I have several friends that make thin sections and we have an informal information exchange. We all use different methods, glues, machinery etc, and all produce good slides. I was never taught how to make slides, but found by trial and error a method that suits my requirements. My machines have been constructed in my workshop, and though crude by commercial standards they work well enough, and cost a fraction of the "standard" ones. All my slides are finished by hand, so any inaccuracy that comes from the machines is eliminated anyway.
So, Starting from a piece of rough rock, a small block 2cm x 2cm x 3cm is sawn by hand on a diamond saw.
The slide/block is sawn as close to the glass as possible using a thin bladed diamond saw. The section is now 1mm to 0.5mm (500 microns) thick.
The slide is now mounted on to the first grinding machine. The slide is retained by vacuum in a slide holder and is held against a rotating diamond flat wheel.
The arm reciprocates to ensure even cutting. This machine reduces the thickness to 200 microns.
The slide is transfered to the second grinding, or flat lap machine.
Using a finer grade diamond disc this can cut to almost the finished thickness, but there is always some score marks left by the cutting process, so the slides are removed when they are about 50 microns. The slide is now ready for hand finishing.
The final stages are done by hand on a glass plate with silicon carbide grit, and repeated checking of the thickness by judging interference colours with the microscope.