# Retro-Reflective-Marker-Aided Target Pose Estimation in a Safety-Critical Environment
## 2 Methods
### Retro-Reflective Marker Design
A retro-reflective marker can consist of a single shape or an array of retro-reflective shapes of smaller dimensions. The advantage of an array-based pattern is that the depth of the marker can be smaller and the shape of the overall retro-reflective region can be tailored. Furthermore, whilst the shape of the retro-reflective area changes with viewing angle for single-shape retro-reflectors, for those composed of arrays of small elements, the shape is independent of the orientation of the marker. On the other hand, such a construction might be more difficult to implement, as it requires a more precise manufacturing process with tighter tolerances. In a preliminary study conducted to determine the viability of off-the-shelf retro-reflectors for use in ITER, we found that the only viable solution belonged to the single-element prism category (Edmund Optics BK-7 glass prism). No ready-made markers were found in the corner-cube array or bead array categories that could be used in our application. Therefore, we propose a custom-made solution consisting of an array of glass beads. Such beads are often used within paint or attached via adhesive to other materials (e.g., paper or plastic). Due to the restriction of using adhesives and pains in ITER environment, the main challenge of using a bead array in our application is their attachment to the surface of the cassette. For this purpose, we propose a custom sieve-like metal holding structure that can hold the beads in place and can be easily mounted into the cassette surface, as illustrated in Figure 2.  
Another potential challenge to this approach is that the retro-reflectance of glass beads is quite sensitive to their refractive index (n) [33], and the refractive index of fused silica (\(SiO_{2}\)) is relatively low when compared to other glass compositions (\(n_{SiO_{2}}=1.4585\)). In fact, if we consider the simplest case of a single specular internal reflection from the back of the silica sphere, we can calculate a divergence value of \(\pm 25\) degrees as follows [34]:  
\[\theta=2\ sin^{-1}\left(\frac{h}{r}\right)-4\ sin^{-1}\left(\frac{h}{n*r} \right)\,, \tag{2}\]  
where \(h\) represents the incident height, as shown in the left side of Figure 3, and \(r\) represents the radius of the glass bead. In the right side of Figure 3, we show the calculated divergence as a function of the \(h\) value. This divergence is higher than required, leading to some loss of intensity. Therefore, this design serves the purposes of the application, even if it does not fully optimize brilliancy at the observation angle. In Figure 4, we illustrate our proposed bead array marker design side by side with the out-of-the-box glass prism, a white diffuse element, and the commonly used bead-based retro-reflective tape that cannot be used for the application, but serves as a reference for a behavior that would be desirable. The alternative of manufacturing a stainless steel hollow corner-cube array could technically be implemented and would have the advantage of being made from a single piece and a potentially larger reflective area. However, while many methods are described in the literature for manufacturing corner-cube arrays [32] on both the micro and macro scale, the commercial availability of such methods is still limited and a suitable manufacturer could not be found. Some customized manufacturing methods were considered, mainly consisting of producing a strong enough inverse tool that could emboss the desired pattern onto a stainless steel piece using a hydraulic press. The advantage of this approach would be the flexibility of producing multiple marker specimens at a fixed cost and the fact that the markers could be a single piece made from a single material. However, a suitable method for manufacturing the pressing tool proved hard to find. We considered manufacturing  
Figure 3: Incident height (\(h\)) and divergence (\(\theta\)) of light in a retro-reflective bead. Figure 2: Retro-reflective bead array marker housing. by electrical discharge machining (EDM).