A telescope mirror is the most accurate tool made by man or machine. Its precision is on the order of one part in twenty million. Making a telescope mirror is one of the great joys for human beings, the intelligent tool maker. Our experience begins with the varied sensations through the hands during grinding and carried through to the cerebral challenge of figuring the mirror to perfectly reflect light. Our experience both ends and begins using the mirror in a telescope to contemplate the mysteries of the universe and the meaning of life.
13 inch [33cm] f/3.0 meniscus plate
glass mirror, 1 inch [2.5cm] thick, sagitta of 0.27 inches [7mm], ready
for aluminum coating
Compare mirror making to rock climbing.
MOYERS: What drew you to climbing?
HOUSTON: It's a beautiful thing to do. You're surrounded by beauty. No matter whether it's a storm, or a sunny day, or clouds, or not, the mountains are simply beautiful. I just liked climbing. I like the feel of the rocks.
MOYERS: The feel of the rocks?
HOUSTON: Rock feels good, yes.
MOYERS: How? I mean, you're talking to somebody who doesn't climb.
HOUSTON: Well, rock climbing; you have a sense of the rock. Almost as though it were a living thing under your hands and you learn to explore... I've never been a great climber. I'm just a competent climber and I know my limits. But I love getting out and doing it. [PBS, http://www.pbs.org/now/transcript/transcript350_full.html]
The Goal
We want our mirror to make as sharp and bright of image as possible. After all, the vast majority of astronomical objects is very far away and appears very small and very faint.
A perfect mirror is limited by the wave nature of light. Fraunhofer diffraction of a circular aperture sets the limits of performance. The circular rim of the aperture diffracts light into expanding spherical waves that interfere with each other at focus, going in and out of phase repeatedly as the angular distance from the center grows. This creates a central dot, the Airy disk, and a series of rings of decreasing brightness. A perfect mirror will reflect 84% of the light into the Airy disk, 7% into the first ring, 3% into the second ring, and so forth, with a total of 16% of the light in the rings combined. [Oldham Optical, UK, http://www.oldham-optical.co.uk/Airy%20Disk.htm]
Less than perfect optics increase the brightness of the rings causing the star image to smear and to lose resolution. Our mirror should present the same Airy disk with approximately the same brightness in the rings.
Mirror Tests
Geometric based methods that calculate the path of the reflected light rays across the mirror face are popular and have a long history. These tests typically measure the longitudinal aberration, or the discrepancy between where the light ray travels compared to where it ought to be. However, without taking into account diffraction, the size of the Airy disk and the brightness of the surrounding rings cannot be determined with certainty, and indeed, in some cases, are non-intuitively correlated with the geometric ray tracing. In other words, the light does not go where the geometric ray traces say it goes, thanks to the diffraction of wave optics. [Jim Burrows, http://home.earthlink.net/~burrjaw/atm/t_verse.lwp/t_verse.htm and http://home.earthlink.net/~burrjaw/atm/odyframe.htm]
Ronchigrams of 13 inch [33cm] f/3.0 mirror, 100 lines per inch [4 lines per mm] grating
Reaching the
Goal
To finish a project doing only the work necessary at each stage, it is useful to imagine the finished product and determine what needs to be done. This betas an earlier stage that we can similarly treat. Eventually we reach the beginning of the project, with a clear path of dependencies or what needs to be done in order to accomplish the stages. The milestones in reverse for completing a mirror are: figuring, polishing, fine grinding, and curve generation. Each stage depends on the previous stage being completed correctly.
Figuring
In order to make an indistinguishable from perfect star image, the mirror surface must be accurate to a small fraction of the wavelength of visible light. The stage of adjusting the mirror surface by preferential polishing is called figuring. To begin this phase, the mirror surface should be smooth and accurate to a wavelength of light.
Polishing
To achieve this preparatory to figuring stage, the mirror is polished to a shape that is smooth and spherical. The rate of glass removal during polishing is exceedingly small. It could take fifty years of non-stop polishing to polish a flat piece of glass to within a wavelength of light of the desired mirror profile. We need much strong action! Using silicon carbide grit, the curve can be achieved in hours, albeit with heavy damage to the mirror face by the grit particles.
Polishing with a pliable material like pitch results in a smoothly polished surface, accurate to a wavelength of light or better, that is ready to begin figuring. The act of polishing is both a mechanical and a chemical process.
Oversized laps and turned edges
Mirrors are notorious for turned edges during polishing. Flash polishing after each stage in fine grinding shows an even edge, so the turned edge must occur during polishing. I’ve found that an oversized pitch lap controls turned edge. Oversized ratios can be up to 6:5, the so called magic oversize ratio that automatically maintains a spherical shape at desired radius of curvature.
14 inch
[36cm] pitch lap for 13 inch mirror; note the micro-facetting in place
of channels
Figuring
13 inch [33cm] f/3.0 mirror with extremely
long 'mirror on top' strokes
Oversized
pitch lap (far edge of lap and mirror are aligned)
Fine grinding
A series of ever smaller grits are employed in order to repair the damage caused by rough grinding, ending with aluminum oxide which leaves much smaller pits and few fractures compared to the silicon carbide. This stage is called fine grinding. I like to use three grit sizes, 220 silicon carbide, 500 silicon carbide, and 9 micron aluminum oxide. Grit of a particular size comes with a wide distribution of particle sizes. Typical are 20% of particles that are twice the stated size. Comparing particle sizes of 400 grit with 500 grit, the size ratio looks to be 4:5. But when looking at the 20% particle distribution, it is a nearly identical 9:10 ratio. Consequently it’s wasteful to run through a long series of grit sizes, as commonly practiced: 220, 300, 400, 500, 600, 25 micron, 12 micron, 9 micron, and 5 micron aluminum oxides. The third and final grit that I use is 9 micron aluminum oxide. Ending with 9 micron instead of 5 or 3 micron reduces the chance of sticking on large blanks and controls scratching. Comparing 9 micron to 5 micron looks to be a nearly two times reduction in glass pit depth, but looking at the 20% particle distribution, the reduction is only one-third.
I use plaster tools cast to the curved mirror with unglazed ceramic tiles glued to the face. Stroking the tool on top of the mirror, I rotate the mirror 30-45 degrees every fifteen minutes. This prevents astigmatism from occurring via print through from the mirror's backside. The frontside of the mirror can flex more over areas where the mirror's backside is thinner. Flexing downward during polishing can result in less glass removal, resulting in a bump when the polishing tool is removed. Mirror on top can also be used to avoid astigmatism, since the tool supports the mirror, but the grit seems to fall down between the tiles requiring more grit and wets to complete.
Rough
Grinding
Unless the mirror comes pre-generated, the initial curve will have to be ground into the mirror. A ring tool of half the diameter of the mirror used on top of the mirror’s flat face with the coarsest grit will rapidly grind a spherical curve into the mirror.
(end of introduction)