Focal length and physical sensor size of a lens affect the resulting viewing angle - the FOV. Thus, it is possible to change the working distance to the scanning object for each FOV within a pretty wide range by changing the lenses.
However, practice shows that the boundary values for the whole set of FOVs is the minimal distance of 30-35 cm for the FOV #3 (not every projector can be focused at this or smaller distance) and the maximum distance of 100-120 cm for the FOV #1 (projected image brightness is significantly lower at this distance and the scanning process becomes less convenient, as a lot of empty space around the scanning object is required).
Recommended distance between the cameras is equal to one third of the working distance to the object - this results in approx. 20 deg angle between optical axes of the cameras when they are positioned symmetrically on both sides of the projector.
For the common 1 / 2” sensor size for all FOVs 12 mm or 12.5 mm lenses will work. Resulting working distances will be approx. 30 cm, 60 cm and 100 cm in that case.
For 1 / 1.8 “ sensors 12 mm lenses will work as well, but the FOV #3 (S) will result in a working distance which is smaller than the projectors focal length - approx. 27 cm. In that case use 16 mm lenses.
Use the following recommendations to select a projector model:
Pick the throw ratio so that the size of projection at the working distance to the object is approx. equal to the cameras view area - this way the effective resolution of cameras is not wasted. E.g. for the cameras and lenses configuration 1 / 2” + 12 mm: