Glass Scratch Removal - How does it work?

Glass polishing or glass scratch removal is a multi-stage process: Here is an abbreviated description:

1) The first phase involves taking off a thin layer of glass surrounding the scratch, just enough until you have reached the bottom of the scratch. The scratch will now disappear because the remaining glass is totally flat. However, the rough abrasives used to remove some of the glass also leave fine scratches of their own

2) The second phase involves gradually step by step removing the damage caused by the previous step. This is done with going over the area with perhaps two or three progressively finer abrasives. Once this phase is completed, we are left with scratch-free, yet frosty (= opaque, milky) looking glass.

3) The third and last phase involves the actual "polishing", meaning bringing back the crystal clear transparency of the glass. This is a partly a mechanical, partly a chemical process using a polishing compound that contains cerium oxide. 

4 Last and certainly not least, what is left is the CLEANUP