Polishing is straightforward and proceeds just as in mirror making. Cerium oxide is fine, although in the final stages, good washed or milled rouge works best. Personally, I can't imagine finishing a fine optic without ball-milled rouge. It leaves an incredibly shiny polish, low surface roughness, and much less intense zones than Cerium oxide.
Making milled rouge is easy and though the unmilled stuff is very dirty to use, milled rouge washes off hands readily with soap and is generally much cleaner to use. To make milled rouge you need a rock tumbler and some ball bearings. Please a few teaspoons of raw rouge into the clean tumbler along with 1/2 cup of water and two dozen ball bearings. The bearings can be of various sizes, but don't need to be made of stainless steel. Ordinary steel bearings work just great. Make sure everything is clean and free of gritty particles before you begin.
The container should not be more than about 1/3-1/2 full and should turn fairly slowly maybe at 20 rpm. You should let it go for at least several days or up to two weeks. Make sure that the tumbler seals well and that it does not get hot during the turning. Put the tumbler someplace where it won't bother anyone and let it spin. It may unfortunately leak a small amount, so place newspapers underneath to catch the drips. Rouge stains amazingly well and can be impossible to remove from fabric. Watch out for your clothes and furniture or your wife will be using the rolling pin!
After it finishes, open the tumbler. It will probably smell like rusted steel. Don't worry about that. The milling process breaks the rouge clumps down into very fine particles, which wear the steel balls a bit and in the process make more rouge-like polishing compound. Dilute the mixture and strain it through a sieve to remove the balls and any large particles. Prepare for a big mess at this stage! Wear old clothes and use lots of newspapers to catch drips! Soap will clean your hands and sink.
The balls can be washed and save for future use. The milled rouge should be strained a couple of times and then diluted further and decanted. Texerau discusses the decanting process (called "elutriation") in chapters 2-4 and 2-5 of his book. Decant the rouge a couple of times, trying to collect just the finest particles which should slowly settle out of the water and leave it clear above them. Pour off the excess water and collect a thick mixture of rouge. This can be applied with a brush to your lap once the Cerium polishing is over. You won't need a new lap, since the rouge will gradually overlay the cerium in the pitch and put it out of action.
Before using your milled rouge you should probably test some of it on an extra piece of glass with a pitch lap to make sure it won't scratch. We use milled rouge all the time at work and never have scratching problems. But you should probably test yours first, just in case!
A little rouge goes much further than Cerium. So you won't need gallons of it for your lens. I recommend that you polish out completely with Cerium first and then do several hours of additional polishing with rouge to improve the surface figure and smoothness. The best procedure is to polish out one side completely with Cerium, then stop and protect that side from scratches before polishing out the other side. A good way to protect glass from scratches is to coat it with lacquer or spray paint, and when that's dry to cover it with a layer of masking or wide vinyl tape. Later the tape can be removed and the lacquer/paint removed with a suitable solvent.
Crown glass should polish out fairly rapidly without problems. But keep going till you can hold the surfaces in direct sunlight and not see any scatter in the sun's reflected image. You want a COMPLETE polish for your refractor. Flint glass is another matter. Because of the flint's softness, the residual pits will be deeper than those on the crown. Hence, they will take longer to polish out. It can be maddening how long flint takes to polish out, but maintain your patience and keep going. This lens will last a lifetime and give you many delightful views. Get a complete polish on your glass and you will be happy.
Another way to find residual pits is to shine a powerful halogen flashlight ("torch"), such as the "Magnalite" sold in the USA, at a glancing angle onto your lens surface and examine the surface with a strong eye loupe. Do this in a darkened room. Opticians use a strong focused beam of light to look for pits. The focus is short and the light's filament is imaged onto the surface of the glass. Residual pitting will actually show an image of the filament, if the glass is still moderately gray. Finally, still another way to search for pits is with "dark illumination." If a lens or mirror is carefully positioned over the edge of a table and a light is put beneath shining up through the optic, then a strong eye loupe will reveal the state of the glass that lies just inside the shadow where the direct lighting ends. This can be a dramatic way of examining an optic!
As to the radii of curvature, don't worry too much if you don't reach your target sags quite precisely. Spherometers aren't always accurate to the last decimal, and small sag errors will either not significantly affect the outcome, or they can be corrected in polishing. During the beginning stages of polishing it's often fairly easy to change the lens's radius by several microns. If you discover the need, try to do it then. Later on when the polish is more complete, changes are harder to accomplish.
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