# Kilohertz Pixel-Rate Multilayer Terahertz Imaging of Subwavelength Coatings
## 2 Materials and Methods  
The terahertz measurement system used in this work is the commercial ECOPS-based platform \"TeraFlash smart\" from TOPTICA Photonics. It consists of two synchronized femtosecond lasers that emit laser pulses at a wavelength of 1.56 um and repetition rates of about 80 MHz. The pulse duration at the end of the external fibers is about 80 fs. Employing the ECOPS scheme, i.e., precisely controlled repetition-rate tuning, the system achieves a measurement rate of 1.6 kHz for terahertz waveform windows of 160 ps length. In our work, the data acquisition unit of the ECOPS system is connected to a desktop-grade personal computer (PC) with a 10-core Intel(r) Core(tm) i9-10900X CPU. This PC acquires and analyzes the data, and it controls the rotation/translation stages (see below). The layer-thickness analysis is based on a retrieval algorithm [1; 3; 16], where a simulation result is optimized towards the actual measurement to obtain the sought-after thickness values. The model of the simulation is based on [PERSON]'s method [17], which outperforms other methods such as the transfer-matrix method in terms of calculation speed. A combination of multiple methods is used for the optimization routine, the individual layer thicknesses being the free parameters of the simulation. By parallelizing the analysis on several CPU cores, we achieve an evaluation rate of several kilohertz. This enables data analysis at the full rate of the ECOPS system, i.e., at 1.6 kHz, which is the measurement speed employed throughout this work. The optical configuration consists of a standard terahertz reflection setup: The terahertz emitter and detector modules [18; 19; 20] are mounted in a compact assembly (\"terahertz measurement head\", see Figure 1), where four off-axis parabolic mirrors with a diameter of 25.4 mm guide the beam onto the sample under test and back onto the receiver. The divergent terahertz radiation from the emitter is collimated using an off-axis parabolic mirror with an effective focal length (EFL) of 50.8 mm. A second mirror with an EFL of 101.6 mm focuses the radiation onto the sample surface. After reflection, another pair of mirrors with EFLs of 101.6 mm and 50.8 mm, respectively, recollimates the beam and focuses it onto the detector. The samples consist of metallic (aluminum) and non-metallic (polycarbonate) disks, each with a diameter of 300 mm, that are spray-coated by hand so that multiple layers are added. An aluminum mask with six cutouts serves to imprint a predefined structure in one of the layers. To this end, the first layer on each sample is produced in two steps: First, a uniform layer is applied without any mask and then, after a short drying phase of approx. 10 min, a second layer of the same coating is added, now with the chopper-blade-like mask in place. These steps imprint a \"negative\" of the mask in the thickness of the first layer. This artificial feature in the thickness of the layer permits a visual consistency check of the thickness results. In the example of the metallic disk, the second and third layer features a metallic base coat and a clear coat, respectively. In contrast, the non-metallic disk is only coated with the metallic base coat and the clear coat, omitting the filler layer. Imaging of the sample is realized in a fashion similar to the setup of [PERSON] et al. [21], where a sample was measured while it was both spinning and being translated. Slightly modifying this concept, we use a spinning sample together with a translation of the measurement head. The disk sample is mounted on a stepper motor with a rotation encoder providing 2000 increments per turn. Given the dimensions of the disks, this corresponds to a spatial resolution of about 0.47 mm on the outside of the disk and even less for smaller radii. The measurement head itself is mounted on an additional linear stage that radially moves the focal point of the terahertz beam across the disk. The combination of the two stages yields a spiral trajectory for terahertz imaging.