I bought some cerium oxide polishing compound, made for polishing glass. Went up to the local Harbor Freight and bought some cotton polishing pads, they were large cone shaped and put on a drill motor. You have to keep the polishing compound wet when doing the job, keep a spray bottle handy when polishing. You have to keep it wet and you must keep moving. Stay in one spot to long and it will build up heat and could possible crack the glass. Takes time but it will remove the fine scratches. If you can feel it with your finger nail as stated earlier, the best you can do is shine it up a little without distorting the glass. Take your time and good luck.