Although I advocate making a Fraunhofer aplanat, ATMs may be interested in other designs as well. Here I shall present 6 other possibilities and briefly discuss their pros and cons.
The best alternative candidate to the Fraunhofer in my opinion would be a Clark-type small objective. The prescription is as follows:
Lens Diameter - 156mm Clear Aperture - 150mm. Glasses - BK7 and F2 (fine or precision annealed) R1 - 1007mm Thickness - 14mm - BK7 R2 - -1007mm Airgap - .131mm R3 - 997mm Thickness - 10.9mm - F2 R4 - -15510mm Back Focal Length - 2231.5mm
As with the Fraunhofer, I assume simply that the original blanks were 15mm thick and that the lenses are spaced with postage stamp squares. Some variation in the thicknesses and spacings will be fine and minimally affect the outcome. The main disadvantage of this design is that coma has returned. In practice it's quite small (OSC = -.0006) and you won't see any flair out to the edge of a 2" dia. field of view, but you will need collimation screws built into your tube so that the lens can be tilted for best axial performance. The design is also not completely corrected for spherical aberration, although the residue is small and can easily be focused out. Alternatively, one can do a small amount of aspherizing r1 to perfect the spherical correction. The conic constant on r1 is only 0.05 (a parabola is -1), so only a perfectionist will bother with aspherizing. If you do bother, then you will either want to flatten the center area of r1 slightly by gently and briefly stroking r1 over the edge of the polishing lap as if r1 were a mirror being parabolized, or you will deepen the periphery of r1 by gently stroking the tool out over the edge of r1 as if the tool were a mirror being parabolized.
If you are willing to AR coat your lenses, then the following prescription gives the related spherically corrected lens:
Lens Diameter - 156mmc Clear Aperture - 150mm. Glasses - BK7 and F2 (fine or precision annealed) R1 - 1006.7mm Thickness - 14mm - BK7 R2 - -1006.7mm Airgap - .113mm R3 - -1002.3mm Thickness - 11mm - F2 R4 - -17100mm Back Focal Length - 2231mm
The temptation to oil-space a lens is great. So here is a spherically corrected design which can be oil-spaced. This one has coma too, but it's even smaller than in the preceding two designs. If you do build this lens, then I'd advise you to carefully test plate R2 and R3 together (as described elsewhere on this webpage), and to get them to within one ring of difference in their radii and make their figures reasonably regular. Otherwise, you may end up with astigmatic images during cooldown, as the two elements contract differently and exert mechanical stresses on one another. It's crucial to avoid axial astigmatism, since this quickly destroys the fine images that an achromat can deliver. You'd might as well just build another 6" Newtonian!
| Lens Diameter - | 156mm |
| Clear Aperture - | 150mm. |
| Glasses - | BK7 and F2 (fine or precision annealed) |
| R1 - | 1035mm |
| Thickness - | 14mm - BK7 |
| R2 - | -981.3mm |
| Airgap - | 0.0mm |
| R3 - | -981.3mm |
| Thickness - | 10.9mm - F2 |
| R4 - | -12326mm |
| Back Focal Length - | 2233mm |
To oil-space a lens, wash and clean the lens well in warm mildly soapy water. Rinse well and dry with a cotton towel. Make sure no water spots remain. Then carefully level R3 of the flint on an elevated ring (put towels underneath to catch the spilled oil), and pour a tablespoon or two of clean clear oil into the center of it without making bubbles (pop any that form). Any clean salad oil will do, or clear mineral oil. Then dust off any large particles from the dry parts of R3 and from R2 and gently lower R2 into R3, trying to touch R2 to the oil at R2's midsection. The object here is to try to avoid entrapping bubbles in the oil.
Once R2 has contacted the oil, gently lower it and drive the oil away from the center of R3 into contact with the outer dry parts of both surfaces. If you do entrap small bubbles, then as R2 settles further into R3, these may slowly migrate to the edges of the lens. You can pop them when they come out. If they don't move you can try to coax them out by moving R2 around on R3. It's not important to remove all the bubbles. A few left over will make a negligible difference to the lens's performance.
Oil will now be seeping out of the lens. Dry this off and keep R2 centered on R3. Eventually, it will stop sliding around. When R2 has come to a rest, let the lens sit for some time, possibly 30 min. in order for more oil to seep out. When the seepage has apparently stopped, you'll need to clean the edges of the lens to purge them of oil. Isopropyl or denatured alcohol can assist you.
Once the lens is reasonably free of oil, then you'll want to tape the edges of the lens with cellophane ("Scotch") tape. Two turns around, without overlapping the end of the second turn on the two layers already beneath, should be sufficient. Now you'll need to carefully wash the exposed faces of the lens (R1 and R4) to cleanse them of oil, and you're ready to install the lens in its cell. As you can see, this process is likely to be messy. That's another reason why I prefer air-spaced designs.
If you need to separate the lenses later, they should just slide off of one another with minimal risk of scratching. Wash the lenses to remove the tape glue from them. It the lenses don't want to slide apart, I recommend soaking them in warm soapy water for a while. Be carefully and don't force them or you risk scratching!
By using slightly different glasses other possibilities open up. One interesting lens is a Clark-type lens composed of BK7 and SF15. The later glass is known as a "heavy flint," because it is denser than standard flints. Nevertheless, it shouldn't much more expensive or difficult to work than F2, if slightly heavier:
Lens Diameter - 156mmc Clear Aperture - 150mm. Glasses - BK7 and SF15 (fine or precision annealed) R1 - 1237mm Thickness - 14mm - BK7 R2 - -1237mm Airgap - .155mm R3 - -1210mm Thickness - 11.5mm - SF15 R4 - -3745mm Back Focal Length - 2239mm
This is a spherically corrected lens, with very small residual coma (OSC = -.0002). The r3/r2 difference is so great that ghosts will never be visible. The best thing about it is that it could be built without a spherometer, by making just two testplates: one for R1/R2 and the other for R4. The radii are all weak and both the test plates and R3 can be knife-edge tested and have their radii measured confidently by means of a measuring tape. The standard Fraunhofer could also be built in this way, but it would require 3 test plates (the additional one is for R2) and its R2/R3 curves are rather strong and more difficult to measure accurately with a knife-edge tester. In the next appendix I'll talk about using test plates to measure radii and give more details about how you would build the BK7/SF15 lens. The one disadvantage of this lens is that dewedging of the flint has to be more complete than with F2 in order to avoid lateral color. With the F2, it was said that wedge had to be controlled to 0.0005"/0.013mm or better. With SF15 the tolerance must be at about 0.0002"/0.005mm or better. This is still possible using a good dial indicator, and if some color were later discovered in the image, the lenses could be rotated with respect to one another (as discussed above) to minimize the problem.
Finally, the Littrow or Littrow-Clairaut lens may attract a few builders. I present two prescriptions, the first a spherically corrected design requiring a large airgap and the second, an oil-spaced design requiring some aspherization. Both of these designs entail a slightly different color correction from that used in all the preceding designs. This is necessary in order to make R4 flat. The color correction brings red to a focus somewhat closer than blue, but is similar to the correction that the Clarks and other great 19th c. makers used. In practice, it should look nearly identical to the correction found in the other objectives presented on this webpage. Both designs show somewhat stronger coma (OSC = -0.0008), but still small when compared to an average Newtonian. They use one different glass: K7 (not to be confused with BK7!), along with our old friend F2. K7 is a standard glass and should be readily available. I am indebted to Rick Blakely for the following design.
Lens Diameter - 156mmc Clear Aperture - 150mm. Glasses - K7 and F2 (fine or precision annealed) R1 - 905.8mm Thickness - 14mm - K7 R2 - -905.8mm Airgap - 2.8mm R3 - -905.8mm Thickness - 10.6mm - F2 R4 - flat Back Focal Length - 2209.4mm
The large airgap is necessary to suppress spherical aberration. It will require a more complicated cell, perhaps entailing a machined spacer ring to hold the crown and flint apart. Or one could obtain a fully adjustable cell and then in autocolllimation, carefully set the gap between r3 and r2 to obtain the best spherical correction. In any case it is a more complicated design, more difficult to mount than the Fraunhofer. At any rate, the large airgap means that the ghost image from R2 and R3 will be completely defocused and unobservable in practice. On the other hand, however, there could be a ghost from the flat surface of R4 unless it is coated. One will just have to make the lens and find out! In principle, one could use R3 as a testplate for R1/R2 and then make or obtain a flat to testplate R4. In practice it would probably be easier to make the testplates for the BK7/SF15 lens.
The last design involves an oil-spaced Littrow:
Lens Diameter - 156mmc Clear Aperture - 150mm. Glasses - K7 and F2 (fine or precision annealed) R1 - 906.3mm Thickness - 14mm - K7 R2 - -906.3mm Airgap - 0.0mm R3 - -906.3mm Thickness - 10.6mm - F2 R4 - flat Back Focal Length - 2230.7mm
This would appear to be the simplest lens of all to build. But in practice, as with the airspaced version, it may be difficult to make R4 well and a ghost could arise from this surface. It is not completely corrected for spherical aberration, but the residual is small and could be focused out. Aspherizing can perfect the correction. Only one testplate is needed, since R3 could with difficulty be used to test R1 and R2. The testplate is a flat for R4, which will not be easy to make. On the whole, I would recommend the BK7/SF15 lens over this one.
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