# Kilohertz Pixel-Rate Multilayer Terahertz Imaging of Subwavelength Coatings
###### Abstract  
The acquisition speed of terahertz time-domain spectroscopy systems has undergone a significant improvement in recent years. With the development of dual-laser-based sampling techniques such as ASOPS or ECOPS, waveform acquisition rates in the kilohertz range have become feasible. Here, we present measurements of sub-wavelength layers in multilayer systems at a rate of 1.6 kHz, where the individual layer thicknesses are analyzed in real time. For demonstration, we image layers on metallic and non-metallic disks with a 300 mm diameter, acquiring 240,000 pixels in only 2.5 min. By combining a rotation of the samples with a linear translation of the measurement head, we maximize the measurement yield. Owing to a \"single-shot\" (625 \(\upmu\)s) dynamic range of 40 dB and a bandwidth above 3 THz of the ECOPS system, we achieve sub-micron repeatability for each layer.  
today 2022124964. [[https://doi.org/10.3390/app12104964](https://doi.org/10.3390/app12104964)]([https://doi.org/10.3390/app12104964](https://doi.org/10.3390/app12104964))  
Academic Editor: [PERSON]  
30 March 202211 May  
successive pulses (i.e., the inverse repetition rate), which is typically as long as 1 ns to 4 ns. Only rarely are these systems realized with high-repetition-rate lasers. As the relevant time window in thickness gauging is almost always in the range of tens to about 100 ps, ASOPS systems record massive amounts of \"dead time\" data, inhibiting an efficient duty cycle. Additionally, sampling ASOPS traces at kilohertz speeds calls for readout electronics of very high bandwidths, which drives the cost and compromises the signal quality of these systems.  
These limitations are overcome by introducing a modulation of the repetition rate difference, as realized in an alternative technique, Electronically Controlled Optical Sampling (ECOPS) [12; 13; 14; 15]. In this approach, the length of the sampled time window can be dynamically controlled and adapted to the needs of a specific application. Compared to ASOPS, the requirements for the readout electronics are much less stringent. Consequently, ECOPS-based systems achieve a higher measurement speed and/or a higher dynamic range than their ASOPS counterparts [13].  
On the data processing side, the analysis of sub-wavelength layer thicknesses commonly relies on so-called retrieval algorithms, where a model-based simulation is optimized with respect to its correlation with actual measurement results. As this optimization usually needs to repeat the simulation many times, this method is computationally demanding. Fortunately, in recent years, the computation time of these evaluation algorithms has been drastically reduced. Efficiency improvements included the parallelization of GPUs [16] and, most recently, the implementation of highly efficient CPU algorithms. In this work, we use desktop-grade CPUs in combination with an efficient retrieval algorithm. This hardware and software matches the speed of the utilized ECOPS-based terahertz system, as it is able to convert each terahertz time trace into a multilayer thickness reading in real time.