Wednesday, June 4, 2014

140603 From the Workshop #6...Tim C

From the Workshop #6...Tim C from SBAU June, 2014 newsletter:

Let's review briefly. We have a tool and a blank that will ultimately become a mirror for our reflecting telescope. We would like our blank to end up an 8", f/6, mirror. This translates to a focal length of 48” and a radius of curvature of 96". At this point we are using 60 or 80 grit silicon carbide to grind our blank to the desired focal length. Our mental state at this stage is optimistic: (1) this blank will become a fine mirror that we will place in a great telescope, and (2) any errors at this point can be redone. How do we know when we have reached focal length? Recall in workshop #4 we used a basic equation to find the depth of our curve of our mirror:  s = r2 / 2R.  Using this equation our 8" mirror will have a Sagitta at its center of .083".  Conveniently, this depth at the mirror’s center may be approximated by the thickness of a drill bit resting under a straight edge. As an example, a 5/64” drill bit has a thickness of .078". Although this drill bit is a “bit” undersized, it can still be used as a crude guide to tell us when to stop grinding since we are near the desired focal length of our mirror. When this depth is reached, a straight edge will easily slide over the bit without rocking. This is a good mechanical test. But we need a test that is a little more precise. We need some kind of optical test. Consider the following.

Wet the surface of the mirror, and go outside when the sun is reasonably high in the sky. Reflect the sunlight onto a surface and watch the image that your “mirror” makes. As you move your mirror toward and away from the surface you will see a spot that becomes larger or smaller. Stop when you see the smallest spot. Measure the distance from your mirror to the surface. Since the sun is essentially an infinite distance away, you have just determined your mirror’s focal length to a precision of an inch or two from the desired target of 48”.  Until we bench test your polished mirror, this is one of the best ways to estimate your mirror’s focal length!

Once you achieve your desired focal length, reverse the roles of the tool and the mirror in order to maintain your mirror’s focal length. With the mirror on top (MOT) you affect the center depth of the mirror. Working with this positioning will tend
to preferentially deepen the center of the mirror, and thus shorten the focal length of the mirror. When the tool is on top (TOT), the mirror’s focal length is increased. Alternating the two positions allows us to (1) maintain the desired focal length and (2) smooth out any aberrations on the mirror’s surface that do not conform to a sphere.  We will use this technique all the way through our list of finer and finer abrasives. Our mirror will become smoother and smoother as it becomes more and more spherical. Ultimately we will move to Aluminum Oxide, a lapping powder, in order to
smooth our mirror even further. But, even after this fine course of material, our mirror will still not reflect light when it is dry. In future issues I will discuss polishing and figuring your mirror and the tests we use in the workshop to determine the quality of your mirror.

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