificial neural network method was preliminarily proved to extract the complex refractive index from THz-TDS data with higher accuracy than analytical method [ 34 ]. However, a general and easy-to-implement neural network model is still needed in this area.…”

Machine Learning and Application in Terahertz Technology: A Review on Achievements and Future Challenges

“…Material parameters are difficult to obtain because they necessitate multiple analysis steps, each of which can introduce errors into the calculations. To replace the conventional fitting function, Nicholas et al [124] proposed an efficient neural network for extracting material parameters and estimating the refractive index of the material. The experimental results show that the method can be used to replace the traditional fitting function with high accuracy, speed, and ease of implementation.…”

Derivation of Expression for Photocurrent Density for Non-Destructive Testing of 3d Printing Filament by Means of Terahertz Spectroscopy

“…The objective of this study is to validate the accuracy of the mathematical calculations in the model THz of [1][2][3], as they form the foundation for further research in this field.…”