Let me elaborate.

To make a rail straight you are changing one degree of freedom so by mounting your camera on a rail truck with the laser pointing parallel to the desired path (and obviously intersecting the camera). A simple measure of how far off the centre of the laser beam gives you the amount of displacement of the rail you need to make before the rail is in line with the laser.

Traditionally, to make a surface planar (or two surfaces separated by a gap) you would use a known good plane - i.e. surface plate and a marking out fluid. Blue up the surfaces and use the surface place to rub the marking fluid off the high spots. This then identifies where you need to scrape to bring both surfaces into the same plane. The marking process is essentially in 3D as it extends along the width, length and heigh of the target surface.

Now for the laser plane method. Mount the laser plane generator on the master rail. Set the plane generator up so it is casting a reference plane parallel to the master rail and not at some pitch or roll error. On the slave rail mount the camera on a truck facing the master rail. Now the offset given by the camera from the laser's centre is how much in heigh the slave rail need to be moved. This is one dimension that has been taken care off. Sliding the slave truck (and maybe the laser plane generator as well) along the rail allows you to sample the height difference along the rail. Second dimension taken care off.

The thing I am missing is how the 3rd dimension is taken care off? What we have done is to set the hight of a line on the slave rail to be the same height as the reference plane where it intersects the focal plane of the camera but not that the whole slave rail is in the same plane as the master rail. Looking at it another way we haven't set the roll (looking down the rail) of the master and slave rails to be the same. Is this a second order effect and it unlikely to be outside the planar tolerance of the trucks across the rails?

Maybe this is covered elsewhere in the thread - I have read the whole thread over the months it has been running, but not in one sitting - and I apologise for the repetition in that case.

On a separate note instead of having a fixed laser and rotating (expensive and hard to get) prism why not just rotate the laser? For this application I would have though the advantages of rotating a small piece of glass over a bulkier laser are necessary.

Dave.