Pilsu: Quality and color are probably going to be two different (if often closely related) questions, though.
There are, ofcourse, many different levels of filtering and refining, from the crude removal of impurities (separating sticks, rocks, dirt, organic matter; from a substance we would recognise as "sand"), and the not-so-crude purifying of that sand, to highly sophisticated adaptations, like lens glass, ballistic glass, or optical fibre.
It seems (to me) like it should be possible to-more or less-refine sand to a point where it becomes a basic, but very high quality material, for adding many different colors and other attributes to. What level of refining a DF alchemist of whatever skill level is capable of, is ultimately going to be up to Toady.
Color, on the other hand, is more likely to remain relatively constant, provided the chemical composition is identical--regardless of whether you're talking about a master glassblower intentionally coloring a flawless crystal goblet, or a lightning bolt accidentally coloring a chunk of half melted desert silt.
The crude shards of green bottleglass you can find scattered under a freeway bridge, and the fine Gibson uranium glass you might find in a gallery, are both recogniseable as green glass.
Again, the *quality* of that color--the purity, clarity, richness, depth--can be affected by refinement and adaptation of the ingredient substances, and the processes we put them through, but those are probably going to be slightly separate ingredients and processes, for each individual shade and hue.