Amateurs in the sciences are probably no less numerous than in the arts. Music may have more devotees than botany, but surely there are more amateur astronomers than Sunday painters. One is impelled to ask: what are these amateurs all seeking? It is this: an expansion of their understandings and of their capacities, and the pleasure that derives from effort. One can appreciate the arts without ever having touched a brush or a musician's bow; similarly, one may keep abreast of progress in science merely by reading. But the purely receptive role is not the one that yields the richest fruit. If that which we acquire is to penetrate deeply, we must in some degree be participants: we must use our eyes to observe, we must experiment, we must build with our own hands. The extensive knowledge contained in books must sound within us echoes of personal experience. Only in this way can a truly cultivated understanding be developed.
Andre Couder, 1951
I have often seen situations where people have been locked out of much of observational astronomy due to a lack of money. It is even more distressing to see this happening with young people. I have also seen others spend money on what can only be charitably called junk. Either way, you may find it interesting to find out what is involved in making a truly superior mirror. It can save you some costly mistakes, you can learn a bit, and maybe you just might catch the bug to make your own. This web page will be the basis of a talk given to the St. John's Centre, RASC, in February, 2001. I gloss over many things here that would be expanded upon in the actual presentation, mainly because others have written so well about them. I hope reading these pages may spark the idea of trying mirror-making yourself. If you have any further questions please drop me a line at "dbourgeo@nl.rogers.com," here.
I believe Mr. Couder said it best. At some point it becomes a fascination for many people to get a better instrument. Unless you have a large pocket book, the only practical way to make a large instrument is on your own. Depending on your resourcefulness and ingenuity, you may save yourself considerable money. The down-side of this is, however, a good bit of time and work. But if the idea of making something accurate to a few millionths of an inch with nothing more than two bits of glass, some common tools, and some jury-rigged testing apparatus appeals to you, then a bit of work won't stand in your way!
Most of our regular members are familiar with the various sorts of telescopes. Briefly, there are two main sorts of telescopes, the refractor and the (Newtonian) reflector. With a refractor it is important to have a good quality of glass because the light you wish to examine is actually passing through it. With a reflector, the glass is being used to support a very thin layer of aluminum or silver. No light actually passes through the glass. Amateurs have made both types, but the Newtonian is easier and cheaper.
There is still some uncertainty as to who made the first telescope (usually a Dutch lens maker). Galileo was, however, largely responsible for publicising the concept through his astronomical use of the refractor. The design, however, suffered from chromatic aberration. Everything you saw through the telescope was fringed with colour. There were other deficiencies. To solve them, telescopes became longer and longer, up to 140 feet. Newton used his superior knowledge of the nature of light gained through many experiments with prisms and the like to design the first reflecting telescope. Newton (1671) realised he could correct many of these deficiencies by reflecting the light.
After Newton, Hadley and others worked to improve the telescope. By the second half of the eighteenth century, James Short and William Herschel had perfected the parabolically ground mirror. The techniques we use today are essentially the same that they used. Herschel lived with his sister and several rooms of his house were devoted to telescope making. Most of the early telescope makers were in fact amateurs, including Herschel. Most of the advances in knowledge were brought about by amateurs.
We pass from the era of bronze to the era of glass with Leon Foucault in 1856. Foucault gave us his knife-edge test. With simple equipment he could easily detect deviations on the order of a millionth of an inch.
Modern amateurs began grinding mirrors thanks to Wassell and English Mechanic after 1885. Rev. Ellison also published there, and his works were brought to America, touching off a boom in amateur telescope making that started in the 1920's and hasn't stopped since then. Many names were involved in these early years such as Albert Ingalls, and Russell Porter (the amateur involved with the Mount Palomar 200 inch, and who inspired machinists in Springfield, Mass. to create the modern ATM cultural mecca, Stellafane).
This tradition continues with people like Jean Texereau (started as an amateur), Richard Berry, and John Dobson (inventor of the Dobsonian telescope, and inspiration behind the Sidewalk Astronomers of California).
Due to the expense in getting large optical quality glass most amateurs have made reflecting telescopes. They are also much simpler to make and design, and contain less elements and surfaces to work on. There have been successful first telescopes that were refractors, but unless you have a deep pocket book, you are limited to three inches or so. You also need some gear, such as spherometers.
There are advantages and disadvantages to either kind of telescope, but most authorities agree a good first telescope is a simple Newtonian, from 6 to 8 inches in size, with a focal ratio of about f/8 or longer. Many beginners have made 10 and 12 inch mirrors or even larger. This is usually not recommended unless you have related knowledge from other fields (one such person I remember reading about started with a 30 inch!).
Young and old, plus pictures
There are four main things you need: a mirror blank, something to grind it with (the tool), abrasive compounds, and testing apparatus. There are other things too, such as pitch, and a stand to work with. Your main expenses will come from these four, and coating.
I am not here to make recommendations as to suppliers, but let's check out the prices at a couple of them. Personally, I have dealt with Willmann-Bell (they also supply many good books and need to update their web site with all their products) and ASM Products here in Canada. There are many others, some are listed at http://www.amsky.com/yellowpages/ and at some of the ATM links below.
You will need a carpenter's tape for measuring the focal length. You can buy commercial Foucault testers (I couldn't find any, though). I highly recommend the Stellafane design at:
So much so, that I am planning to build one myself, even though I already have a tester. Making your own tester involves a trip to the hardware store for some plywood (better yet, use scraps of wood). You also need a few odds and ends, all of which can be got at your average hardware store, Radio Shack, etc. If you want really accurate measurements you can spring for a micrometer. These are usually expensive ($100 or more), but the Stellafane group seem to have a super cheap source, at $15 (I plan to buy one!). Nevertheless, you can get by with the common hardware screw or the really neat kinematic designs found in Howard (unfortunately, out of print, but probably still available at the Arts and Culture library).
On a personal note, I fondly remember at the tender age of 12, upon the inspiration of Howard, going to the local drugstore to procure some supplies for my very own Foucault tester. The cashier questioned me very closely, especially concerning what a fresh-faced youth such as myself wanted to do with that bizarre combination of bottles, rubbing alcohol, and those razor blades! I'm not sure she was satisfied with my answer, either.
Basically, you begin with two flat pieces of glass, start pushing them one over the other with a bit of water and grit, and eventually you have two curved pieces of glass. With the mirror on top, the centre of the mirror (and the outer part of the tool, on the bottom), gets most of the wear during your strokes. The only two surfaces that can smoothly move over one another are a plane, or a section of a sphere. If your mirror gets too deep in the middle, simply put the tool on top and grind that way for a while.
I don't want to bore you with conic sections and the like, but there are two basic bits of information you will need to know. First of all, the only surface that will reflect parallel light to a point is a paraboloid. A cross-section of a paraboloid is a parabola. All this light goes to the focal point, where you examine it with an eyepiece or camera. But first, it has to be diverted to the side by your smaller secondary mirror. The parabola, like a circle, has only one shape, and like the circle it varies only in size (radius).
The point where all parallel light comes to a focus is called the focal point. About twice as far away from your mirror is a point we shall call R. The distance from this point to your mirror is the "radius" of the paraboloidal shape on your mirror (don't confuse this with the radius or diameter of the circular mirror blank, the two are at right angles to one another). At this point I should draw a picture. If your mirror were a perfect sphere, any light that comes from R would be reflected perfectly back to R. If the surface is instead a parabola, the light won't be reflected back to a point (remember, "it is only parallel light that a paraboloid deals with perfectly"). We shall take advantage of this fact with the knife edge test of Foucault.
One other thing you should be aware of is the wave nature of light. Because of this, light "diffracts" and does other interesting things. Diffraction of sound energy is the reason why we can hear people walking outside in the corridor even when there is not a direct line from them, through the open door, to our ears. (I am ignoring, of course, all the reflected sound waves bouncing around, and sound coming through the walls themselves for the purpose of this analogy.) Because of this wave nature of light, even if you built a perfect mirror all the light would not come to a perfect focus, instead it would form what is called an Airy disk. A perfect mirror would produce a perfect Airy disk, with the right amount of light in the central disk, and the right amount of light in each of the outer rings around the central disk. This is why stars never come to perfect points, and why bigger telescopes have better resolving power to see details. If you have a small telescope and try to use too much power, you only end up magnifying the blur. A small telescope collects less light, and has less resolving power.
Looking for the Airy disk under high power is a pretty good test for a telescope. You may not find it because of atmospheric interference, however.
[N.B. I am playing fast and loose with some concepts here, particularly to do with the radius and focal point. These are in common parlance in the ATM community, and a book like Texereau should help.]
With rough grinding, you start with larger grit sizes, such as Number 80 Carborundum, and take your mirror from a flat condition into a sphere with the necessary radius. If you remember, you divide this radius in half to get the focal length of your mirror. The ratio of this focal length to the diameter of your glass mirror is your focal ratio, the famous f-number of your mirror. At this point we should get a volunteer to demonstrate for us.
With fine grinding, you continue using the same basic principles. You work your way down from larger grit sizes to smaller ones. You are trying to gradually smooth your surface and decrease the size of the craters or pits that are left over from each of the larger grit sizes that went before. Hopefully, you will clean everything in sight within an inch of its life before you change from a larger grit size to a smaller one! See the Guide to Not Scratching Glass for more information, http://www.astronomydaily.com/atm/scratch.asp. I prefer to wear a lab coat (clean coveralls work too if there are no pockets where dirt can collect) and maintain scrupulous attention to where my hands go every second, where I lay things down, and the relation of my body to anything that might have grit on it. This avoids a few cleaning steps, but you have to be rigorous in a way. The really good ones look casual, but they are fooling you. Any really large professional telescope project is almost as much about cleaning, and cleaning, and cleaning the workshop, as it is about anything else. You have been warned.
After you have made your own mirror you will never again be casual about cleaning a mirror, or looking after its surface, whether its yours or a commercial one. You will understand what one single piece of dirt can do to utterly ruin a mirror. With enough scratches, a finished mirror's performance will seriously degrade.
Here we melt down pitch and apply it to the surface of the tool. Channels are cut in the pitch so that we end up with something that looks like a waffle iron. The tool, with the pitch over it, is "pressed" onto the mirror. This means that you put some weight on your mirror, put the mirror on top of the pitch (which is on top of your tool), and wait about fifteen minutes for the pitch to slowly take the shape of your mirror. Then we make up a "slurry" of optician's rouge or cerium oxide and proceed to polish. The rouge is so fine that it works at a microscopic level. After some time, you have a surface that is polished perfectly. You no longer have a whitish disk you can't see through, but a clear, smooth piece of glass. If you have been careful to follow instructions, this will have a spherical cross-section accurate to a few millionths of an inch. You have done nothing very special or difficult to get here, except going around your tool in a lot of circles.
After you have left off with polishing you have a mirror with a spherical cross-section. The next step is to "sort of" deepen it just a little. This will produce a parabolic cross-section. This procedure is where the art enters into mirror making. It takes the practice of making a couple of mirrors and learning to read and interpret the Foucault test to master this step. However, it is not quite the black art it is made out to be. It is very helpful for the beginner, however, to have someone experienced guide them at this point.
With conventional parabolizing you prepare your mirror just as if you were going to polish it, as above. Press the pitch for at least fifteen minutes. It only takes about 5 minutes of W-strokes that concentrate on wearing down the central portion of the mirror to do the job. This is a bit rushed, however, and can cause problems, so most will slow down and do, say, four sets of 5 minutes of less vigorous excavation, for a total of 20 minutes. You let your mirror cool for a while and then go test it with the Foucault tester. You run your measurements through your calculator and generate a test data sheet (or just use Sam Brown's 1/4-wave tables and throw away your calculator). You also look at the overall appearance of your mirror to see if there are any local defects that you may need to get rid of, or other special problems (a lot of these occur because you weren't careful in producing your sphere in the first place).
At this point you have to decide what to do to get your mirror from the surface it currently has to the desired parabolic shape. Thanks to the unevenness of the parabolizing stroke, your mirror may be in any number of evil states. If you are careful, follow directions, and get the feel for the precise, and yet not quite precise, movements required, you should avoid most of them. Texereau's group used to slow things down and take an hour, using several different people to better average out errors. Many could parabolize "automatically," from habit. If worse comes to worse, you can always polish things back to a sphere and start over.
There is a sort of repertoire of techniques that people have developed over the years to deal with problems. You try something out, let the mirror cool, test it, and repeat until you get it satisfactory. All the major stuff you need to know fits on 11 pages in Sam Brown's book, and most of that consists of his wonderful drawings. It is not complicated, but does take some practice and experimentation. For example, one technique they used on the Mt. Palomar 200-inch telescope was to touch-up local spots with their thumb, using talcum powder. This would remove glass one-millionth of an inch at a time in a local area.
The room you do all this in had better be fairly uniform in temperature, with no drafts. As long as the temperature changes slowly, such as a degree per hour, you should be all right. As dramatic evidence of the sensitivity of the Foucault test, put your thumb on the mirror for a second. You will see an enormous hill right on that spot, because the glass expanded from the heat of your thumb! It may have only expanded 10 or 20 millionths of an inch, but it sticks out like a sore thumb in the Foucault test! (See the wonderful book, The Perfect Machine, by Ronald Florence, where Hale used to impress all the important "money people" with this one.) Its amazing what a slit, a straight-edge, and a light source can show you.
This promises to be a great revolution in mirror-making, one of the most important. It was introduced in the November 2000 Sky and Telescope issue. Many people have tried micro-flexing, but usually end up with astigmatism. This is yet another example of amateurs advancing the state of the art.
According to Adler, if you start with a sphere (much easier to create a perfect surface than a paraboloid) and pull it into a parabolic shape with some glue and some screws and an annular ring, you have the potential to end up with surfaces that are extremely accurate, even beyond what is done in professional shops. Adler has a couple of mirrors made this way, one of which tests out at 1/40-wave. Even a beginner can approach this (hence the revolution).
This approach is too new for me to recommend it, and has some potential problems. Fortunately, you aren't spending large amounts of money. I plan to test it out on an 8-inch blank. No one has made mirrors larger than 12-inches this way, but calculations indicate it should work (dealing with astigmatism may be the problem). But after I learn from the 8-inch, I plan to work on an 18-inch using this technique.
It also has the potential to fix up many commercial mirrors that have problems. Here is one example:
Better yet, you can skip parabolizing your mirror altogether if the f-ratio is high enough. At about f/10 for 6 and 8-inch mirrors, for example, a sphere produces a "good enough" image for most people. This is where the junior set usually leaves off. Such a mirror is just as accurate as one that was parabolized at f/7, for example. The disadvantage is the longer tube, and the smaller angular views of the sky that you get. The advantage is a smaller secondary. You have less obstructed light, and less diffraction effects from the secondary. These are often called "planetary" Newtonians because of their increased ability to detect fine contrast.
Most amateurs will buy the diagonal, or secondary, as these are pretty cheap. If you are really on a budget you can make your own diagonal. It has one or two of its own unique tests, but nothing expensive need be involved. You also grind this one with a tool, the main distinction being you want to make it flat, and not start digging a hole in the middle, like with our main, parabolic mirror.
Again, eyepieces are usually bought, though they can also be made. Making eyepieces really needs some specialized equipment. However, just this year Sky and Telescope had an article on how to make your own eyepieces from things you can get on the optical second-hand market. These are pretty cheap.
Before you send your wonder off to be aluminized, you can proceed to build the mounting (another talk for another day). Never make a mounting before the mirror is finished, because you won't know the precise focal length until after you are finished. Even a 6-inch f/8 bare glass telescope will pick up about as much light as a 1-1/4-inch refractor. You will have plenty of light to try your telescope out on the moon. More importantly, you can do a star test with your telescope (say, with Vega). This is another whole topic, but a star test is a pretty sensitive overall test of a mirror. It is good to learn, even if you never plan on making a telescope. Once you are confident in your mirror, send it off to be aluminized. Pack it very carefully....
Some intrepid souls with access to vacuum equipment have even aluminized their own mirrors. Unless there are leaks, foreign chemicals, or a bad design, you automatically get a good, even coat. Most amateurs who want to do this will silver the mirror instead. This involves some messy chemicals, and takes a bit of skill to get an even coat. Silver won't last very long (with our lovely, salty ocean air you will be silvering your mirror every 6 months, or even more often). The one good thing about silver is its high reflectivity, but special coatings on aluminum mirrors get pretty close for most purposes.
Here is a bit more on the Foucault test, courtesy of the Victoria Centre's site:
As a bit of a side trip, here is a guy who made his mirror in 10 hours flat. He also explains a variant of the Foucault test that is often used:
At this point we are going to make use of our now rather skimpy knowledge about the wave nature of light. We can use this to decide how mirrors may be rated. There are several different ways to decide as to what is a good mirror. They are all to one extent or another arbitrary. The standard 1/4-wave mirror is pretty OK (the Raleigh Condition). Many prefer 1/8 or 1/10. For most purposes, going beyond 1/4 only gives more marginal improvements because of the wave nature of light. However, 1/10-wave does give your mirror more room to maneuver with temperature, plus the Raleigh condition doesn't tell the whole story about the mirror's surface. Note that it is somewhat doubtful that a Pyrex blank subjected to winds and slight changes in temperature will allow anything more accurate than 1/10 (Texereau). However, it is possible to figure a mirror to 1/20 or even better. If you are into low contrast work over an extended area, such as planetary observing, a mirror accurate to 1/16-wave would be better (Texereau).
Thanks to all these different methods, some manufacturers can tell you one thing, and mean another. The most common being whether they are talking about the wavefront, or the actual surface of the mirror. Thanks to reflection, any errors in the surface are doubled in the wavefront. The Rayleigh criteria is for the wavefront. So read those ads very carefully. Another thing to concern yourself is with what fraction of what colour light (wavelength) are we talking about? At the ultimate extreme, you could always pick a radio wave as your reference point and have a super accurate mirror, even if it was perfectly flat.
Here are all the gory details, courtesy of Mel Bartels:
For more on the effects of secondary obstruction, and some excellent pictures of the Airy disk:
(I have almost every book there is, even the out of print ones, so ask me to bring one along if you would like to see it before buying it at a book seller.)
Web pages:
An excellent place to search on individual topics:
Here is another good web page, discovered long after the talk:
A good beginner's site on how to grind out a mirror, though I recommend getting a book like Berry's or Texereau's, or both. Berry has better designs for building, Texereau has more help on technics.
And I seem to have forgotten the best resource of all for supplies, the ATM Resource list:
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