Testing for color correction, if you can afford to buy the narrow passband filters for the C-and F-lines, should really proceed along with figuring in autcollimation. If you can't afford the filters, then testing for color correction will have to be made at the eyepiece with a star test. In fact, one should really make a preliminary test for the color correction before figuring and in fact before the end of polishing. One should actually only polish out R1, R2, and R3, and give a flash polish to R4. This is because if the color correction is wrong by much, it can easily be corrected by regrinding R4 alone, as explained below. It would be a bad idea to completely polish the lens and then find that R4 needed to be ground again! The only reason why I did not this problem earlier was because you needed to develop a basic understanding of how to interpret the knife-edge and Ronchi tests when applied to a lens. Now that you have this understanding we can backtrack to what should be an earlier part of testing and correcting the lens.
It is a good idea to get your lens cell and tube ready before you begin to polish. Not only will you need the cell for autcollimation, but in a pinch you can use it for star-testing, if need be. It's also fun to see how figuring affects the star image. This is a place where refractor builders can get experiences hard to acquire with a reflector. For most people it would be a hassle to repeatedly silver a mirror for a star test and then strip the coating for figuring. And testing without a coating on your mirror, unless it's quite large, will produce a rather pale image. A refractor objective, by contrast, gives you all its light from the start! You can really see what figure aberrations do to the image!
All right. Polish out or almost polish out R1, R2, and R3. Put a good flash polish on R4. Assemble your lens as explained in the next section, and install it in its cell. Autocollimate the lens. With your C-line (red) filter and a nice Couder test mask from your last 6" or 8" mirror in front of the lens, try to find the knife-edge location where the 70% or 80% zone of your lens cuts off evenly (for this test a knife-edge is better than a Ronchi), just as you would do in mirror testing. This will be somewhat hard, because the lens won't look very bright in red light and the poor polish on R4 will diffuse more light. Certainly your flat had better have a good aluminum or fresh silver coating. Otherwise, you will most definitely be looking thru a glass darkly. Shut all your room lights off and do it at night or in a dark basement and ignore those clanking chains! Alvan is just envious that he didn't have it so good in the 19th c.
Once you find--or think you've found--the cutoff, then switch to the F-line (blue) filter. The cutoff should look the same. Incidentally, the blue filter is even darker than the red, to my eye at any rate. If the cutoff looks different, then try to find where it is. You should also do this for the same zone with the e- or d- filter. Now put your old Foucault skills to work and start measuring the same zone in the three colors. You need to know how far the C- and F- foci fall from the e- or d-. The differential amount should ideally be roughly 1/2000th part of the focal length, if C- and F- cut off identically. But there's one more catch! Remember that you're working in double-pass, so everything including the secondary spectrum's dispersion is doubled. If your light source is of the fixed type, then you should see a dispersion of 1/1000th part of the focal length. But if your light source is moving, then the movement cancels the doubling and you should measure 1/2000th part.
Chances are that the cutoffs - if you can measure them confidently - will not be exactly the same for C- and F-. That's nothing to worry about unless they are grossly different. If F- falls close to e-/d- or in front of it, or if C- does likewise, then you'll certainly want correction. But if F- falls only half as far from e-/d- as C-, or if C- falls half as far from e-/d- as F-, then you could probably leave the lens alone. All the great 19th c. makers chose a correction similar to the last mentioned, with C- falling closer to the lens than F-. The is called the "B-F" correction, because the obscure "b-line" of the spectrum (longward of C-) was made to coincide ("achromatized") with F-. You can see a graph of various color corrections for the great makers in L. Bell, "The Telescope" (Dover, 1981), p. 91.
I have also seen an objective made by a well-known contemporary maker with F- brought closer to e-/d- than C-. Perhaps this was a mistake, or perhaps it was an attempt to bring more of the blue part of the spectrum into focus. I don't know and I'm not sure if it matters. A star test or a test on the planets is the only real way to decide if these color correction differences are truly important, or just hair splitting the one bad feature of achromats.
Doing this test with a Ronchi grating will be more challenging. It might be easier to view the lens as close as possible to the focus for green light (where the bands expand and disappear or cutoff the image like a knife-edge) and then switch to red and blue. Do the fringes seen in red match the number of those seen in blue? If there is a difference in the number of the bands in these two colors, then the red and blue foci do not coincide. Try to figure out how far apart the foci are and where they fall with respect to the green focus.
If you don't have the narrow passband filters, then a star test is in order. Taylor gives complete instructions for this. Suiter, pp. 229-231 also has some excellent comments. If you can get hold of some cheap eyepiece filters for planetary viewing, particularly #56 (green), #38A (deep blue), and #23 (red) or deeper versions of these same colors, then you can perhaps simplify your life. Maybe an amateur astronomer friend has some. In any case, the goal here remains the same: do the red-light and blue-light foci occur at about the same distance from the green light? Take the green filter into your fingers and hold it in front of a high power eyepiece (40-50X/inch) and focus on a moderately bright white star, while looking through the filter. Get a good focus and try to see the tiny Airy disk. Don't screw the filter into the eyepiece base because you'll have to change it for the red and blue filters in a minute, and you don't want to move the eyepiece in an uncontrolled fashion. Once you've got a good focus for green, next look at the image in red. It should look slightly defocused. Now switch to blue. The star should look equally defocused. Try to keep your eye relaxed if possible during all this. Pretend that you're looking toward infinity. Otherwise, your eye's ability to focus will interfere with the test.
Next, try focusing on the star in blue light. Did you move the eyepiece outward to find the focus? You should have. Switch to red. Is the star in focus now? It should be. Try to find the foci for the different colors. Do they seem to fall approximately where they should? Incidentally, you can do this same test using your narrow passband filters, where the effect will probably be clearer. You could also try the eyepiece filters on the knife-edge cutoff. It might be helpful. I don't know.
Finally, look at the moon or Jupiter at medium power (30X/inch). Does the color look normal, aside from a blue fringe around the outside of these objects. Jupiter's bands may like slightly violet, but the disc itself should look white. The Lunar maria should look light gray as usual. Traces of blue may be seen in the darkened parts of the craters.
If you don't see these appearances, or if the red and blue foci are clearly wrong in relation to green, then you'll need to regrind R4 to correct the problem. This is very unlikely to occur if you bought your glass from a reputable supplier, or at least know for certain the glass types. I know of one case where an ATM picked up a second-hand half-completed lens, finished grinding what he thought were the right curves only to find the color correction way off. In my own case, I've never so far had this happen. I have tweaked the correction on my 8" Fraunhofer objective to get the blue more even with the red. But the change was almost certainly trivial as far as performance is concerned.
So, it's unlikely that you'll need to alter the correction which you get from grinding. But in case you need to or want to, here's the secret: the radius on R4 has a profound effect on the blue focus. If you make R4 stronger by about 100mm in radius, it will roughly halve the distance from the green to blue focus and somewhat increase the distance from green to red in our Fraunhofer design. It will also shorten the lens's backfocus by 30mm or so and slightly affect the system's spherical aberration. On the other hand, if you weaken R4 by the same amount, it will extend the blue focus, draw in the red focus and lengthen the backfocus by corresponding amounts. This is the key to fixing any residual color error in your lens.
Of course, it would be best to do your own raytracing in on your particular lens, after you carefully determine by knife-edge cutoff where the red and blue foci fall with the dielectric filters, but the point here is that if you're careful and enterprising in the true ATM spirit you can do almost as well for much less money. Perhaps the truest ATM scope I've ever made was my 6" f/15 refractor recently finished. I spent barely $20 on the whole thing including the superb cell that I got for free. The glass was all undocumented. The tube is two sonotubes glued together. The focuser and finder I had previously. I made baffles from spare plywood, etc. You really can get an excellent instrument in this hobby for not much money if you try hard enough. I hope that this article will spur ATMs to become nutty about achromats. They ain't perfect, but just damned nice!
If you do the knife-edge cutoff or the Ronchi test with the filters against the flat after you've finished figuring your lens, you may notice something strange. The figure looks good in green, but overcorrected in red and undercorrected in blue. If you noticed that, then you saw spherochromatism in action. Spherochromatism is the variation in spherical aberration with color. It occurs with varying degrees in all refractive systems, even apochromatic refractors. It's relatively easy to see in testing achromats. There's not much of practical effect that you can do about it in your lens, and for a small visual refractor you needn't worry about it.
It can be mostly corrected in an achromat by giving the lens a large airgap, as was done on some of the giant visual refractors of the past. The Baker achromat, designed by the optical engineer James Baker 40 years ago, diminishes spherochromatism and eliminates coma too. In some ways it is the best of all achromats. But it requires a well-machined metal cell. For small lenses the Fraunhofer works almost as well and is much easier to mount. I mention all this more to satisfy curiosity than because it's important in making your 6" lens.
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