April 1998 Newsletter

Stockton Astronomical Society

Valley Skies

Valley Skies - April 1998 Issue

The Telescope Nut
by Jeff Baldwin

Curve Generating

Mirror makers start with two pieces of glass, one of which will end up being the mirror, the other being referred to as the tool. They are both disks, flat on both sides. Typically, a starter project for a mirror maker would be an 8" mirror, but size doesn't change things much as far as the process goes. An 8" project would probably have an 8" tool. The mirror will end up being concave on the mirrored side, and the tool will end up being convex. These two sides will have been worked together to form the concave mirror, and the tool ending up convex is just the result of this work.

Here's how we make the mirror a concave shape. We sprinkle silicon carbide, a very hard abrasive, onto the wet glass that will become the mirror. We place the other glass, the one that is now designated to be the tool, on top of this gritty glass. With force being applied downward onto the project we rub the two together in strokes. This causes the glass on both the tool and the mirror to be worn away. It's noisy and dirty. Our immediate goal is to wear the glass away to make the mirror concave and the tool convex, so the stroke we use should wear away the mirror in the middle and the tool on the edge. To do this we move the tool sideways so that its edge will stroke over the center of the mirror, wearing away the center of the mirror and wearing away the edge of the tool. As we do this we walk around the project, which is sitting on top of a barrel, thus making the whole project uniform around the glass (surface of revolution). We also rotate the mirror and the tool frequently. When the noise is reduced, then the grit has broken down to a useless size and we wash it up and do it again. We keep repeating this and eventually the glasses become curved.

If we keep doing this the glass would become TOO curved, so we need to know when to quit. The deeper the curve the shorter the focal length of the mirror. A shallow mirror will have a long focal length. We have a formula to figure out when to quit digging. I'll give you the formula, then I'll give you a couple of examples.

The formula is s = r² / 2R , where s is how deep the mirror is (sagitta), r is the radius of the mirror, and R is the radius of curvature of the mirror, which is twice the focal length. OK, don't panic, here's how it works. If you have an 8" mirror and you want it to be an f/6 (meaning the focal length is 6 times as long as the diameter of the mirror), then the focal length will be 48", making R = 96". The radius of the mirror, r, is 4". This makes s = 4² / 2*96 = 16 / 192 = .083" , or 1/12". This means that we work on making the mirror curved until we can measure its depth as being 1/12".

Let's try one more example. We have a 16" mirror and we want it to be an f/4.5. The s = 8² / 2*144 = 64/288 = .056". This means that we will work on the curve until it is .056" deep.

We can measure how deep the curve is by placing a straightedge across the mirror and measuring how deep the gap is under the middle. Another way is to make the mirror wet with water and focus the sun's image onto something that won't burn and measuring the focal length. This method sounds logical but the water may not take the exact shape of the glass and may create an error in estimating the focal length, so I never personally do it. Another method is to make a spherometer. Call me if you want to know how to do this.

Let's back up one step. Mirror making is an exacting project that will eventually be measuring things down to less than one millionth of an inch. For this reason we don't want errors that will cause a deviation. One of those errors is letting the glass wobble as you work it. In order to prevent that the back of the mirror needs to be flat so it won't wobble on the barrel as you are working on the business side. We can fix that by grinding the back of the mirror flat first. This can be done by grinding the back of the mirror with the back of the tool with a "W" stroke. This will make the two flat against each other so they won't wobble when you are working on them.

OK, back to the business sides. When your mirror is deep enough it may not be spherical. The mirrors will eventually be paraboloidal, but we deal with them as though they are spheres right up to the end. If the mirror is deep enough but not spherical, then the tool will not mate with it perfectly in all positions. So, when you have made the mirror deep enough, then we change the strokes from being the edge of the tool over the center of the mirror to a "W" stroke. This is a back and forth stroke that also goes side to side, a series of Ws that cause the mirror and the tool to be equivalently ground on all regions. This will grind glass away from both of them until they mate perfectly. An indicator that you have achieved Spherical Contact is that the bubble between the two glasses roll along at half the rate the tool is moving over the mirror. If the tool and the mirror are in perfect spherical contact, then they are mating perfectly with little balls (rocks) of grit between them that will roll along like bearings. They will roll not at the same rate as the tool, but at half the rate since the mirror is stationary. If there is a low spot on the mirror (the glass on the bottom), then there will be a vacancy of these particles that doesn't move, rather hovering over the low spot on the mirror. If there is a low spot on the tool, then there will be a vacancy of these particles that moves along at the same rate as the tool, rather than half the rate. If the contact is perfect, then the entire surface will appear uniform in the particles moving at half the rate.

OK, you should not have spherical contact with your mirror and tool at this time. Your curve generating is now complete and your mirror is ready to progress through grinding to a smoother surface, which is where I'll start next time.

Clear Skies.

Be sure to visit the A.T.M. link on our club web-site.

Clear Glass...Jeff Baldwin
For more information on Telescope Making jump to the ATM page.