52 replies to this topic

[Irido]

I know Schmidt corrector plates are made at a commercial scale by sucking glass down over a vacuum, then doing the shaping, then removing the plate from the vacuum surface. A thin plate deformed by having a uniform force applied to it produces a curve that is described by a fourth-order polynomial radially, and this fourth-order approximation is close enough to the "true" shape of a Schmidt corrector.

 

There's probably an obvious answer to this, but why not just deform a relatively thin glass mirror blank over a vacuum in the same way, then grind a spherical surface into it, then remove it to produce a corrected spherical mirror that closely approximates a paraboloid? The vacuum applied could be adjusted such that the fourth order terms in the Taylor expansion of the equation describing the spherical surface and the polynomial describing the plate deformation exactly cancel, producing a mirror that, ideally, only deviates from a parabola in the sixth degree. This sixth degree deviation would be so negligible as to make the resulting mirror a paraboloid for almost all intents and purposes. 

 

So, why not do this? It seems like it should speed up the process of mirror making by obviating the need for much of the typical parabolizing. I can think of a couple problems (for instance, sensitivity to wedge in the blank/mirror), but none that seem fatal to this idea. At the same time, I figure there's a reason this isn't already done--there's no way I'm the first to think of this.

[TOMDEY]

Such things have been tried... but for "onesies" where the disc is only supported at the edge during fine grinding and polishing, the mechanicals are terribly squirrely... actually horrendously so. Myriad other problems with the hypothetical technique: Thickness of the mirror glass too thick to vacuum pucker. Would have to grind and polish it to the best fit sphere and then expect it to ~pop~ to the correct asphere when released --- just not going to happen. And other technique killers. Where I worked --- we pretty much tried all of these and uncountable other cute/creative production techniques. Around one in ten new techniques passed the "promising" hurdle, only one in hundred proved worth further pursuit toward a production process, and a pathetic one in a thousand made it to successful quantity production. The winners that I witnessed at work were: B&L "Soft Lens" contact lenses, Eastman Kodak molded glass aspheres (single and double sided), Kodak Ion Figuring (giant space optics, Keck 1 and 2 nearly all segments final figuring), Kodak Dey & Walsh "Abrasive Air Spray" --- exciting and promising --- but couldn't generate corporate interest... sigh...

 

Oh... another... selective vacuum deposition (Dey) suggested, but corporate not particularly interested.

 

If you've ever worked in Research Labs (corporate and/or government) you fully expect to hit on a winner about 10% of the time, which is actually a good batting average. The best (most productive) researchers always have several irons in the fire simultaneously. One of the greatest skills in the world of competitive invention is to know when hold 'em; know when to fold 'em.  Tom

Edited by TOMDEY, 07 December 2024 - 12:59 AM.

[Irido]

Such things have been tried... but for "onesies" where the disc is only supported at the edge during fine grinding and polishing, the mechanicals are terribly squirrely... actually horrendously so. Myriad other problems with the hypothetical technique: Thickness of the mirror glass too thick to vacuum pucker. Would have to grind and polish it to the best fit sphere and then expect it to ~pop~ to the correct asphere when released --- just not going to happen. And other technique killers. Where I worked --- we pretty much tried all of these and uncountable other cute/creative production techniques. Around one in ten new techniques passed the "promising" hurdle, only one in hundred proved worth further pursuit toward a production process, and a pathetic one in a thousand made it to successful quantity production. The winners that I witnessed at work were: B&L "Soft Lens" contact lenses, Eastman Kodak molded glass aspheres (single and double sided), Kodak Ion Figuring (giant space optics, Keck 1 and 2 nearly all segments final figuring), Kodak Dey & Walsh "Abrasive Air Spray" --- exciting and promising --- but couldn't generate corporate interest... sigh...

 

Oh... another... selective vacuum deposition (Dey) suggested, but corporate not particularly interested.

 

If you've ever worked in Research Labs (corporate and/or government) you fully expect to hit on a winner about 10% of the time, which is actually a good batting average. The best (most productive) researchers always have several irons in the fire simultaneously. One of the greatest skills in the world of competitive invention is to know when hold 'em; know when to fold 'em.  Tom

Interesting. I wonder if you could use something like Alan Adler's spherical mirror pulling cell instead of a vacuum, It would probably more easily adjustable than a vacuum setup. I don't think that such an apparatus would be useful for instantly turning spherical mirrors to perfect paraboloids, but perhaps it could be of some use in producing something closer to a paraboloid during grinding?

[Jon Isaacs]

I know Schmidt corrector plates are made at a commercial scale by sucking glass down over a vacuum, then doing the shaping, then removing the plate from the vacuum surface. A thin plate deformed by having a uniform force applied to it produces a curve that is described by a fourth-order polynomial radially, and this fourth-order approximation is close enough to the "true" shape of a Schmidt corrector.

 

There's probably an obvious answer to this, but why not just deform a relatively thin glass mirror blank over a vacuum in the same way, then grind a spherical surface into it, then remove it to produce a corrected spherical mirror that closely approximates a paraboloid? The vacuum applied could be adjusted such that the fourth order terms in the Taylor expansion of the equation describing the spherical surface and the polynomial describing the plate deformation exactly cancel, producing a mirror that, ideally, only deviates from a parabola in the sixth degree. This sixth degree deviation would be so negligible as to make the resulting mirror a paraboloid for almost all intents and purposes. 

 

So, why not do this? It seems like it should speed up the process of mirror making by obviating the need for much of the typical parabolizing. I can think of a couple problems (for instance, sensitivity to wedge in the blank/mirror), but none that seem fatal to this idea. At the same time, I figure there's a reason this isn't already done--there's no way I'm the first to think of this.

 

Corrector plates are very thin and the amount of material that is removed is very small.  The necessary deflection in infinestimal. 

 

An actual mirror is relatively thick and a great deal of material, by comparison, must be removed.  Vacuum is limited to 15 psi. With a plate of reasonable thickness, my engineering intuition says the the deflections would be tiny under such a minimal pressure.  I could get out my copy of Timoshenko's Theory of Plates and Shells but I will leave that to someone else. 

 

Jon

[dan chaffee]

Here's another reason not to do it. Bulk polishing tends to yield

a nearly spherical figure on a rigid substrate, so with nearly full

sized polishers, an already parabolized surface would undoubtedly

be zoney after hours of just getting it polished. And if you were polishing

by hand, a small lap would take forever to get there and would also

produce zones and roughness.

[davidc135]

I know Schmidt corrector plates are made at a commercial scale by sucking glass down over a vacuum, then doing the shaping, then removing the plate from the vacuum surface. A thin plate deformed by having a uniform force applied to it produces a curve that is described by a fourth-order polynomial radially, and this fourth-order approximation is close enough to the "true" shape of a Schmidt corrector.

 

There's probably an obvious answer to this, but why not just deform a relatively thin glass mirror blank over a vacuum in the same way, then grind a spherical surface into it, then remove it to produce a corrected spherical mirror that closely approximates a paraboloid? The vacuum applied could be adjusted such that the fourth order terms in the Taylor expansion of the equation describing the spherical surface and the polynomial describing the plate deformation exactly cancel, producing a mirror that, ideally, only deviates from a parabola in the sixth degree. This sixth degree deviation would be so negligible as to make the resulting mirror a paraboloid for almost all intents and purposes. 

 

So, why not do this? It seems like it should speed up the process of mirror making by obviating the need for much of the typical parabolizing. I can think of a couple problems (for instance, sensitivity to wedge in the blank/mirror), but none that seem fatal to this idea. At the same time, I figure there's a reason this isn't already done--there's no way I'm the first to think of this.

The mirror surface would need to be deformed by a positive pressure, not a partial vacuum which would give an eventual oblate figure after grinding and polishing.

Containment of the pressure around the edge of the disc could be tricky.

 

I was going to try the idea and had made a fine ground 8'' f3.6 meniscus 10.7mm thick along with a supporting aluminium pan. Required pressure can be gotten from Matt Considine's Schmidt calculator if appropriate figures are fed into it. I don't think it's too extreme. 

 

In theory it seems doable and testable. With the rig set to the right pressure you'd be wanting to polish a smooth sphere. Maintenance of a constant pressure, irregularity of support and eventual astigmatism are some of my bogeys but I ought to have a go.

 

David

Edited by davidc135, 07 December 2024 - 04:52 AM.

[Jon Isaacs]

 

I was going to try the idea and had made a fine ground 8'' f3.6 meniscus around 12mm thick along with a supporting aluminium pan. Required pressure can be gotten from Matt Considine's Schmidt calculator if appropriate figures are fed into it. I don't think it's too extreme.

 

The sagitta on a 8 inch F/3.6 mirror is 0.14".  I don't see deforming a piece of 1/2 inch glass 0.14"... 

 

Jon

[davidc135]

The sagitta on a 8 inch F/3.6 mirror is 0.14".  I don't see deforming a piece of 1/2 inch glass 0.14"... 

 

Jon

The sagitta has been pre-ground. Pressure has to deform the disc by a further small sag which will have a fixed relationship to the needed aspheric deviation.

 

David

[davidc135]

Here's the mirror meniscus, tool and pressure or vacuum pan. The pan has an inlet and outlet port. I envisage floating the mirror on a 1mm x 5mm ring seal of silicone whilst cementing the edge of mirror and pan with a glass fibre band.

 

Not sure about that, I need an adhesive that can easily be removed once it's all finished.

 

David

 

Edited by davidc135, 07 December 2024 - 06:18 AM.

[davidc135]

The forces are very modest. I get around 2.5psi and max surface stress of only 2Mpa for my 210 x 10.7mm f3.6 mirror. It could be made thicker.

 

Very likely Tom is right.

 

David

[tturtle]

As a structural engineer I’ve been involved in a few research projects to develop new concepts mostly related to bridge engineering which is my specialty.  One thing I learned from that is that new manufacturing techniques and materials are constantly being developed so if something was investigated years ago and deemed not feasible it doesn’t necessarily mean that it is not feasible or economical today using some new recently developed material or manufacturing process. 

Edited by tturtle, 07 December 2024 - 07:46 AM.

[TOMDEY]

The Keck Segments were "stress polished" to (attempt to get) each to take on it's own custom correct local figure. Although the process worked OK, it did not achieve the required tolerance. Nearly all of them were therefore sent to Kodak Precision Optics to Ion Figure the topologies to within spec --- each one different and requiring different mapped remaining correction. The Ion process is wonderfully deterministic and therefore convergent. Most landed within spec in one iteration. The required local Zernikeish differential from spherical corrections are dominated by Zernike astigmatism and coma, with higher order terms. The process of sphere > stress polished to approx asphere > ion figured to tight tolerance --- was achieved successfully and efficiently, but still sophisticated and still costly. The optical testing of each segment is also non-trivial.

 

What I'm getting at is that machining and figuring large precision optical parts to diffraction-limited tolerances  --- to this day --- is still inherently $$$; even though we've come a long way and reduced processing cost maybe an order of magnitude --- it still remains in the professional precision category. Experts continue to invent, explore, and develop... and so do amateurs --- but it's still tilting windmills. I'm no doubt coming across as jaded... reasonably jaded. Like a WWI grunt returning from the trenches, optimistically reporting that "things are ~going well~, but we're still grinding through a lot of fodder and expense".    Tom

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[davidc135]

The Keck Segments were "stress polished" to (attempt to get) each to take on it's own custom correct local figure. Although the process worked OK, it did not achieve the required tolerance. Nearly all of them were therefore sent to Kodak Precision Optics to Ion Figure the topologies to within spec --- each one different and requiring different mapped remaining correction. The Ion process is wonderfully deterministic and therefore convergent. Most landed within spec in one iteration. The required local Zernikeish differential from spherical corrections are dominated by Zernike astigmatism and coma, with higher order terms. The process of sphere > stress polished to approx asphere > ion figured to tight tolerance --- was achieved successfully and efficiently, but still sophisticated and still costly. The optical testing of each segment is also non-trivial.

 

What I'm getting at is that machining and figuring large precision optical parts to diffraction-limited tolerances  --- to this day --- is still inherently $$$; even though we've come a long way and reduced processing cost maybe an order of magnitude --- it still remains in the professional precision category. Experts continue to invent, explore, and develop... and so do amateurs --- but it's still tilting windmills. I'm no doubt coming across as jaded... reasonably jaded. Like a WWI grunt returning from the trenches, optimistically reporting that "things are ~going well~, but we're still grinding through a lot of fodder and expense".    Tom

 

 

Still, for small items that are made for fun without caring about commercial viability it's worth planning as best you can and then just jumping in.

 

One of the problems with making Schmidt plates is their thinness. They are discs of jelly. Compared to a c.p my thin mirror should be around 10 times as stiff, hopefully resisting distortion and astigmatism.

 

I might just rely on the silicone adhesive without the edge band. I'd find out quickly if it didn't work as the mirror on its pan could be tested for astig etc at any stage, under pressure or not, at its radius of curvature.

 

David

[Irido]

Corrector plates are very thin and the amount of material that is removed is very small.  The necessary deflection in infinestimal. 

 

An actual mirror is relatively thick and a great deal of material, by comparison, must be removed.  Vacuum is limited to 15 psi. With a plate of reasonable thickness, my engineering intuition says the the deflections would be tiny under such a minimal pressure.  I could get out my copy of Timoshenko's Theory of Plates and Shells but I will leave that to someone else. 

 

Jon

I think the force is lower than one might expect. Even very fast spherical mirrors deviate from a paraboloid by only a couple wavelengths of light. Once more using Adler's Flex calculator, a force of a couple hundred pounds is the maximum needed to deviate say, an 8 inch f/5 sphere, into a paraboloid. That should be easily achievable with air pressure. David is right--I made a sign error in my calculation! The required pressure is positive, bowing the mirror outwards, rather than vacuum bowing the mirror inwards.

Edited by Irido, 07 December 2024 - 05:16 PM.

[TOMDEY]

I do love this topic... which comes up here periodically in the context of optical production. How to maybe make optical elements "Faster, Better, cheaper". The history of technologies is measured in terms of progressive successful inventions. Even though the global batting average ~successful~ patents is a few % at most... at least we're thinking creatively --- which is a positive metric of a healthy society. When I started my 1st ~real job~ in Optics (B&L summer intern age 17) operating a vacuum coater --- I noticed these "Suggestion Boxes" on the walls here and there. They looked beat up and appeared to be rarely availed or even serviced. I started stuffing my hair-brained ideas in there... figuring I would make the corporation a fortune and maybe even be awarded with a pat on the back or coffee mug. Nothing happened... nothing. I started composing detailed suggestions comprising sketches, computations, illustrations, marketing arguments, reduced cost #s, etc. "How to squeeze 128 Mr-15's onto a 112 part plate", "How to sandblast 108-inch circular aluminum cathodes automatically" "How to load ZnS Howitzers without breathing in the dust" These suggestions were too big to fit into the suggestion box slot... so I gratuitously handed them (one a week) to the bosses' bosses' bosses' secretary. Eventually she would look up smiling and say, "Thanks, Tom", (she knew my name!) and reverently place it in Mike's ~In Basket~.

 

At the end of the summer, my bosses' boss told me that they were happy with my performance and would invite me back the following summer... and none of the other interns. I had passed some kind of secret ~gate~ that I wasn't even overtly aware of. Fast forward a decade and I was a happy corporate ~senior research Scientist~. The rest is history.

 

Got "brilliant" Ideas? --- Don't Give Up!    Tom

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[Mike Spooner]

Failure is because you don’t try - concluding that a vision didn’t pan just opens the door for another go at success. 
My junk pile is just material for a future project!​ 

 

Mike 

[Irido]

The sagitta on a 8 inch F/3.6 mirror is 0.14".  I don't see deforming a piece of 1/2 inch glass 0.14"... 

 

Jon

I fear I may have misrepresented my idea. The concept is not to bow out a flat blank under pressure, then grind/polish it flat, then to relieve the pressure, somehow getting a usable mirror. Rather, I am proposing bowing out a flat blank under pressure, grinding/polishing a spherical surface into it, then relieving the pressure to produce a mirror closely resembling a paraboloid. The blank only needs to bow out by a couple wavelengths of light, enough such that when the pressure is relieved, the center is a couple wavelengths lower than it would be on a spherical mirror.

Edited by Irido, 07 December 2024 - 09:57 PM.

[davidc135]

The change in sagitta due to pressure difference has to be around 17 times the needed aspheric deviation on the surface or 8.6 times the required wavefront correction, which comes to 34.5 waves green light for my 8'' f3.6. Which isn't huge.

 

David

[ccaissie]

OK.  having flexed f/7  8"  x .88" spheres into paraboloids, I see the major problems are the degree of accuracy you need with a flexing a faster mirror vs. the extremely tight tolerances of the fixture.  I think the tolerances at f/3.6 for wedge, homogeneity, concentricity and force stability are too tight for this to work

 

I would use Adler's flex.exe formula & program to rough in the forces and the tolerances required by simply plugging in the numbers.  Deforming a sphere into a -1 conic (paraboloid) by pulling should be equal to the force required to deform the sphere into a +1 conic by pushing and then spherize it. Your puller (actually air pressure) would be about 95% of your mirror diameter. 

 

All wedge should be removed from the mirror.  Sealing the mirror blank to the edge of the pressure fixture is the crux.  This joint should be ground in after all wedge in the blank is removed.  The amount of premissable wedge is in Adler's program. The blank and fixture need to be very round and very concentrically fixed. I'd make a fixture slightly smaller than the blank diameter and glue it on with an Epoxy making a fillet of epoxy all around.   Press until well cured.  

 

Foucault test for any astigmatism.  Add pressure until you get a +1 conic, (so here the magic goes away and you need to test an asphere)  record your air pressure because that's the only way you will be able to get a repeatable flex while you polish to a sphere. From the first pressure application to the final sphere you won't know what the figure of the glass is or what it will be until done.   

 

If all goes well you'd have a very smooth conic, but it will not magically be a perfect paraboloid because of inaccuracies in the pressure and other factors.  Flexing by pulling starts with a nulled 100% sphere and an initially designed flex rig but inevitably requires final adjustment once it's assembled and used...... but you adjust by star test to 100% correction, so that's no problem.

 

This reverse flex method lacks the ability to SET the flexed mirror conic accurately enough to prepare it for the spherizing while flexed.  Not likely to be 100% corrected when released off the fixture.  So where are you then?  Hand figuring a paraboloid.  

Edited by ccaissie, 07 December 2024 - 08:16 PM.

[MeridianStarGazer]

I know Schmidt corrector plates are made at a commercial scale by sucking glass down over a vacuum, then doing the shaping, then removing the plate from the vacuum surface. A thin plate deformed by having a uniform force applied to it produces a curve that is described by a fourth-order polynomial radially, and this fourth-order approximation is close enough to the "true" shape of a Schmidt corrector.

There's probably an obvious answer to this, but why not just deform a relatively thin glass mirror blank over a vacuum in the same way, then grind a spherical surface into it, then remove it to produce a corrected spherical mirror that closely approximates a paraboloid? The vacuum applied could be adjusted such that the fourth order terms in the Taylor expansion of the equation describing the spherical surface and the polynomial describing the plate deformation exactly cancel, producing a mirror that, ideally, only deviates from a parabola in the sixth degree. This sixth degree deviation would be so negligible as to make the resulting mirror a paraboloid for almost all intents and purposes.

So, why not do this? It seems like it should speed up the process of mirror making by obviating the need for much of the typical parabolizing. I can think of a couple problems (for instance, sensitivity to wedge in the blank/mirror), but none that seem fatal to this idea. At the same time, I figure there's a reason this isn't already done--there's no way I'm the first to think of this.

I thought of this idea too years ago. A meniscus sphere pulled under vacuum deforms to a parabaloid. So polish that back to a sphere, and release the vacuum, and you get a parabaloid.

I spent a year sitting on this secret invention, thinking I'd sell cheap, big, thin mirrors of high accuracy. Too bad Mark Cowan is not here to say "huberis". Well, then I calculated that the weight of the lap would deform the glass out of sphere, complicating the polishing. So it seemed it would not work.

Others have told me it can be done with blocking pitch.


I worked out a lot of calculations for how much pressure is needed to get the paraboloid. Turns out if the thickness stays constant, the glass gets floppier, and the extra surface area of the vacuum still works for the new aperture, if the focal length is the same.

Also, heat causes air to expand. So it might work better at a thickness that requires a full vacuum.

Edited by MeridianStarGazer, 07 December 2024 - 08:25 PM.

[ccaissie]

I fear I may have misrepresented my idea. The concept is not to bow out a flat blank under pressure, then grind/polish it flat, then to relieve the pressure, somehow getting a usable mirror. Rather, I am proposing bowing out a flat blank under pressure, grinding/polishing a spherical surface into it, then relieving the pressure to produce a mirror closely resembling a paraboloid. The blank only needs to bow out by a couple wavelengths of light, enough such that when the pressure is relieved, the center is a couple wavelengths lower than it would be on a spherical mirror.

"Rather, I am [NOT] proposing bowing out a flat....."

You must mean you bow out a SPHERE....

The distance bowed out is the difference between the sphere and a +1 conic oblate spheroid.

 

The above calculation of 34 waves of distortion required IS HUGE.

[ccaissie]

I thought of this idea too years ago. A meniscus sphere pulled under vacuum deforms to a parabaloid. So polish that back to a sphere, and release the vacuum, and you get a parabaloid.

 

No, you get an anti-paraboloid, a +1 oblate.

[ccaissie]

 using Adler's Flex calculator, a force of a couple hundred pounds is the maximum needed to deviate say, an 8 inch f/5 sphere, into a paraboloid. 

Flexing force rises quickly....you might find flex force for a 3.6 is much higher than 5.  Do the design carefully with the real figures.  What about the extrememly tight tolerances derived in the program?  

[MeridianStarGazer]

Another issue is spherising strokes often don't perfectly make spheres. And parabolising strokes can be effective enough.

And making a meniscus requires hogging, grinding, and polishing twice. Or with a kiln, first casting a disk, then slumping the disk, then grinding and polishing both sides. It is faster to cast once, grind once, polish once, and just do the parabolising strokes.

[MeridianStarGazer]

Flex pressure increases with the reciprocal of the cube of the focal length, and of course the cube of the thickness. Pressure needed is unaffected by diameter when thickness and focal length are held constant.

A 20" f4 sphere 3/4" needs about 1.2 psi to flex to paraboloid. Harvard said negative pressure was used, and a perfect paraboloid was achieved.

Now you got me scheming work arounds again. I have ideas.

Would 16" f4 be most in demand?

Edited by MeridianStarGazer, 07 December 2024 - 08:58 PM.