Starting the Fine Grinding

October 6, 2002

I started fine grinding with #120 silicon carbide I think in December of 2001 (I had misplaced my notebook and didn't keep notes for this part). Because our garage is unheated and too cold to work in during the New England winter, I moved my grinding workbench into the house and put it into a spare bedroom.

One recommendation I have for anyone making a telescope is that the experience is vastly more enjoyable if you create a pleasant working environment. Grinding in the house, with my back to the wall looking out into the room, and playing CDs on a boom box while I ground made the work go a lot faster.

The tile tool gradually wore into contact with the mirror as I ground, starting with the corners of the tiles. By the time I finished the 120 on the primary only a small spot of glaze remained on the tiles of the primary tool, and only a little on the outside edge of the secondary tool.

(I made a small tile tool for the secondary but you will see that I would have done better to have used a glass tool for the secondary.

I put over two hours of grinding 120 on the primary. That's more than is ordinarily needed for a grade of grit during fine grinding, but I wanted to get the tool fully into contact with the mirror. I also wanted to make small adjustments to the radius of the primary.

It's faster to change the radius with #80, but you have better control and the spit test works a little better when the mirror is ground finer. I tried buffing the mirror with automobile paste wax as some have suggested on the ATM list, but I didn't find this helpful. I was later told that this doesn't really work until the mirror is much more finely ground, at #320 or beyond.

Someone suggested I do a couple wets with #320 when I wanted to measure the radius, but I didn't do that. But note if you try this you should take care not to get your finer abrasive contaminated - pour a little out into another bottle that you use just for this purpose of you're going to try it.

I bought a few electronic bits at Radio Shack so I could use an LED as the source of illumination when measuring the radius. It makes the test a little more accurate than using a candle, which I found was otherwise the best light source. A flashlight is just too broad. I had hoped to use a knife edge to find the center of curvature with the LED, but again the mirror was still too coarsely ground to focus that well.

Colin Caissie of the Central Maine Astronomical Society lent me a copy of Telescope Optics, Evaluation and Design by Rutten and van Venrooij. I used the formulas in it to set up a spreadsheet in Quattro Pro, which allowed me to vary the parameters of my scope to see how different parameters would work out. When I clean up the spreadsheet some and add some explanatory notes, I'll post it here in a couple different formats, as I think others will find it useful.

I settled on an f/3 primary, with the secondary being ground such that the effective focal length of the whole system is f/12, or 96 inches. I plan to have the cassegrain focus fall 10 inches behind the front of the primary, which should allow me to use a diagonal (for comfortable viewing) while still having room to clear the top of my head. Some guy on the list suggested I measure the height from one of my pupils to the top of my head, and I did just that!

I decided also that I would use a 2 inch eyepiece holder. That's large for an 8 inch primary, and would require a rather disproportionately large hole in the primary (as well as a large secondary) but I have found I often like to look at larger objects at low magnification rather than extremely small ones at high magnification. If the focal plane is 2 inches in diameter, this would give a field of view of 1.2 degrees (although in practice the field stop of a 2 inch eyepiece will be smaller than that).

I also have in mind doing astrophotography with the medium format camera I dream of getting someday.

Colin Caissie also lent me a spherometer and gave me a couple pyrex blanks for the secondary. Both of the blanks were larger than I needed in part because that's what was available and in part so they would fit in the spacing between the ball feet of Colin's spherometer. I would need to cut the secondary down to size by trepanning it later on.

Grinding with 120 on the secondary also went well, but I stopped for a long time (about 8 months) as I described on the list:

FROM: Michael D. Crawford
DATE: 09/28/2002 06:53:54
SUBJECT: ATM Progress on my 8" R-C

I've been working again on my 8 inch ritchey-chretien travel scope again after setting it aside for several months. I have a web page about it at:

http://www.geometricvisions.com/atm/rc8/

There are no pictures yet, but I have gotten my scanner back from the movers and I also bought this really cheap 'n nasty digital camera from Wal-Mart so I'll be posting some photos soon.

Things were very hectic for my software consulting business for a while, and it was very hard to find the time to work on it. Also I had done most of the 120 fine grinding early last winter, but didn't want to go to the next stage until I was able to visit Colin Caissie to get him to measure the radius of the spherometer that he had lent me. It just took me a long time to get it together to go over to his house.

But since I've resumed work again I've realized that even when I am busy it wouldn't be that hard to find just an hour or two a week to grind. It contributes so much to my peace of mind. I think I'd be a more productive programmer and certainly a more contented one if I spent more time working on my scope.

I have two mirrors to grind, the 8" primary and the secondary which is about 3" across right now, but which I will trepan to a smaller size soon. One reason I am grinding the secondary with such a large blank is that it fits Colin's spherometer - had I ground the right size blank I wouldn't be able to measure its radius!

I had a small disaster after I thought I was done with the 120. I am using tile tools for both mirrors, but the secondary's tool turned out to have its tiles spaced so close together that it's hard to wash the grit out when I change grades. So I tried to use a diamond tool chucked in a hand drill to gring the notches wider. Unfortunately the sideways pressure knocked a tile off the tool. I only have four tiles on the tool so I couldn't continue without it.

I considered starting over at #80 again with a new tool, but in the end I was able to glue the tile back on with candle wax. I heated both the tile and the dental stone before I pressed them together with melted wax in between, and pressed down very hard on the tile after I put it back in place. I think it worked out OK.

But then of course my tool wasn't in proper contact anymore so I ground a long time just to get it back to a sphere that was in full contact. Unfortunately that lengthened the radius of my secondary significantly. So then I spent over an hour shortening the radius, slow going with #120. When I was done I only had enough abrasize left that I could do one more wet.

In the end I think I might have done well to have gotten a new tool. One other reason for this is that someone pointed out to me that it is much better to use a glass tool for a convex secondary, because you can put a slight polish on the tool (or shine in with car wax) and use a knife edge to get an accurate measure of its radius. It turns out to be difficult to get really accurate measurements with a spherometer.

This combined with all the extra time I put into it means that it probably would have been worth my while to start over with a glass tool.

In any case I'd like to point out that one should always use tiles small enough relative to the size of your tool that it wouldn't matter if a couple fell off. For my secondary they would have to be very small.

If you measure something repeatedly and average the results, you can get a more accurate measurement than doing it just once, and from the spread you can get an estimate of how accurate your measurement really is. There's a mathematical procedure that physicists use for this called "propagation of errors" that allows you to plug your measurement into a formula while also getting an estimate of the error in the formula's results.

For reasons that are to complicated to go into at the moment, the error in an average is inversely proportional to the square root of the number of measurements. Four measurements will yield an average that is twice as accurate as one measurement. Nine measurements will be three times as accurate. Measuring twice is only 1.4 times as accurate.

Measuring only once cannot produce an error estimate so you should always measure more than once. It's OK to make just a few measurements to check your progress but any measurement that really matters should have lots of samples.

On August 23, I took nine measurements with the spherometer and propagated the errors the way my lab instructors flogged me to do in school and got a secondary radius of 18.21 +/- 0.03 inches. Most of the time I take four measurements each of the flat surface I use and the convex secondary.

I can also tell from the spherometer formula that the result is only slightly sensitive to errors in the distance of the balls from the micrometer at the center, and errors in the diameter of the balls are pretty much insignificant. However, the result is extremely sensitive to errors in the sagitta.

For a spherometer it is very worthwhile to use a high-quality micrometer or a dial indicator. After a lot of practice now I am able to get measurements that are reproducible by +/- 0.0003 inches or so. Averaging over four samples gives an acceptable precision.

Another important reason to estimate your errors is so that you can tell if your measurement is really meaningful. You may think you've got an eight-wave mirror from the Foucalt test but if your error is +/- a quarter wave then your measurement isn't meaningful. If you find that your measured error estimates are bigger than your tolerances, then that is a good sign that you need to find a better way to measure, perhaps by building a better test rig.

So finally after something like four or five hours of grinding with 120 on my secondary, the dimensions I have are:

primary radius: 48.5" +/- 0.5 or so (measured by reflection) - that's f/3!
secondary radius: 18.61"

I haven't propagated the errors for my secondary measurement yet but I would guess it's about +/- 0.1 or so.

I have a spreadsheet that calculates everything based on the formulas in an optical design book that Colin lent me a while back. If the cassegrain focus falls 10" behind the front of the primary, then this gives a focal length of 95.4". I was aiming for 96.

The truss tube of my scope will be only about 20" long, with the focuser sticking a few inches out the back. I planned for 10 inches in the back to allow room for my head when a diagonal is used.

I've been thinking of writing a web page about how to do error propagation, and giving the error formulas for some common ATM equations. Before I do I'm going to try to find out if someone else has written up a web page for error propagation, because it's pretty complicated when considered in full detail.

You can find a pretty dense treatment of error propagation in "Experiments in Modern Physics" by Adrian C. Melissinos.

The next things I need to do are to trepan both my mirrors, and to pour the dental stone foundations for the pitch laps.

When I trepan them I will probably use Cambell's tomato soup cans as the tools. A soup can is about the right size and worked great when I bored my 10" in high school. I won't cut all the way through but close enough that I can finish the job after I'm done figuring without worrying about stresses in the glass screwing up the figure.

My neighbor owns a furniture shop and has a drill press he says I can use for this.

Then on to the 220!

Anyway
--
Michael D. Crawford
GoingWare Inc. - Expert Software Development and Consulting
http://www.goingware.com/
crawford@goingware.com

Tilting at Windmills for a Better Tomorrow.