toroid

How to make a toroid Yolo mirror

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Grinding:
A Yolo mirror typically has a long radius of curvature (ROC). Because of that, the curve is very shallow and rough grinding goes very fast. In my case, the curve was deep enough in about a half hour of rough grinding! The 6 inch secondary had a depth around 0.010 inches at the center.

A handy tool to have is a spherometer. I made this one with a mechanical dial indicator. First, the spherometer is placed on the convex grinding tool and the dial is set to zero. Next, the spherometer is placed on the concave mirror and the reading is noted. Using the formula at the bottom, the ROC can be calculated. The ROC is measured frequently during rough and fine grinding. If the ROC is short, continue grinding with the tool on top. If the ROC is long, continue grinding with the mirror on top. For these shallow curves, try to measure the depth as accurately as possible. If you can judge the depth to within 0.0001 inches, you should be able to control the ROC to within a few inches. (note: If you zero out the spherometer on a flat and then measure the mirror, there is a "2" in the denominator of the formula.

Polishing:
Polishing continues as one would make a normal telescope mirror. Be sure that you polish the glass fully. A quick check for this is to clean the mirror and aim a red laser pointer at the front surface of the glass. Start by aiming the laser pointer at the center of the mirror. The spot where the laser beam hits the glass should be very difficult to see. Only a few specks of dust here or there should be seen. As you aim the laser pointer out near the edge of the mirror, the spot should not brighten. If it does, the edge area is not fully polished out. If you were to have the mirror aluminized at this point, you would see a noticeable foggy area near the edge. That would cause scattered light an reduce contrast.

Testing:
Arthur Leonard (The Yolo Reflector booklet) and Jose Sasian (S&T Aug.1988) have used a modified Foucault tester where the light source and knife edge are separated by a substantial distance, placing them at the foci of an ellipse. Also, two knife edges are used. (One vertical and another horizontal). One can adjust the knobs and measure both axis of the toroid without having the get up from the chair. This is a very elegant test set up. I however, did not have the room for a permanent apparatus to be set up. Instead, I chose to use the standard type Foucault tester. Because of that, I had to rotate the mirror 90 degrees between measurements.

Full Lap

Bar Lap

Jose Sasian describes polishing in the toroid figure using a pitch lap with portions of the pitch removed. (Bar lap, Sky and Telescope, Aug1988) Before polishing, draw a line on the back side of the mirror and lap, across their diameters. Marks on the side are also helpful. From here on out, the orientation of the mirror to the tool must be maintained. No rotation allowed. The line drawn on the mirror and the line drawn on the tool must be kept parallel. I worked with the bar lap tool on top using ž diameter strokes. Walking around the barrel gives strokes from all directions, while still keeping the lines parallel.

As I continued polishing with the bar lap, and testing with the Foucault tester, I saw slow and steady progress of the toroid figure taking shape. The difference in radii I call the deltaR value. For my scope, the deltaR value was just over 2 inches. The deltaR value can be calculated from a spreadsheet found on my web site. This took about 3 hours to polish in. At this point, there appeared to be a turned down edge, especially seen in the Test A setup. Actually, the edge area was just lagging behind the rest of the mirror. Once the deltaR is correct, polishing continues with the full lap to smooth out the surface. Here again, the orientation of the mirror to the tool must be maintained. No rotation allowed. The line drawn on the mirror and the line drawn on the tool must be kept parallel. I worked with the full lap on top using 1/3 diameter W strokes. Walking around the barrel giving strokes from all directions, while still keeping the lines parallel.
After about an hour of smoothing with the full lap, the surfaces seen at testA and testB were both absolutely smooth. Just like a perfect sphere would look like in the Foucault tester. However, the deltaR value had reduced quite a bit. I was tempted to quit at this point. Having a lower deltaR value meant that the secondary mirror would be located somewhat inside the incoming light path of the finished scope. So I continued further with the bar lap for a while, then smoothed with the full lap. The remaining smoothing process became quite stuborn. Once I had the correct deltaR value, testA appeared smooth, testB showed a slight turned up edge. Later, deltaR ok, testA slight turned down edge, testB looked nice and smooth. One trick that I tried was to vary the stroke length as you move around the barrel. At times you notice a slight hill or hole at the center. They seem to come and go. This game went on and on for about another 7 hours before I was happy with the view in the tester. All this was done working a little at a time (average 30 minutes per session) over a couple months. I should mention that before every polishing session, the mirror and lap were either warm pressed or cold pressed for a while for optimum contact.

Test for axis orientation:
Once during final smoothing, the surface looked a bit irregular in the tester, no matter where I put the knife edge. It really had me puzzled. What I was noticing, was that the true axis of the toroid had turned a little and was not true to the line drawn on the rear of the mirror. Reasons for this may be that one of my arms is stronger than the other, or I didn't pay close enough attention to the lines as I pushed the glass. Regardless of the reasons, there is a quick and easy test to verify the true axis of the toroid figure.

First, place the mirror in the Foucault tester and set up for testB (the longer radius).
Next, position the knife edge at the location that is midway between where it would be for testA and testB.
On my tester, the knife edge in on the left hand side. As I move the knife edge to the right, cutting into the returning light beam, I would see the dark shadow on the mirror also moving to the right. With the toroid axis lined up correctly and the knife edge verticle, the shadows edge is also verticle.

If the mirror was rotated about 10 degrees counter-clockwise, you would see a similiar shadow. However this time the shadow would be tilted about 20 degrees counter-clockwise.

If the mirror was rotated about 10 degrees clockwise, you would see a similiar shadow. However this time the shadow would be tilted about 20 degrees clockwise. There seems to be double the shadow tilt compared to the mirror tilt. The idea here is to rotate the mirror a little at a time until the shadow edge is verticle. If the line drawn on the back of the mirror is somewhat tilted, it can be redrawn level again. Having an accurate measure of the axis is helpful when collimating the optics in the finished scope.

An extreem case is when the mirror is tilted 45 degrees. Here I rotated the mirror clock-wise. OH NO! It's the dreaded Yin-Yang shadow of astigmatism. The scourge of the glass pusher. Here the middle of the shadow actually moves downward as the knife edge is moved across. Sometimes this happens by accident for the novice mirror maker. Perhaps while polishing with the mirror on the bottom, there was not uniform support underneath the mirror. That would cause the mirror to flex a little and result in some polished in astigmatism.