## 3 Results
### Proposed Calibration Models  
HoloLens uses its own method for creating a system of coordinates, mapping, and understanding the environment. When opening an application in HoloLens, it uses its position, i.e., its top, side, and front reference, to create its coordinate system. Thus, if the same application is opened with the device pointing to another direction, for example, the coordinate system will be different. Therefore, when it is necessary for holograms to appear in the same location as the physical environment, a fiducial marker (Figure 4) is used as a calibration point to always generate the same coordinate system.  
Figure 3: HoloLens sensors. (1) Environment-understanding cameras. (2) Infrared laser projectors. (3) Depth camera. (4) High-definition camera. (5) Light sensor [13].  
Figure 2: HoloLens sensors. (1) Environment-understanding cameras. (2) Infrared laser projectors. (3) Depth camera. (4) High-definition camera. (5) Light sensor [13].  
When the HoloLens moves through the scenario from a point A to any point B, it uses algorithms for mapping and understanding the world to virtually determine its position in the virtually reconstructed real setting. These algorithms will be called device self-localization. They are proprietary and cannot be modified.  
For use of the glasses in spaces larger than five meters, the documentation provided by the HoloLens manufacturer recommends the use of spatial anchors to stabilize the holograms. That is, when instantiating a hologram in space without using a spatial anchor, it is unstable and, consequently, inaccurate. A spatial anchor is a virtual representation of a set of characteristics extracted from the real world over which the system will maintain control over time, and its objective is to provide a more precise position for the hologram [14]. However, to ensure adequate precision, another important manufacturer recommendation is to always position a hologram less than three meters from a spatial anchor.  
The use of anchors improves accuracy but does not guarantee high accuracy. There are other variables that influence the results of hologram precision and stability in an industrial scenario. One of these is calibration. As previously mentioned, the calibration strategy proposed in this study is the use of fiducial markers. The quality of the recognition of the markers proportions and orientation is indispensable to ensure the correct alignment between the virtual three-dimensional coordinates with their corresponding real three-dimensional coordinates. However, as accurate as computer vision systems may be, distortions in the dimensions and characteristics used to determine the distance and perspective of the marker add erroneous information in the translation and rotation of points in the virtual environment relative to their equivalent location in the real environment. As a consequence, there is incorrect alignment between the holograms of the virtual environment and their corresponding points in the real environment.  
With the objective of mitigating the discrepancy associated with the recognition of the fiducial marker in AR systems developed for HoloLens, in this study a calibration model was developed to address the distortions caused by incorrect recognition of the marker. This model was called two-step calibration and is detailed in the next section.