Parabolica or Spherical?

I like your idea. Whether the glass shape is parabolic or spherical really doesn't matter in my mind because the amount of curvature is small and you are only dealing with a small fragment of the total arc that a parabola or a sphere makes.

The downside is that irregularities in the glass will cause the glass to sag with some error as well as any thermal differences through the glass. So, I would expect that you will still need to do some grinding to achieve the figure you are after. By figure I am talking about the optical trueness to the desired mirror shape.

Now, if memory serves, the thicker the mirror glass, the more thermally stable the mirror. I am thinking that good mirror blanks are pretty thick, so bending them by the method you propose would be really tough. You would need to heat the glass to its melting point and I wonder if that would impact the glass's thermal properties or introduce some other undesirable trait?

I don't know

I was thinking of a focal length of 1.8m which would give me an S value of 31microns at center point. With a sperical mirror, problems of focus occur due to the non columination of the light. It is true that mirror blanks are thick, for example, a 12 inch mirror would be about 1inch thick. I am trying to do away with the grinding process.

Glad you like my idea, It´s been rattling around my head for ages!

I was thinking of a focal length of 1.8m which would give me an S value of 31microns at center point

A mirror with a 300 mm diameter and a focal length of 1.8m (radius of 3.6m) would have a sag between the OD and center of 3.1 mm.

I like the idea! The curve would be parabolic. Unfortunately, controlling the curve would be really difficult, because you'd have issues with uneven heating, uneven internal stresses in the glass to begin with, etc.

Bubble canopies are sometimes formed this way, but I think plastic is a little easier to work with (and the curves are less critical). With glass, there is a high probability that the whole thing would suddenly sag almost uncontrollably, or that hotter sections would suddenly "give" before cooler sections.

If you had a surface against which the glass would bear after it stretches, that would help control the process. (This would be a variation on conventional vacuum forming.) In any case, you'd need to grind the glass to final shape. You might be able to develop a honeycomb like support, to keep the glass stable.

Here's an idea: There are extremely large CNC router systems that can route the honeycomb support from a piece of (lets say) 100mm thick honeycomb material*. Some of these should be cheap to run if it were not for the fact that the capital cost is high. So if you find one of these, and it happens to be doing nothing at the time, and the guy who owns it likes you... you could end up with a honeycomb concave blank into which you would vacuum form your glass. You'd still need to grind, I think, but not too terribly much.

* Hexcel can do this, and Janicki machine has such a system too.

I am just realizing that you probably intended the vacuum to hold the glass in its curved configuration -- not simply to serve as a means for vacuum forming a heated piece of glass. I'd have to agree with another poster that maintaining a consistent ratio between the vacuum drawn and the necessarily varying atmosphetric pressure would be very difficult, as would be overcoming the non-uniformities in thickness and stiffness distribution in the glass itself.

I don't know the answer to the bending glass question, but it put me in mind of something I saw a few years ago that was really neat.

A Professor at Union College developed a "parabolic" mirror for a solar hot water heater in the following way:

1. Take 2 large sheets of mylar film, one silvered and one not. Cut into circular shapes. These can be several feet in diameter.
2. Put a hole through the reflective film, near the edge, and glue a tire valve in place.
3. Cut a wooden frame just less than the diameter of the mylar sheets (say, using a 4x8' sheet of plywood. The frame consists of two circular wooden rings a few inches wide. Drill holes through the rings at regular intervals. These will be used to bolt the rings together.
4. Put the two sheets of mylar between the rings. Silvered sheet on the bottom with the silvered side up, valve stem facing out. Clear sheet on top.
5. Use bolts and glue to clamp the rings tightly together, forming an airtight seal around the perimeter of the mylar.
6. Inflate the space between the sheets through the tire valve. The sheets will "puff apart"
7. The result is a mirror - it's not really parabolic, but it's parabolic enough to concentrate significant solar energy at the focal point. Mount it on a frame and circulate a working fluid (e.g, water you want to heat) through the focal point.

I've always liked this idea. It seems like a cheap way to make a home solar concentrator. I have no idea how it would hold up over time, but one of these days I'm gonna try it out, just to see.

.... sorry for the diversion.

Steve

"want to make a telescope mirror"

Get a pyrex or equal telescope mirror and tool blanks of the desired size 290 - 300 mm. and assorted grades of abrasives and polishing agents, and grind a proper mirror in the time honored way of all genuine and/or dedicated amateur astronomers.

For best image quality you will need to figure the mirror to a parabola after first achieving a spherical surface.

I think it may be catenary.

it could be served as a kind of parabolic surface.

if your pressure is average.

just think of the rope between two poles. it has only gravitation itself.

With a rope suspended between two poles, the gravity vector is not perpendicular to the rope except at its midpoint. Consequently, the shape is a catenary. In the case described above, the force vector is perpendicular to the glass at every point, resulting in the ever-popular Hencky Curve. Not your best shape for an astronomical mirror. Even after the glass deforms, the force vector at every point is still perpendicular.

-e

It may be hencky curve. but its really out of my depth. in fact I almost forget all my litltle dynamic and mechanics knowledge. I try to turn out my book in old box and have a review.

on the other way I thnk the words of the gravity vector is alway downward is right. I understand the force your meaning must be compositon force or resultant force. you must type wrong. the rpe element has three forces, and their resultant force is different from direction of gravity difrection. except terminal support points.

I dont know if I have a capability to read the paper. because my english is very poor. but let me try if I have got a time.

To bend the mirror into its parabolic shape you propose to use a vacuum. Problem is that it would be necessary to control the vacuum pressure to a very fine tolerance. Otherwise the focal length would keep varying: not a very good thing for an astronomical telescope. As for the thermal problem, I would imagine it would not be the glass which would be more affected; but the gas in the vacuum.

I've just been round our factory measuring some of the glass viewports on our vacuum chambers. The ones I was measuring are 8mm thick kodial glass and the average centre depression is 0.06mm using a depth micrometer with a 63mm wide base which gives a radius of 827mm. The pressure in the vacuum chamber is 1x10-9 torr. There was a variation between the viewport centre depression of 0.04-0.10mm even though they are supposedly identical & at the same pressure.

Because the forces acting on the glass plate are due to fluid pressure, the force on the glass will be everywhere normal to the surface. This symetrical situation means that the shape that will be obtained will be spherical (think of it as being a section of a bubble). This neglects forces due to mounting which would be negligable if it did not restrict bending (eg. if it simply rested on a sealing o ring). If you're after a parabola, this can be obtained by spinning a liquid surface- the shape results from balancing the force due to gravity with the centripetal force. Some very large telescopes have been made with spinning mercury mirrors- the disadvantage, of course, is that they are restricted to pointing straight up!

I'd jumped to the conclusion that the somewhat flattened shape I'd anticipate was, in fact, parabolic, rather than spherical. Your post led me to look it up:

Past investigations of membrane mirrors have led to the conclusion that they are not suitable for imaging in visible light because their shapes when inflated differ too much from paraboloids. In particular, upon inflation, a previously flat membrane of uniform thickness assumes an oblate spheroidal shape described by a function named the "Hencky curve" after its discoverer. Although there have been suggestions that radial variations in thickness might result in inflated shapes that equal or closely approximate paraboloids, the necessary variation in thickness has not been published until now.

I'd think that a material with substantial beam strength and stiffness (such as plate glass) might not conform to the Hencky curve, which I suspect applies to thinner materials, in which the straightening force from differences in stretch on opposite sides of the material are insignificant. The rest of the article:

http://www.nasatech.com/Briefs/Jan01/NPO20952.html

For a good astronomical mirror the surface figure should produce a wavefront better than 1/4 of a wave. If you are usinhg visible lilght around 550 nm, that would be a surface error better than 1/2 of the wavefront error or 550/8 ~ 70 nm = 0.07 microns!

Yes, you need a parabolic figure. The difference between a sphere and a parabola of 300mm diameter and a focal length of 1.8m is 1.2 waves surface at a waveledngth of 550 nm. That is a wavefront of 2.4 waves! Much larger than the required 1/4 wave for a diffraction limited telescope.

Stability of the surface during use is important. I agree with the comments about the difficulty of a vacuum to hold a stable figure down to this level.

Thermal stability is also an issue. Astronomeres worry about thermal currents in the atmosphere and variation of temperature across the mirror.\ and take precautions to keep their mirrors at a constant temperature to stabilize the observed stellar image.

The material for the mirror is important. Simple window glass would not have a small enough coefficient of thermal expamsion (CTE). You would at least need to use borosilicate glass (Pyrex is one brand). Better yet is Schott's Zerodur or Corning's ULE. Both have essentially a 0 CTE at ambient temjperature.

I´ve been searching the web for info on wavefronts and the like and agree with you. people started on about aire disks! got me thinking about reducing the focal length but could not find anything on optimum focal lengths for a 300mm dia mirror! maybe you could direct me to a site or suggest a focal length! I want to attach a ccd camera to the scope if that is of any interest!

You have many questions. A good starting point for information and definitions of optics and photography is http://www.wikipedia.org/

First of all, I rechecked my calculations and I was off by a factor of 2!! I will try to be more careful today. For diffraction limited performance need a parabolic primary mirror as your specification of 300 mm diameter (Dia) and 1.8 m focal length (FL) would produce 1.23 wave PV wavefront at a wavelength of 550 nm. (That is a surface error of 0.61 waves.) This scales as the cube of the focal ration, F# = (FL/Dia). If you double the focal length then the PV wavefront becomes 0.15 waves and this is diffraction limited as a sphere! In fact around F/10 or a 3000 mm focal length a perfect sphere produces a 0.25 wave PV wavefront.

Now you said you wanted to put a ccd camera to the scope. This brings up some more questions:

Are you placing the camera at prime focus (at the focus of the primary mirror) or are there other mirrors or lenses in your telescope? I will assume that you are placing the camera at the focus of the primary mirror or simply have a flat secondary as in a Newtonian telescope.

And What is the size of a pixel in the camera? The diameter of the Airy diffraction disc for 1.8 m FL is 8.07 microns. If you double the FL to 3.6 m, the Airy disc doubles to 16.1 microns. If the image size is larger than the pixel size, the image will look blurry (or you could display the picture at a reduced number of pixels.

What is the field of view? Or What is the diameter of the CCD chip? So far I have been talking about an image at the center of the field of view. A parabolic mirror is only good on axis. At the edge of the field there is some coma and a small amount of astigmatism. These aberrations grow at different rates in the field, but for small fields (1 degree or less) coma will dominate. Also there is field curvature which means an object at the edge of the field will have a different focus than at the center of the field. I put a little table together for your 1800 mm FL mirror and a 3600 mm FL mirror using a ray trace program. Using semi-field of view (FOV) of 0, 0.25, and 0.5 degrees, I have listed the semi-diameter of the image at the focal plane in mm. And I have listed the geometrical blur in microns of the image at each field point. If the geometrical blur is larger than the Airy diffraction disc, then that value may be adopted to compare with the pixel size of the CCD camera.

I hope this helps.

Thanks for the info and link GWJ,

To be honest, last year I rushed out and purchased a telescope without thinking too much! Now I am disappointed with it,(sounds too familiar eh!) Problem is I live in the south of Spain now and there are no outlets for optics, or interests in telescopes, only growing tomatos and the like! Being of an inventive nature, I thought I could do better, so finding information is vital to this project. In the past, I have tried ordering things on the internet such as eyepieces, but my location is v.hard to find for the local people and things usually end up in the wrong place and disposed of. My budget is v.limited aswell, so to buy a mirror would be a big risk.

My ´telescope´ ( I use this word loosely!) is a Pentaflex 130mm/900mm, the optics are rubbish, hard to focus, lots of movement, and I think the mirror is made out of an old tin can! as you can see, I am disapointed! Many years ago, my father got me looking to the stars, only to be cut down in his prime.

To grind a mirror is impossible for me as my shoulders are shot, need a ccd camera because my eyes are not too good! (is there hope for me!!)

I was going to use the salvagable bits from my telescope to build the new scope, ie the focuser, but apart from that, I am in no mans land!

I thought that if I were to form the mirror using pressure and set its curve with say fibreglass resin, that it may work, but looks like I will have to try something else.

The camera was going to be put on the end of the eyepiece. I had a little sucsess with an old webcam looking at saturn, saw the rings but it was so small and lacked any detail (a white disk with an oval white disk about the size of a pea!)

I need to see more because here the skies are clear nearly all the time and every night I look up, the passion grows!

So thanks again GWJ and everybody else who has contributed,

My quest continues......

Thanks for all the ideas and info. with regard to ´why don´t you just grind one in the time honoured way...´ the expression if you´ve never made a mistake, you´ve never made anything holds good for me! with the vacuum chamber, what would happen if I used a thermally stable resin that set after the shape was formed? do you think that the setting process would also tend to change the form?

yes, creating idea is any where. see this wonderful arts.

go a head, you may inovate a now way of spheral mirror processing.

but the heating is difficulty to control uniformly

we may simulate it as a beam supported by two fulcrums at its terminals.

I was metioned by E-man who related to Henchy curve, this curve was heard by me at first time.

if its right, we can use flexibilty equation of a simple beam to simulate.

Why not make the mirror out of metal? If you know where you can get a piece of steel turned and ground/polished the electro plated to give it the reflective coating.

It would not break, you can get it re-plated any time, if for any reason the shape is not quite right it is easily corrected, the mounting is also simpler to achieve.

The thermal constraints can be more easily over come as well. Just an idea. No doubt I will get a barrage of silly reasons why not. Come on discuss this idea.