The Bayeux Tapestry is one of the most famous pieces of medieval art. Our objective is to report on a 3D image processing experiment carried out to test and prepare further dedicated and more systematic observation campaigns. We have tested the capacity of the Structure-from-Motion photogrammetry range imaging technique to compute detailed 3D models of the Tapestry through its protecting window, using a Nikon Z7II full frame mirrorless camera. Tests have been carried out both at the global scale and at the local scale on four scenes, including the Halley comet. We show that 3D details up to the fabric weft level can be obtained locally using this photogrammetry technique, in addition to a global digital model. We have also computed a 3D model of the interior of the nearby Bayeux Cathedral. A Virtual Reality simulation has been created to showcase a subset of the Tapestry inside the Bayeux Cathedral, in order to validate a proof of concept for potential future digital outreach and scientific enhancement projects.