Computationally efficient multi-layer thickness determination using sparse CW THz spectroscopy

Continuous wave (CW) terahertz spectroscopy systems are a proven and convenient solution for industrial non-destructive testing and multi-layer thickness determination. For these systems to find use in real-time inline monitoring applications, a high acquisition and data evaluation rate is required. One approach that can increase and potentially enable kHz acquisition rates is to scan through only a few selected frequencies instead of a full spectrum. However, the data analysis can become a bottleneck when realizing measurement systems capable of operating at these speeds. Here we show the feasibility of extracting multi-layer thicknesses from a sparsely sampled spectrum by using a real-time evaluation scheme capable of runtimes below a millisecond with a thickness uncertainty comparable to a full spectrum evaluation. This is achieved by reducing the number of computations by three orders of magnitude. The proposed measurement scheme requires complete knowledge of the sample composition and the refractive index of each layer. Additionally, achieving these high evaluation rates assumes that individual layer thicknesses deviate by no more than 200 µm from their nominal values. However, both conditions are often met in an industrial setting. The sparse evaluation is demonstrated on a three layer sample, the achieved standard deviation of the layer thicknesses remains below 5 µm for each layer. These measurements confirm the effectiveness of the sparse sampling approach for THz spectroscopy and demonstrate the ability to address industrial applications with measurement rates in the kilohertz range.