This page describes a technique for quickly and accurately setting the appropriate cheater (index splitter) angle after transferring a stone. It can also be used to replace a dop in the machine under other circumstances - for example to touch up the star facets after completing the table. The technique does not require any further cutting or polishing of facets, and it can be used at any time to restore the desired cheater angle (provided that there is a polished girdle facet). The entire procedure takes approximately 5 minutes, and is very accurate.
(If you already understand cheater adjustment after transfer, you can skip to the next section.)
Transferring a half-completed stone to a new dop involves two factors which can cause misalignment of the pavillion and crown facets. The first of these is simply removing the dop from the machine (which may be necessary or helpful even when not doing a transfer). Despite various keying schemes, the second dop is invariably somewhat rotated with respect to the first, requiring some cheat to bring things into alignment. The second factor is imperfect transfer, possibly due to misalignment or keying problems in the transfer jig, slight shifting of the stone, etc.
To counter these difficulties, faceters have developed a variety of schemes to determine the correct cheat angle. One common strategy is to cut a row of facets after transfer. Incorrect cheat angle shows up as a slight spiral cut, producing an offset between the last and first facets cut. The faceter applies some cheat in the appropriate direction , cuts another row of facets, and checks again. A few iterations should produce an even row of facets and hence the correct cheat angle. Rob Kulakofsky wrote an excellent description of this method (AFMS faceters list archive).
Unfortunately, there are several problems with this technique. First, it is very slow, since accuracy depends on adjacent facets being cut to exactly the same depth. Any overcut of a facet halfway through a row forces the faceter to compensate or start over with that row. Achieving maximum yield from expensive rough is also inconsistent with cutting multiple test rows of facets. In addition, many gemstone designs do not have continuous facet rows. Check the first crown cut. If it does not produce a continuous girdle line, you will have to cut all the way around the stone at the largest angle. This may be problematic for some gem rough. Finally, this technique does not help with the problem of replacing the dop in the machine at times other than transfer.
I got very frustrated with the cut and check technique for getting the right cheat after transfer, and therefore started looking at alternatives. My experience in astronomical instrument design started me thinking about possibilities for optical alignment. The method outlined below is based on a standard technique known as retroreflection, in which a beam of light returns exactly to its source after reflection off the surface being aligned.
The figure at left outlines the basic principle. A mirror placed on a flat reference lap bounces laser light exactly back along its incoming path. A second mirror held at approximately 45 degrees allows the incoming and outgoing beams to be horizontal, a configuration better suited to long optical path lengths in typical rooms (no cathedral ceilings in my little workshop!). Also, adjusting this 45 degree mirror is much easier than positioning the laser for perfect retroreflection.
Note that if the light goes exactly back to the laser, the optical path between the two mirrors is by definition exactly perpendicular to the lower mirror, and hence to the reference lap.
The next step is to tie the orientation of the gemstone into this reference. Setting the protractor to 90 degrees and selecting an index exactly opposite a girdle facet should make that facet also parallel to the reference lap and upward-facing. If the gem is properly aligned, the laser should retroreflect off the girdle facet just as it did off the lap mirror (I usually cover the lap mirror with paper to minimize confusing reflections). Adjusting the index splitter (and protractor) for perfect retroreflection gives the proper cheater angle. Voilà.
To do this yourself, you will need the following items:A Laser Pointer 2 Small (25-50 mm, 1-2 inch) mirrors A jig to hold the 45 degree mirror
Laser Pointer. I use a cheap laser pointer purchased at a discount house for less than $20. The only requirement here is that the laser stay on continuously. My pointer has a recessed momentary-on switch, which I hold down with a breath mint and an elastic band.
Mirrors. Almost any mirror will do. The one lying on the lap should provide an accurate reference. This means it should either be a first surface mirror face down, or at least a double surface mirror that is very parallel. You might be able to judge how parallel such a mirror is by rotating it 90, 180, and 270 degrees then checking whether the spot stays fixed after retroreflection. Edmund Scientific has suitable inexpensive mirrors.
Jig to hold 45 degree mirror. I began with a hobbyist's "third hand" - the gadget with alligator clips and wing nuts. This was difficult to control, so I rigged together a mirror holder with screw adjustment. For the ultimate in ease, try to scrounge surplus hardware from an optical bench. Like this.
1. Place the lap mirror on a clean reference lap. I use a mirror approximately 30 mm in diameter laid on my master lap. Place the mirror where you usually polish. The mirror will rest on top of any small hills on the lap, averaging the slope over the area it covers.
2. Setup up 45 degree mirror and laser. I place the mirror holding jig directly on the lap, so that the 45 degree mirror is directly above the lap mirror and pointing across the room to the table where the laser sits.
3. Align laser to lap mirror. See figure at right. Turn on the laser and adjust it so that the beam strikes the 45 degree mirror. If you have trouble getting it to line up and stay put, try embedding the laser in some plasticene (Play-Do). Adjust the 45 degree mirror so that the spot of light returns to the laser. This does not have to be exact , as long as you send the laser back to the same spot in step 4.(see here for a discussion about this).
4. Align the gem to the lap. See figure at right. First, cover the lap mirror with a tissue to prevent distracting reflections. Then dial in 90 degrees on the dop arm and set the index so that a polished girdle facet faces upward (do this from the design, not by eyeball! For instance, if there is a girdle facet at 24 on a 96 tooth gear, set the index to 72). Make sure that the downward-travelling laser beam strikes the girdle facet. A small white index card can be a great help here. Reflection off the facet then the 45 degree mirror sends the light back toward the laser pointer. You might get addtional confusing reflections off other facets. Inking unused facets helps here. Adjust the protractor and cheater angles until the spot returns exactly to the laser (or the location it was before). That's it. Do some reality checks (step 5) then start cutting!
5. Do some reality checks. You should check the laser-lap mirror alignment afterward. Just move the stone out of the laser beam and remove the tissue covering the lap mirror. The spot should stay put. There are some additional useful checks. For example, you should check the spot location using different facets. If the spot moves around slightly, repeat step 4 using the facet which represents the approximate middle position. How much variation is acceptable? Compare the amount of cheat you have to apply to bring the spots to the same point. If this is small compared to the amount of cheat you apply during normal faceting, you should be all right. Read some additional comments about accuracy here.
This optical alignment technique is very accurate. We can estimate the cheater angle error using the laser spot uncertainty and some simple geometry. For example, with my setup, I can usually retro-reflect the laser to within 1 mm or so of its original location. With a total path length from the gemstone to the laser head of about 2.5 meters, this corresponds to an angular accuracy of 1 part in 5000 (note that when you rotate a mirror - or a gem facet - by one degree, the reflected light is rotated by 2 degrees). One part in 5000 corresponds to approximately 0.01 degrees or 0.7 minutes of arc. For a 96 index gear, it is about 1/300th of an index setting.
Is this accurate enough? The simple answer is yes, for at least two simple reasons. First, you will likely find as I did that aligning this way produces no discernible error with the traditional cut-and-check technique. Second, you will notice that cheater adjustments that you would normally consider minute during faceting produce significant shifts of the laser spot.
A longer path length would allow greater accuracy, although it becomes harder and harder to judge the center of the spot of light, particularly that produced by an inexpensive laser pointer. Yes, a HeNe gas laser with less beam divergence would improve things.
Imperfect retroreflection - that is returning the laser spot to a point slightly displaced from the laser head - does introduce some inaccuracy. The figure below explains why.
A Word of Caution
This technique should simplify the procedure of finding the correct cheater setting, but it is subject to error. Obviously, referencing to the polished girdle facets in this way presumes that you have an accurate girdle. Bumping or moving the lap, mirrors, or laser during the measurement can cause problems as well. As a matter of practice, I usually cut a test row of facets to confirm accuracy, but I rarely have to cut more than one row!