If you want to know more about laser measuring systems... Check out Laser Interferometry. Optics industry uses laser measuring systems like a Zygo interferometer all the time.
There was a machine called the Large Optical Diamond Turning Machine (LODTM) that was once considered the most accurate lathe in the world. It used laser interferometry to determine exact positioning down to angstroms. Kind of how modern machines can use scales to extract true position in a closed loop system.
Funny, You reminded me that a good majority of commercial diamond turning machines are based in the US. Namely Moore Nanotech and Precitech.
Hexagon is a huge conglomerate that owns reputable brands like Brown and Sharpe, Etalon, and Tesa.
I voted Mitutoyo as that's what we have most of but swiss premium really does stand out. Etalon is top top end but they make only a select variety of measurement tools. And unfortunately Brown&Sharpe is slowly falling towards the Starret line (lower quality, value focused items).