To properly mount a small achromat is not hard, but it is different from mounting a mirror. Lenses by their nature are resistant to damaging flexure, unlike mirrors. Astigmatic images are unlikely to occur unless the lens has either been badly ground or polished, or it is being violently pinched in its cell. Tube currents too can often induce wavefront errors that look like astigmatism. That's one reason why all amateur refractors, just like all amateur reflectors should be equipped with fans on the sides of their tubes. Even if your tube is sealed and unventilated, the fan will mix the air inside the tube and destroy slow moving temperature gradients which cause tube currents.
Defective grinding and polishing shouldn't occur unless you have worked carelessly and in haste, not heading the warnings often given to mirror makers about turning their optics every 15 minutes or so on the grinding stand. But those who have never mounted a lens may not realize the importance of not constraining it too tightly in its cell. Before you mount your lens, I strongly urge you to have a look at H.D. Taylor's "The Adjustment and Testing of Telescope Objectives," (Newcastle upon Tyne, 1946), chapter 9 ("Mechanical Strains"). This invaluable book will show you the proper way to mount your masterpiece.
Once you finish polishing and testing your lens, you should wash it carefully and blacken its cylinder walls with a good permanent marker. This may help to reduce stray reflections inside the lens and is a standard practice in the optics industry. You might want to let one set of the numbers on your lenses remain visible, so that whenever you clean the lens you can reassemble it correctly without trouble. Next you will want to install the 3 permanent postage stamp spacers around the R2 or R3 edge. You might also want to carefully blacken the non-gummed side, though this is perhaps splitting hairs. Still, it will impress others if they look at the front of your lens in its tube and see the tiny blackened spacers. They'll know that they're dealing with a serious ATM! Put the R4 of the flint down on a soft cloth; brush of the R3 and R2 of the crown with a soft cotton cloth (old tee-shirts, clean and well laundered are excellent wipers and dryers of optics), wiping away any particles carefully. Then quickly invert R2 and gently lower it onto R3. Try to make contact on one of the spacers and don't play the castanets, as opticians say, by clinking the glass together! It would be a shame to break a lens at this point! Now your pride and joy is together. You might want to put one or two bands of cellophane tape around its edge to keep it that way. But don't pull hard on the tape! Be gentle to your glass always.
Nowadays a metal cell is not essential to hold an achromat. If the blanks have been turned accurately round, then a plywood cell can work just fine. In this case edges of the lens should be taped together so that the assembled unit can be held in a cleverly contrived wooden ring of some sort. I leave it to the ingenuity of ATMs to devise their own cells. One source of inspiration might be the cell which Richard Berry built for his own achromat some years ago, detailed in "Build Your Own Telescope," (Scribners, 1985), chapter 8. My only reservation with this cell is that RTV never comes completely off glass and it's a shame to get any on the edges of an expensive achromat. Different spacers and O-rings might do just as good a job. But it's your glass!
A last word of caution on this subject. A well-made metal cell, black anodized and lightweight is a great joy for holding an achromat. If you can find a good machinist willing to make one, then I heartily recommend it. But if not, then get out the saw and the router! Read Taylor first to see what's needed. Principally, you don't want to pinch the lens by constraining it too tightly. A mirror that jostles around in its cell is a nuisance. It never stays in collimation and you constantly need to adjust it. But a lens SHOULD jostle just slightly. A few thousandths of an inch of play, so that the lens audibly shifts in its cell when you shake it, is a good thing. So build that in. Don't worry about losing collimation form that source. You won't, since it's too little and the lens will shift together. Just make sure that the crown and flint don't become separated from one another laterally as they shift around in their cell. The tape should help, but make the cell wall square with your router and make the three peripheral contact points and the three contact points on the floor of the cell flat. Smooth vinyl electrical tape or strips of postage stamp can make good contact points on the inside of the cell.
If you have not built the Fraunhofer or one of the other coma-free objectives detailed in Appendix 1, then you'll need to install push-pull screws on your tube to collimate your objective. But if you did build the Fraunhofer, then make sure that it is attached squarely to the tube and that your focuser points squarely at its center. Otherwise you could see astigmatic images due to defective alignment.
Collimating a refractor is much like collimating a reflector. Various methods can be used and Berry in the above cited chapter shows one method. I like the star test and find it to be best. But it lies beyond the scope of this webpage to discuss that. Many amateur astronomy books discuss it and I leave you to find them. Richard Suiter's "Star Testing Astronomical Telescopes," (Willmann-Bell, 1994) may be of assistance.
Collimating a non-aplanatic refractor is much like collimating a reflector. Various methods can be used and Berry in the above cited chapter shows one method. I like the star test and find it to be best. But it lies beyond the scope of this article to discuss collimation. Many amateur astronomy books do that and I leave you to find them. Richard Suiter's "Star Testing Astronomical Telescopes," (Willmann-Bell, 1994) may be of assistance.
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