Mirror Confusion

[trek_fan]

I am attempting to build my own scope. Details of which i can expand upon later, but at this point i am confused over mirror grinding. The first step in my vourney to building my scope is to make the mirrors. So i have searched the internet and watched "youtube" videos until i feel my eyes are close to bleeding. I like the Zeiss grinding machines and was planing on building one to grind my mirror. (As a side note, I know it could be done by hand, but I enjoy machine building) Anways, as I watch the motions of the machine one thing became very confusing to me. The mirror is fixed in space and is rotating axially while an arm on a cam is moving lateraly across its surface on a fixed plane. The adjustments I can see are :

1. Speed of mirror rotation.
2. Length of arm travel adjustment along its plane.
3. Speed of arm travel.
4. Maybe downward pressure if weights were added to grinding tool.

Here is a very telling link:

[ame="http://www.youtube.com/watch?v=gbLNNQZC-ew&feature=fvw"]Video 1[/ame] Fairly Short but very telling in movement

[ame="http://www.youtube.com/watch?v=eMDHA8IE014"]Video 2[/ame] About 10 minutes long

Ok, now to the crux of the matter. (Pun very much intended) knowing that all these points are fixed in space and the the arm only moving in one axis, how can a true spherical shape be imparted into the glass? It would seem to me that the lowest point on the cutting tool, being the center would just grind down a flat surface along the length of travel and only allow a curved area to be imparted after the length of travel, where the cutting tool is radiusing away. Other than the fact the person in the first video made an expensive sprirograph, i just do not under stand how it could impart a spherical surface to the glass. It seems to me that the the cutting tool would need to rotate on an independate axis following an arc.

This is another example here:

[ame="http://www.youtube.com/watch?v=WBfr0d-zp70&feature=related"]Video 3[/ame] Fairly short.

This video raises more questions.

1. If this is truely a dome shapped cutting tool and if it were 90 degrees to the mirror, would it not be cutting a low spot on the edge of the mirror and making the mirror convex instead of concave?

2. If this is a flat cutting tool, it should only be making contact with the mirror one the outer edges give flat walls and making a cone shaped mirror.

3. If this is truely a dome shaped cutting tool and it its truely off axis by the degree needed to match the radius, then it would make the proper concave shape on the mirror surface.


I have watched videos of people grinding mirrors by hand and it seems to me that either purposefully and unbeknownst to the person, the mirror is rotated around the cutting tool with the wrists allowing a concave surface. Of the machine videos the only way I could see the proper result is in the 3rd option of the video above.

I guess I am just having trouble visualizing this process.

[plateglass]

don't worry too much on why it grinds a spherical surface just make your mirror, i would advise to make it by hand because you will save time and money. machines are only really needed for making lots of mirrors or really big ones too.

[trek_fan]

Well, to be completely honest, I enjoy manufacturing, and have pretty much free access to every kind of cnc equipment you can think of from laser cutters capable of surgical precision on anything up to 3/8 stl plate, and if i wanna get heavier i can use the cnc plasma to go to 1 inch or better. Not to mention cnc machine centers, so building a machine is not a big deal. Material is basically free, and machine time is free as well. I am also really not on a strict timeframe, so I am sort of casually building my scope. I would like to really embrace all the aspects of it, and gain a very complete understanding of it all. As a side note, when I built a cnc 4x8 router table, it took me several years and i had to learn everything from pbasic for the micro controllers so i could build my own servo drives to hand scraping ways for the linear rails. I have to say I enjoyed every bit of it, and would not have traded the experience for anything. The one thing i regret from the router project was i did not record much of it, i would complete a task then move on , and it was all left in memory. With this scope project I want to record the entire event from begining to end, and share the milestones. If the group here would have a long winded air bag like me, i would chronicle the project here, and welcome any thoughts on it. Anyways, I digress, and in response, I would have to say that building a mirror grinding machine would cost me little to nothing, and I would enjoy the side project.

I just looked up and realized I have been getting longwinded again, so let me scram !!

[AustinPSD]

Most mirrors, specifically for reflectors (Newt's, Dob's) are parabolic.

Think of the mirror manufacturing/construction process as four major steps:

1. Blank fabrication

2. Grinding

3. Polishing / Figuring

4. Coating

Each of these major steps has several sub-steps. For now focus on step two and three, grinding and polishing/figuring.

The grinding tool starts flat. It can be another glass plate the same size as, or within about 75% the diameter of the target blank. During grinding, successively finer grit is used. In the initial stages, grinding produces a surface that is optically "flat" on the target blank. During successive grinding stages, one surface, the target blank naturally takes on a concave shape, while the tool takes on a convex shape. The rapidity of this process depends on several factors, including the size difference (if any) between the target blank and the grinding tool, the design of the grinding tool, the stroke pattern, whether or not the target blank is rotated under the tool, and the grit steps/grit type used.

The eventual result through between four and six grinding stages is a spherical concave surface on the target blank.

The polishing/figuring step uses a different tool, called a "pitch lap". There are different steps and materials used in this step, but the idea is that the pitch lap is pressed into the target blank at the spherical stage, and a polishing compound, usually cerium oxide is wet placed onto the pitch lap, where it falls into gaps in the lap face. There are specific strokes used to rotate the pitch lap and/or target blank to convert the spherical concave surface of the target blank into a parabolic section. During polishing/figuring, tests are performed to check the mirror shape, depth of curvature (sagitta). The tests can vary, depending on the figuring methodology, but consist of either or both of Focault or Ronchi testing, or in more sophisticated environments, interferometry in some form.

The polishing/figuring is critical, as this is what removes the spherical shape and related spherical aberration from the mirror, and produces the parabolic shape that focuses light into a point (circle of least confusion).

[WWPierre]

PlateGlass is doing some neat experimenting with diamond cutting wheels and simple mechanisms.

I like your approach. I built a factory for making architectural sub assemblies on my property before I started building buildings.

[sbooder]

If expense and time are not problems, the solution seems obvious. Build more than one mirror. The first you grind by hand to get a feel for what is going on with the grinding process, which motions work best how the grinding affects both mirror and grinder/pitch plate, and record the info in a way that can be used for machine design and construction. Machines (in my experience) tend to work better if the designer has a physical human understanding of the job at hand.

[tinkerer]

I thought about this very issue when I first built a telescope 30+ years ago. The way I finally looked at it is as follows:

Imagine that in a single stroke of the tool across the mirror blank it cuts a groove the width of the tool and .01 inch deep. Assume the tool is smaller in diameter than the mirror. (These figures are way to big but maybe they help to visulize the process.) Now turn the mirror 90 degrees and stroke the tool across it one more time. It cuts another .01 deep grove. Except where the grooves cross, it is now .02 deep. So now the center of the mirror has .02 cut away and the outer edges of the mirror has .01 or more realistically nothing cut away. Nothing cut away since the very outer edge only saw a tiny bit of actual grinding as the tool moved away from it or stopped moving as it approached it. Also the center of the tool is no longer in contact with the center of the mirror after this .02 material removal, it is largely supported out at its edges. Consequently the edges see a higher level of grinding and it becomes convex. Both parts begin the process of turning into slowly deepening spherical curves.

Now repeat the process thousands of times rotating the mirror and tool. The center of the mirror tends to get ground much more than the outer edges. Also any high spots will receive more pressure and the grit will be more active in such areas.

The only geometry that allows the tool and mirror to stay one grit particle diameter apart regardless of where and how the tool and mirror are oriented is a pair of concentric spheres separated by a grit particle diameter.

That mental model works for me. Hope it helps!!