Should you use polymer thin solution?

I doubt the polymer mirrow is not that thernal stable. And also even it is possible, a homogeneous layer on the glass surface is not readily achieved.

The polymer would be between the two layers of glass. If you have ever noticed windows in a high rise building, they curve outward due to the air pressure inside the building.

I want to reverse that process by lowering the air pressure between two

sheets of glass. but fill that space with a polymer so the glass maintains

a constant surface curvature.

Perhaps spinning the mold on a horizontal platen while applying negative pressure, and let the Polymer cool and harden to maintain the curved shape.

The final polishing of the glass would produce the paraboloid

I am just trying to think of a way that a large diameter mirror could be produced

at a significantly lower price, and still produce good quality optical results

The polymer would need to be quite thick to make it a rigid laminate.

I see what you need. It seens to me that the polymer laminate should have very good mechanical properties. Try polymer-carbon nanofibers composite or some other polymer composite with good optical quality.

Gerard Lemaitre from Marseille has produced active mirrors by elasticity and negative pressure. See e.g. Astronomical Optics and Elasticity Theory, G. Lemaitre, 2012, Springer, or US Patent 3,693,301, 1972 or papers. However he does not use polymers since it is an active mirror. With the same methods, he has also stressed mirrors beyond the elasticity limit, and produced a permanent curvature.

Corning glass has a flexible glass that would be suitable for this. The way I see it this would be better if you used a computer control system on large mirrors to focus the mirror as this would be a better control system. By changing the vacuum pressure between the sides and hence the curvature. This could be done with extreme accuracy given the outside pressure and the inside pressures. You could make mirrors that had an infinite range. Or a mirror that could help detect small movements in distances.

The main problem is not to obtain a curvature, but to produce the intended curvature. See any textbook of elasticity about the shape of a circular plate under uniformly applied pressure. Then see the maximum allowable stress for the glass plate. Maybe reading the book suggested by Michel Boër you will find some answers why no telescope was build this way so far.

That is great but have they considered the newest of the flexible glasses that are making it possible to do many things that were not possible before this?

Perhaps that is a possible solution.

Inject the hot plastic to fill the void between the glass sheets, spin the sheets horizontally, and apply uniform pressure by spinning the sheets inside an

air pressure chamber to approximate the curvature needed.

Hi Michael

Sounds mechanically possible (and thus congrats for a great idea). But let me pose a few concerns.

1) What about diameters? How large do you thing you can make them? The sag of the first curving mirror is the minimum thickness of your polymer layer, if I understand. The larger diameter, the larger sag, the more polymer you need.

2) Setting the right radius does not look simple at all. You need even calculations with computational fluid mechanics (CFD) to fix a radius with a given diameter. And I bet this is not easy to perform in practice.

3) Thermal stability. I'm not sure if you'll lose all your assumed cost advantage using a very specialized polymer, and the proof and reject procedures in each cycle.

4) You should also consider how repeatable your process will be, and which parameters will it be sensitive to (pressure, temperature, potential bubbles in the polymer, plastic stability with time...).

My feeling is too expensive for low diameter telescopes, too unstable for large diameter ones...but there are magic materials out there, so I'll be happy to retreat!

I had thought of a thick sheet of glass for the bottom, and a thin sheet of glass

for the top, and a polymer with hollow glass spheres in between.

Heated and cured overnight in a pressurized chamber to approximate the

required shape.

The idea is to lighten the glass, and reduce time required to grind and

polish the mirror, to reduce the cost.

The mirror may actually end up as thicker than usual.

It might work, It might not. There is not much tolerance for changes

in shape of mirrors at light frequencies.

I am sure this would take some experimenting.

University of Strathclyde (Mech Eng) did some work on evacuating spaces for large mirrors about a decade or more ago, using flexible Mylar sheet drawn down over an evacuated drum arrangement. The results were generally quite good but as has been stated here the profile is not quite what you need, resembling a bathtub. In other words it’s flattened at the bottom and too steep at the sides. Also there was a bit of wasteage athe the edges so not all the area ( something over 50%) was available for viewing. This later formed the core of an idea for a tracked 3D viewing system that I was heavily involved in as a curved mirror is one way to project a nice 3D display without using glasses. At the time (pre –AVATAR film) the marketing people told us that there was no market for 3D so the project ran out of money. The other approach to large mirrors was to turn (lathe) the surface, and draw the mylar reflector onto it, however surface imperfections become magnified by a sort of tent effect over any small raised areas that had not been correctly manufactured. Thus it might ironically be used as a method to detect imperfections since the size of these faults were themselves magnified (x 10 or so) by the mirrored mylar. We also tried metallisation but the results weren’t great. Some details on the optical arrangements and manufacturing can be found here on our patent material: International Patent Application (from above) (2004) No. WO 2004/086771 A2, 7th October 2004 (McKay Stuart, Mason Steven, Mair Gordon, Harrison, Colin) “A Stereoscopic Display” University Of Strathclyd

If you put the mylar across a liquid surface. put a clear epoxy as a thin film and then spin the liquid, wouldn't that form a nice curve (maybe the wrong shape) by the vacuum between the liquid and mylar? When the epoxy sets, you'll have the mirror fixed and can stop spinning. Or could you electrostatically attract the mylar to a surface by controlling the charge distribution below?

This idea is similar to the mirrors used for focusing x-rays in synchrotron facilities. The mirrors are usually pieces of silicon (relatively thick) with a heavy metal thin film such as Pt on the surface for enhancing reflectivity. The Si is stressed in the center to give it a curve. The mirror is narrower on one end than the other to make the curvature appropriate for bringing focus to a single point. The x-rays strike the mirror at a glancing angle to get reflection, so those that reflect from the far side are bouncing from a point closer to the target, thus needing greater curvature. The width is narrower there to give more deflection. If you want to see the details, look up Kirkpatrick-Baez mirrors (KB mirrors).

Something like this may be workable in the circular form as well. KB mirrors have been made quite large, but their curvature is likely much less than would be needed for an optic that is designed for "normal" reflection than glancing.

I thought this was my own original idea back in 2004, and I even still have a 25-foot roll of aluminized Mylar, five-feet wide, in my storage room.  I've made a few mirrors, and was able to use electric fields to bend a laser beam off of a flat mirrored piece stretched inside a circular aluminum holder.

As I recall, using a vacuum to make the mirror forms a catenary curve, which is unsuitable for use in astronomy, which prompted me to consider using a circular array of electric field generators, balanced using an automated feedback system with microcontrollers.   I haven't done any serious calculations, other than very rough, but my estimates suggest that the potential might be between 50 and 100 kV in order to generate the very large forces required to bend this material, once stretched for a four-foot mirror.

After discovering that this idea has been around since the 1960's, I'm not sure that I want to put my time and money into building this telescope, knowing that it's hardly patentable, and once I design and build it, for a fraction of the cost of a glass-substrate mirror, the telescope companies would be very quick to upstage me and put me out of business.

It might be interesting and fun to try it, though.  If anyone has a suggestion for financing, I'm all ears.  I saw a recent SBIR solicitation from NASA, looking for an ultra-lightweight telescope, but I'm afraid I've just missed the window.

The downside for me is that I'm not an optics expert, and I understand that there are various orders of aberration, up to 7th order, which I don't know how to compensate for, so these might not ever be better than hobby-grade.  I think that one of the advantages of this technique is that, as we shift through different wavelengths of light, the mirror can be dynamically reshaped to compensate for those (depending on he elasticity of the material, and how much it can be stretched and returned - there's a name for this property that I can't remember right now).  This might help to eliminate much of the glare that we get from stars.

You can see some of my mirrors at wherearemyplacebos dot com.

The concept of using two sheets of glass, One thick, and one thinner with the evacuated space in between filled with a mixture of glass beads and epoxy resin might work.  The problem is the variation in the atmospheric pressure combined with temperature changes that effect differential rates of expansion and contraction between dissimilar materials.

Additionally, when a mirror is placed at an angle, it will sag under its own weight, thus large mirrors need to be stored horizontally so the sag is uniform over the entire surface.

Perhaps spinning a mirror on a bed of molten lead would lead to a shape that when cooled would take far less grinding time than conventional mirrors.  The Big money is in the elapsed time required to grind mirrors from a flat sheet to a concave sheet.

If you can use molten temperatures, and rotational dynamics to approximate the required shape, then use final polishing to finish the shape, the price of large mirrors could be reduced significantly.

Interesting method, however, if the intention is to observe astronomical objects surface variation of the reflective surface should not exceed L/4 where L is the wavelength of light (for a particular color ). Temperature difference combined with variation in the glass material may not help to keep this minuscule surface variation when a vacuum is used. It will be great if you can analyze the thermal behavior of such a system.