Rough Grinding The Mirror
Making a 4.25 Inch Dobsonian Reflector Telescope
A Grinding/Polishing Bench
You will need either a stand or a bench to do your grinding and polishing. The traditional method was to get a old oil drum, and fill it with sand for stability. You could then walk around the drum as you worked the glass, leaving the tool or blank stationary. In the class I took, Dobson described in a video the use of a board on two stands. This being my second attempt, I built something a little more elaborate. Note that you want a slight slope so as to let excess fluid and mud drip off in one direction. Dobson suggests a special kind of nail to keep the tool in place, but I found that small pieces of wood nailed in worked just as well. For most of the grinding you will put the tool on the bench and move the mirror back and forth. If you over-grind your mirror, you can reverse the blank and the tool to flatten out the curve.
If you mirror is bigger than 6", start with #60 grit carborundum. That's grits that are approximately 60 per inch or 1/60th of an inch in size. With a smaller mirror starting with #80 grit is ok. If you buy a kit, that's the size grit that will come in the largest size. You place your tool on the bench, lock it in place. You spread a small amount of grit on the surface, and then add a small mount of water. Trial and error will teach you how much is a good place to start. At first the grit will have a dark gray color. You will also hear a rather loud noise, rather like sawing wood. After a while the grits will become worn down and turn a lighter grayish color. When the grit is significantly worn down, you need to replace it.
The Grinding Pattern
You might ask, why would grinding the mirror and the tool together cause there to be curved surface. The answer is in the grinding pattern. You want to hold the blank on either side of the tool and rub back and forth. You don't want the mirror to slip so a distance of about 1/3 the width of the blank is good. After you have rubbed the mirror back and forth a few times, on the left and on the right, you will want to spin the mirror either clockwise or counter clock wise. After doing rotation the mirror a few times, you will want to move the tool underneath a similar amount. So you end up spinning the blank a lot more than the tool. All of these operations, the number of times you rub back and forth, the amount you spin the mirror, how often you turn the tool should all be done without concern for constancy. In fact you want to avoid any consistency in your grinding. Consistency can cause various problem with the curve of the mirror. An obvious question is how can you consistently grind inconsistently? My method was not to pay too much attention. You want to pay enough attention to make sure you aren't accidentally being too consistent. Is that clear?
What Are We trying to Do?
I'm glad you asked. What is the goal of this grinding two surfaces together, turning the blank and the tool, and doing it all a little inconsistently. While you find the activity tiresome and tedious (I recommend listing to hard rock on an iPod) you are doing a very rough activity in two dimensions that will create a very precise result in the third dimension. If two surfaces can slide back and forth smoothly in two dimensions, then they are either both perfectly flat, or both perfectly spherical. That is the goal, a spherical surface. As you grind, wherever the surfaces aren't perfectly matched, the grit will cut away.
How Long Will this Take?
The dumb answer is as long as it takes. It will depend on which grit you are using, how often you replace it, how quickly you rub back and forth. The two biggest factors are first how big is your mirror? The 4.25 mirror only took just few hours. The 12.5 inch mirror took 5 or 6 days, maybe 6 hours a day. The second issue is how deep do you want the curve. This is a very important issue that is covered in another section, The Focal Length.
How Do You Know When You Are Done?
This is an important question. The obvious but un-useful answer is when the focal length is close to where you want it. But how can you figure this out. There are three methods that I can suggest.
1) On a sunny day, cover the mirror with a layer of water. Reflect the sun off the mirror onto a wall. Move the mirror back and forth until the image of the sun is as small as possible. Then measure the distance from the mirror to the wall. This method is not particularly accurate, but if you are not too particular it is easy and works well. The method was suggested by Dobson.
2) Measure the sagitta of the mirror with coins or a spark plug gap gauge. What is a sagitta? A picture serves best.
Roughly speaking, it is the depth of the curve on your mirror. To measure the sagitta, you can place a metal ruler across a diameter of the mirror, and measure the distance underneath it at the center. You can use coins to approximate the size you want, or use a spark plug gap gauge. To figure out what you want the sagitta to be check this link.
3) Use a spherometer. A sperometer is a simple device that stands on three legs in the shape of an equilateral triangle. A gauge in the middle of the triangle moves up and down, measuring distance to a very high accuracy. You have to zero the device by placing it on a known surface that is very flat. The Wikipedia linked article describes the formula for calculating the focal length from the gauge measurement, but if you remember your high school geometry, it is easy to figure out. This is the most accurate way to determine the focal length, however it has it's limitations. The surface of mirror is still #60 grit rough. You have to adjust the gauge in a consistent manner in order to get a good reading. The grinding is still not complete. These factors make it hard to get the focal length closer than a few inches. For this reason, it is best not to cut your tube until the mirror is in the polishing phase.
Note that a spherometer does not measure the sagitta.