Optics Fabrication- Ribbed Mirrors

Light Weight Ribbed Mirrors

George Willis Ritchey

Pause for a moment to remember George Willis Ritchey, the pioneer of ribbed mirror technology, and consider the setbacks in his life at the hands of powerful evildoers. His method of gluing glass structures together is now obsoleted by thermal fusion bonding techniques of the great Canadian mirror making teacher, Ric Rokosz. Since the palomar 200, light weight ribbed mirrors are standard practice for large telescopes. Ribbed mirrors are a lot like aircraft: as with airplanes, you want great stiffness, low drag, and low weight. Telescope makers can learn a lot from aircraft designers.

Specific advantages of light weight ribbed mirrors are:

The mirror is light weight; the astronomer does not get a rupture hauling his equipment.
Less glass is used, the cost is reduced.
Commonly available thin salvage glass can be used, the cost is reduced.
The thermal mass is less, so the mirror cools to operating temperature quickly.
Unless the mirror is VERY large, commonly available glass can be used. I have used 1/4" plate glass to build a 13" mirror. If you believe in linear extrapolation, you could do a one meter mirror with commonly available 3/4" plate glass.
You will never be obstructed by large industrial mirror blank companies who are difficult or impossible to deal with.

State of the Art, 1927. Close examination of these reveals a lot of unpublished knowledge about rib pattern design.

Design Considerations

Front and back plate thickness
The front and back plate thickness should be sufficient to withstand a polishing pressure of about 1/4 psi with flexure less than what you deem appropriate for your mirror quality. If you use beam theory to estimate the flexure, you will have a conservative design. With a little more work, you can use a finite element analysis program such as FlexPDE, Nastran, Algor, or Adina to model the deformation of the glass over each region between the ribs. Obviously, the glass thickness must be compatible with the rib pattern.
Rib thickness
The rib thickness will be the same as the thickness as the front and back plates if you cut all pieces from the same sheet of glass. (This assures that all parts of the structure have the same thermal expansion.)
Rib pattern
The best rib pattern has been a subject of great debate in the literature. What is "best" depends on your fabrication capabilities. Most amateurs are able to bond ribs to the front and back plates by pressure of gravity, but will not be able to bond ribs to each other (as in the Hubble space telescope). The square mirror rib pattern of George Ritchey (in the photo) shows considerable sophistication: the open cells at the edge of the mirror have been bisected because they are subject to greater deformation under polishing pressure. Ventilation holes help to cool the structure by convection.
In calculating overall deformation of the mirror, you can disregard the ribs. Deformation of the mirror will consist of shear and bending. Shear is the same, no matter the mirror thickness, so use the thickness of a solid piece of glass. Bending stiffness can be estimated by considering only the top and bottom plates under compression and tension. These stiffness properties can then be used in a finite element program such as Dave Lewis' PLOP to optimize the flotation system.
The mirror rib pattern must be compatible with the flotation system. Flotation systems usually have a three fold or a four fold symmetry, so the rib pattern must match whichever flotation system is selected.
Some typical rib patterns:
- Straight Radial: originally used by Ric Rokosz. This provides best possible air circulation through the mirror for convective cooling. You have good access to the interior of the mirror for cleaning out the cerium and other residue prior to coating.
- Bent Radial: used by Schwartz to prevent rotational collapse during fuzing, while retaining the good air flow when air is blown into the center of the mirror. This design also reduces the gap between ribs near the edge, where the span between them is greatest.
- Cellular: there has been great debate in the literature over the relative merits of hex, triangular, and square patterns. To study this requires high power finite element analysis and a definition of what you mean by "best". One problem with cellular mirrors is that they are hard to clean!
Rib details: there is much work to be done!
- Holes: I have not tried holes in my ribs as in the Ritchey ribbed mirror. Although it is possible that holes will reduce weight and improve convective cooling, it is also possible that during fuzing, the holes will allow the top of the rib to slump away from the upper plate, resulting in a gap in the bonding. Ritchey used adhesive instead of thermal fusion bonding, so the holes were compatible with his fabrication methods.
- Edge Treatment: I have not tested the idea of tapering the ends of the ribs to improve air flow and to mitigate thermal stress at the ends of the ribs. This is a subject of ongoing investigation by finite element modeling.

Materials

Ordinary plate glass has proved satisfactory for fabricating ribbed mirrors, provided that the structure is protected from thermal insults (thermal shock and thermal gradient) during the grinding and polishing of the optical surface. Differences in thermal expansion between the parts of the mirror can be minimized by cutting all of the pieces of an assembly from a single sheet of plate glass. Salvage plate glass commonly available from some glaziers at low cost is satisfactory.

If thermal insults cannot be controlled, pyrex sheet can be used. This will reduce the chance of the glass cracking, but will significantly increase the cost of the structure. Pyrex sheet is no more difficult to cut, grind, and fuze than plate glass; the only problem is its cost.

Because you will most likely be working with 1/4" or 3/8" glass, the circular front and back plates are easily cut out with the score-and-break method shown elsewhere in this web site. Most of the work will be making the ribs.

You must fabricate the ribs accurately. The ribs edges must be parallel and the width of the ribs should be identical. The edges of the ribs that will be fused to the front and back plate must be perpendicular, flat, and fine ground This is easily accomplished with simple hand tools.

Start by cutting out the ribs by the score and break method. Allow for glass to be ground away at the edges of the ribs by making the ribs one glass thickness oversized all around. Some of the ribs will be wrecked when you are working them, so you should make about 20% more ribs than you actually need.

Grind one long edge of each rib straight, flat, and perpendicular to the rib surface. I use the same diamond bit in my drill press that I use to edge the glass, but before I had diamonds, I used a flat metal plate with water and #120 carbo. (photo of drill press setup)(photo of flat metal plate grind)(photo of one good edge)

Now take the ribs inside and set them up with an accurate right angle fixture; a drill press vise works well for this. Use a blow torch and pitch to fasten the ribs together: just paint the edges of the pieces, apply the blow torch, and the pitch will wick into the interfaces and hold the pieces together. When the block has cooled, turn it over, clamp it together, and apply pitch to the un-ground side. (photo of blocking)

(photo of hand grinding) Next, work all four sides of the block on a flat metal plate with water and number 120 grit. As you work, check the block thickness at all four corners with a mike or vernier caliper. Try to use a little more grinding pressure on the high corner (or the high edge). When you have ground all of the broken edges away and the four corners of the block are the same thickness within about .04" (.1 mm), run hot water over the block and separate the ribs. Rotate alternate ribs and reverse their order in the stack so that their narrowest portion is now between the thickes portion of their neighbors. For the odd-numbered ribs that are being turned over, their bottom north-west spot on the block should move to the top south-east.

Now re-assemble the block with pitch and a blowtorch as you did the first time. The bottom of the block will be flat, and the top not so flat. All you have to do is work the bad side of the block on a flat metal plate until there is uniform contact all over. If you will check with a mike, you will find that the four corners are amazingly identical. You should also grind the ends of the ribs so that they are all the same length. Finish grinding both sides with finer aluminum oxide. Although Bob Goff of HexTec recommends polishing the edges of the ribs, I quit with three micron optical fining powder (Aluminum Oxide). (photo of reblocked ribs)

Separate the ribs with hot water, and clean them with turpentine. Due to an embarrassing accident, I no longer recommend the use of turpentine in a pressure cooker for this purpose.

Assembly

Place the front disk of the mirror blank face down over a full sized drawing of the rib pattern. Place the ribs in position on the back of the front disk. If the edges are properly prepared, there should be no difficulty getting the ribs to stay put on their edges. Use cyanoacrylate crazy glue to anchor the ribs. Take care not to glue your fingers together. When all of the ribs are attached to the front plate, place the back plate over the ribs and glue it into place with the crazy glue. If the ribs are properly made, there should be only the slightest gap between the rib edge and the back plate. Crazy glue sets very quickly; you can pick up the structure as soon as you are finished assembling it.

Cooking

Cooking combines glue removal, fusion welding, slumping, and annealing into one step. You will need a programmable pyrometrically controlled furnace that can reach 640 degrees centigrade. Ordinary ceramic artist kilns that use "kiln sitters" will not be able to do this work.

What you end up with

Place the assembled mirror face down on the slumping form. Arange the work area so that, with the kiln lid open, you can see the reflection of a lamp in the back of the mirror. The flat glass should touch the curved slumping form only in the center. Raise the furnace to 640 degC as fast as you like. Once you achieve 640 degC, open the lid and check the lamp reflection every 10 minutes. When you see that the back of the mirror is starting to warp according to the rib pattern, you are done with fuzing and slumping. Cool the furnace immediately to 575 degC by leaving the lid open. Cool from 575 down to 375 degC at a constant rate not exceeding 13.3 degC/hour. From 375 degC down to room temperature, do not exceed 30 degC/hour. When the furnace reaches room temperature, take the mirror out. If it is at all warm, even if it is quite comfortable to handle, PUT IT BACK!!! Leave the mirror in the furnace with the lid open until it no longer feels warm. At this point, you are ready to make a conforming tile tool and begin grinding and polishing.

Well, sometimes you get this... keep trying!

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