Polishing with pads.
If you're lucky, you may have a shop near you that actually makes lenses for eyewear but that's not a guarantee as not all optometrists bother to make their own lenses. Wholesalers for the trade sell a roll of pads for about $20-$30 containing 300 or so of the self-adhesive pads on a carrier strip. Each pad is about 2" x 3" (best shape for us as you can butt them together - there are also round pads but those won't provide as much working surface) in size and are shaped like an 8 petal flower in a somewhat rectangular shape. If you're just going to do one mirror and want to try the pads method of polishing your mirror, you might want to find somebody who is using the pads and finagle a few out of him for your use. The alternative is to get the eyeglass maker to give or sell you a few for your use or just buy a whole roll and resell the remainder to someone else, either as the roll or what they will need to cover their tool. Places like GotGrit.com also have pads in the quantities needed if you want to go that way.
Pads are a moderately quick way to get the mirror polished in quick order. The problem that I have seen with the pads is that the figure is not very good although it takes only a little time to get the mirror to a spherical shape when you go to the pitch lap to do the finishing of the mirror. Getting the glass polished first is the biggest chore and the use of pads helps as your pitch lap won't be deformed by the extensive polishing that is needed to get a good polish. I might also note that I have never seen anybody successfully figure a mirror with pads although one attempt got to about 1/5th wave on the wavefront was obtained by an individual. The figure was just to jumpy in it's movement to finish up to at least 1/10th wave surface that I ask for.
You start by applying the pads all over the tool (make sure the tool is good and dry and clean), insuring that they are in good adhesive contact with the tool and are applied smoothly. Insure that the pads are well pressed down as they may come loose if water gets underneath them and allows them to move about. What I normally do is put the (tile) tool in the microwave oven and heat it up after making sure that the face is completely clean of any water, dirt or oil and then apply the pads on that hot, dry surface which will allow the adhesive to work better. Just as soon as all the pads are on, I press the mirror onto the tool and wait for things to cool a bit. The heat will allow the adhesive on the pads to "melt" and thus allow the pads to conform to the curve of the mirror a bit more than without the heat.
You then spread some Cerium Oxide and water mix over the pads and start polishing. Don't put too much on as the Cerium Oxide can overload the pads. If the tool surface itself is holding Cerium Oxide, you have probably put a bit too much on. Also, make sure that the pads are kept good and wet. If the appearance of the pad surface is shiny then you don't have enough water on the pads. While polishing, you want to make sure that the mirror surface has some CeO on it as you pass over the surface. When you can't see any CeO on the mirror, it is time to add more. You will also notice that just before the water dries up from the surface, the forces for polishing are quite high. This is the region where polishing is the strongest providing that there is CeO being left on the mirror.
The nice thing about this method is that you can indeed go fast with the strokes and even hang over side to side more than you would with a pitch lap. Don't go so far that you end up tilting the mirror off of the lap or you will, naturally, scratch the mirror in the process. Applying heavy pressure also seems to work well with this process. Don't forget to rotate the mirror and walk around the barrel as you do the polishing. Also, don't forget to change the length of your stroke and work the mirror at different offsets from COC. I haven't seen anybody actually do a badly turned down edge with the pads so if anybody learns how to do a good spherical surface and then parabolize the mirror with pads, the pitch method will probably become obsolete as the method of finishing a mirror.
If you find that you're having a problem with polishing out the edge, flip the mirror and tool and continue. You will want to do it that way long enough to insure that you have a good smooth surface of one basic radius when doing this so keep polishing. About the same amount of time that you spent with the mirror on top should do it. If your final stages of grinding were properly spherical, the edge should polish out almost as fast as the center. Since pads don't "move" like pitch does, the curvature of the mirror isn't going to change signifigantly as you work.
After you have gotten a good polish, put the mirror on the test fixture and see what the shape looks like. If the whole mirror is properly polished, you will see a nice dark surface over the whole surface when the light surface is fully cut off. If you see a bright center or edge and it looks fuzzy, it's not fully polished out and you're seeing the scatter from the pits remaining. You may want to put the glass in the tester setup just to see this effect before the glass is fully polished out so you can see what I'm talking about. You will probably see all kinds of strangeness in the shape with the Foucault test, including some or even most of the following: Central Hole/Hill, Depressed or Raised Ring(s), Strange Steps in radius and others. It is always interesting to see what shapes are generated by the pads and the interestingly, the shapes aren't guaranteed to be the same on several mirrors done on the same set of pads. Don't worry about the shape of the mirror at this point other than to insure that you don't have a turned edge. This can happen somewhat but usually won't as pads don't change their ROC like pitch does as you work them. If you find big differences over a fair part of the mirror, go back to the pads and change your stroke length and offset from the center to get rid of the particular pattern that you have developed. It might be noted here that regular strokes do tend to make the zone problem look worse as the pads aren't all that even in their height.
After you have gotten the mirror fully polished out, it's time to go and make the pitch lap and finish up the mirror with smoothing out the surface and then figuring the mirror.