I've used similar to centre tools on a diamond turning lathe. The scope was rigidly mounted near the headstock and I knew the distance from the microscope cross hairs to the spindle centreline. I recorded the X value when the tool was at the crosshairs set X0, move the distance from crosshairs to centreline and reset X0.
It was also handy to set the tool height by focussing on the tool cutting edge.
Finding the distance from the scope to the spindle centreline I achieved by pointing another microscope at a flat I'd cut and rotating it to find the centreline. I then racked this scope across to the first one and recorded the X value when it focused on the crosshairs. This was the distance from scope 1 to the spindle centreline.
My system was a homemade job, so professional ones will probably be better, but the principle will be the same.
I love deadlines- I like the whooshing sound they make as they fly by.