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kfrederick
Carpal Tunnel


Reged: 02/01/08

Re: How many points for a primary cell ? new [Re: mark cowan]
      #5282458 - 06/21/12 03:37 PM Attachment (24 downloads)

as you can see the sides are diferent length and the hole is offset

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mark cowan
Vendor (Veritas Optics)
*****

Reged: 06/03/05

Loc: salem, OR
Re: How many points for a primary cell ? new [Re: Starman1]
      #5282459 - 06/21/12 03:38 PM

Quote:


That error, P-V, is a little higher than I'd feel comfortable with.
It's about 1/9 wave.




No, it's twice that, those are surface measurements.

But I said
Quote:

(the numbers are just relative)


and they are NOT what the as-built support should deliver in this system. And no I haven't lost my mind, yet.

So allow me to explain (my design criteria for mirror support agrees with Nils Olof at <=3nm RMS surface error BTW):

This is an experimental meniscus mirror. It's a consistent 1/3" thick, 14.7" f/3 quartz mirror. The cell design is an extrapolation from Mel Bartel's 1" thick 13.2" f/3 mirror, which rested in testing on a 3 point support. Mel was surprised at the lack of cell error and he built his ZipDob with the same cell design - 3-point. Obviously it works.

Now if you run plop for a 13x1" f/100 plate (the meniscus squashed flat) you get about 1/4 wave PVW support error. But (read above link and think about it) the real error was obviously far less. I'm going to ask Dave Lewis if he can add an option to PLOP to curve the back of the glass as well and model it, but for the time being I'm just optimizing to the same reported support error (around 12-16nm RMS surface) as Mel's built design shows (squashed) and expecting the geometry of the two f/3 meniscus mirrors to work the physics for me. There'll be ample opportunity to turn the 9-point into a 27-point if needed. (My new "flex-cell" design goes only in steps of 3, but it's dead simple easy to build. It'll be shown publicly at the Oregon Star Party in August. )

Unless Kevin objects I won't start a new thread on this as I don't want to spend a lot of time going into details as this work at this time is mostly empirical.

Best,
Mark


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careysub
Pooh-Bah


Reged: 02/18/11

Loc: Rancho Cucamonga, CA
Re: How many points for a primary cell ? new [Re: Houdini]
      #5282695 - 06/21/12 06:10 PM

Quote:

...There's no need for ultra-high precision, working to the mm (1/32" or 1/16") is good enough....




Since people usually use support pad on the order of 0.5-0.75" diameter, would not even lower tolerances be acceptable?

I remember someone modeling the definitely not point-like pads uses in real mirror cells with a large number of small point cluster,and IIRC it showed relaxed tolerances.


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careysub
Pooh-Bah


Reged: 02/18/11

Loc: Rancho Cucamonga, CA
Re: How many points for a primary cell ? new [Re: Larry Geary]
      #5282709 - 06/21/12 06:16 PM

Quote:

This thread is convincing me that constructing a proper, optimized cell for my Dob is beyond both my own minimal mechanical abilities and the abilities of my non-CNC machinist. Is there a commercial maker of high quality, Plop optimized Dob cells that anyone can recommended?




Square aluminum tube (3/4" or 1" depending on mirror size, 1/16" thick), a drill, bolts, a hack saw or jig saw, and a file are all you need to make an excellent light cell.


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Mauro Da Lio
sage


Reged: 09/12/04

Re: How many points for a primary cell ? new [Re: polaraligned]
      #5282756 - 06/21/12 06:46 PM

Quote:

My triangles will be banged out on my CNC mill. I see no problem hitting 0.0005" or better over these distances. You probably can have a shop do the same for a reasonable price. Yeah, these variable angle designs are not for the hacksaw ATM.




Even if you make the perfect geometry, points are small contact areas where you cannot predict where the centre of the contact forces will pass. It depends on microscopic tribological factors (pressure may be uneven in the contact patch due to very small uneveness). Moreover there is friction.
What actually matters is the line of the centre of pressure forces in the contact patch and that may be displaced form the geometric centre of the patch (e.g. say 1/10th).

The very asymmetric triangles are design that are not "robust" meaning that they amplifies any tiny kind of mechanical noise (geometry, triboloy, friciton). Instead large equilateral triangles or large bars (compared to patch size) tend to reject noise and are much more robust.

6 points is the most robust design. If it works in the computation, the real implementation will not be much worse. As you move to tinier parts (or asymmetrical parts) then you loose robustness.

It is possible to carry out sensitivity analysis to asses the robustness of a design (eg http://www.cs.berkeley.edu/~jonah/18plus/p18.doc ). I made such an analysisi for a 18 point cell supporting a 600 mm 1/10 thick mirror and I found that under the hypothesis that every contact point (line of action of the force) could be randomly displaced somewhat like 1 mm, the rms drops from 1.35nm (ideal design) to 5 nm rms. Moreover a 27 point cell, with 1.5 times the number of sources of noise drops fro a theoretical 1 nm to an even worser value.

Use the smallest number of points and if your really really really need to go up with the number of points you must tighten tolerances, decrease the contact patch sizes and reduce contact friction (the latter being hard to achieve).


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Mauro Da Lio
sage


Reged: 09/12/04

Re: How many points for a primary cell ? new [Re: mark cowan]
      #5282773 - 06/21/12 07:01 PM

Quote:

PLOP has a Monte Carlo function where you can enter errors .




As far as I know random variations can be applied to the design variables. Tat means that if you use the same variable (eg the radius of a circle of support points) a random variation results into correlated variation of all the radiuses (when one point moves out the other do).

To achieve a real sensitivity analysis every point must have its own independent variation and that seem to be very lengthy to carry out.


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Starman1
Vendor (EyepiecesEtc.com)
*****

Reged: 06/24/03

Loc: Los Angeles
Re: How many points for a primary cell ? new [Re: Mauro Da Lio]
      #5282784 - 06/21/12 07:13 PM

Stick-on furniture sliders (VERY low friction with the mirror) are available down to fairly small sizes. A similar, low-friction, material could be used in even smaller sizes (I'd have to shop the various supply places, like McMaster-Carr to find out what's available). Since these are often rounded somewhat, the contact points would be smaller than the diameters and allow some decent calculations for errors.

It does seem the fairly standard felt pads are not an ideal pad material. Variable thicknesses and flexure in the pads would make pressure points indeterminate.


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Mauro Da Lio
sage


Reged: 09/12/04

Re: How many points for a primary cell ? new [Re: Starman1]
      #5283268 - 06/22/12 02:39 AM

Agree Don. Basically small contact patches due to small size of the pads combined with hemispheric/rounded shape can help reducing the uncertainty of the centerline of contact forces. Teflon as a material can help reducing fricition (we aim at sticking/static friction so lubrication is not important here).

However this holds for the points of contact with the glass. There are however also the pivoting points which may have similar problems.

The more the parts, the more the mechanical noise (a 6 point cell has 6 pads and 3 pivots, a 9 point cell 9 pads and 3 pivots, a 18 point cell 18 pads and 9 pivots)
The less symmetric the parts the more sensitive the system is. The tinier the parts compared to patch size the more sensitive the system is.

Edited by Mauro Da Lio (06/22/12 02:46 AM)


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kfrederick
Carpal Tunnel


Reged: 02/01/08

Re: How many points for a primary cell ? new [Re: Mauro Da Lio]
      #5283407 - 06/22/12 08:10 AM Attachment (25 downloads)

The mirror is the same size as the plate and the dows are in holes with the triangles mounted under this plate .

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kfrederick
Carpal Tunnel


Reged: 02/01/08

Re: How many points for a primary cell ? new [Re: kfrederick]
      #5283409 - 06/22/12 08:11 AM Attachment (20 downloads)

another pic

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kfrederick
Carpal Tunnel


Reged: 02/01/08

Re: How many points for a primary cell ? new [Re: kfrederick]
      #5283413 - 06/22/12 08:16 AM Attachment (17 downloads)

triangles mounted upside down under the plate

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Nils Olof Carlin
Pooh-Bah
*****

Reged: 07/26/04

Re: How many points for a primary cell ? new [Re: mark cowan]
      #5283499 - 06/22/12 09:17 AM

Quote:

Now if you run plop for a 13x1" f/100 plate (the meniscus squashed flat) you get about 1/4 wave PVW support error. But (read above link and think about it) the real error was obviously far less.




Intuition is not a reliable guide, but... I would imagine that a deep meniscus mirror would be far more resistant than a flat mirror to spherical aberration, but I very much doubt that it would be more resistant to astigmatism (low order "potato chipping", trefoil or higher order terms).
It would be interesting to know the results of a finite element simulation (you know if you can do it!). Maybe a solution would be 9 or 12 support points on one circle?

Nils Olof


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Mauro Da Lio
sage


Reged: 09/12/04

Re: How many points for a primary cell ? [Re: Nils Olof Carlin]
      #5284273 - 06/22/12 06:24 PM

If I did no mistake here it is a meniscus 13" diameter, 1" thick, F/3 (1981 mm radius?!?), 25% obstruction.
I placed the three support points in the same location suggested by PLOP.

PV is 52.5 ( +38 nm (P) -18.5 (V)). Which becomes 42 nm PV if the central obstruction is accounted for. The rms is 10.3 nm (lambda/53 surface).
http://i49.tinypic.com/2dkeud3.jpg

The "flat" mirror, according to PLOP would be 81 nm PV and 20 nm rms. So there is an improvement but not that huge.


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Nils Olof Carlin
Pooh-Bah
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Reged: 07/26/04

Re: How many points for a primary cell ? new [Re: Mauro Da Lio]
      #5284813 - 06/23/12 04:50 AM

Nice work, Mauro - I thought you could do it!

At least it does not obviously disprove my conjecture - the meniscus shape may offer some, but not much, resistance to astigmatism.

PLOP has the nice feature of offering the Zernike coefficients of the deformation - once you get around to identifying them! *) I have tried to plot the (low order) sph abb and trefoil (the main ones) of a "normal" mirror, when moving the 3 supports along their radii. Near center, sph abb is large, with a minimum about halfway (IIRC- I haven't PLOP handy here), growing again outward. Trefoil is minimum at center (of course), growing first slowly, then faster towards the edge, and the total minimum occurs somewhere inside the sph abb minimum, about 0.4 of radius, where the terms are (approx.) equal.

So, for that mirror, 12 points on one circle, at perhaps 0.4 radius, would do about as well as an 18 pt cell for a flat mirror? Just a guess. Or would even one center support be OK for such a relatively deep meniscus???

Nils Olof

*) IIRC, the Wyant numbering minus (or is it plus?) one


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Mauro Da Lio
sage


Reged: 09/12/04

Re: How many points for a primary cell ? new [Re: Nils Olof Carlin]
      #5284828 - 06/23/12 05:54 AM

Hi Nils. Here is a file with the coordinates of the upper and lower surfaces (you may easily segment the data to discard bottom face). A fourth column reports the z displacement as they come out of the FEM.
https://dl.dropbox.com/u/1563839/meniscus.txt
I fitted piston, tilt and defocus in them (*) to remove them and plot only the residual aberration (the picture yo saw).


(*) Fitting equations is 3.61556*10^-9+2.89776*10^-8 x+5.95971*10^-9 y-8.03721*10^-6 (x^2+y^2) where x and y are the coordinates of the point and the various terms represent piston, tilt and defocus.
After these are removed yu may try to fit zernike polys (be aware that the sampling points are unevenly spaced as they are produced by the FEM).

PS I do not know if MirrorMesh3D is freely available. http://www.cruxis.com/scope/scope1100_mirrormesh3d.htm

Edited by Mauro Da Lio (06/23/12 05:57 AM)


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Mauro Da Lio
sage


Reged: 09/12/04

Re: How many points for a primary cell ? new [Re: Mauro Da Lio]
      #5284830 - 06/23/12 05:56 AM

Further considerations.

a) The radius of the bottom surface could be smaller that the front one). This would produce a tapered section that perhaps works even better (and here we come to the concept of tapered mirrors such as those of Royce).
b) Lateral supprto should be investigated. Where to place the lateral constraints and do they cause potato chip deformation (esp. for tapered designs)?


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Nils Olof Carlin
Pooh-Bah
*****

Reged: 07/26/04

Re: How many points for a primary cell ? new [Re: Mauro Da Lio]
      #5285073 - 06/23/12 11:05 AM

Thanks Mauro,

I don't have the tools or skill to work out those coefficients.

As for edge supports, my simplified (but perhaps useful) view is that to avoid (or better call it balance out!) the "potato chipping", the force top-down by gravity should be balanced by an equal force side-to-side. This happens with a sling, as well as with + - 45 deg ("diagonal") point supports. And, I believe , as near the plane of the COG as possible (wherever that may be - should be calculable with some effort, perhaps from the known COG of a plane-concave blank). If not, I believe there will be some asymmetry of forces on the back.

The essential idea of a tapered mirror, I believe, is to allow a single center support. An appealing idea, and intuitively credible, but I have never seen or heard of an actual analysis of the deformation of such mirrors of realistic sizes. It must have been done though, at least by manufacturers of large Schmidt-Cassegrains, I should presume. Given a large enough tapered blank, deformation must be significant, of course.

Nils Olof


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Mauro Da Lio
sage


Reged: 09/12/04

Re: How many points for a primary cell ? new [Re: Nils Olof Carlin]
      #5285325 - 06/23/12 01:33 PM

Ideally there is a plane where lateral support forces combines in way that zero effect is produced on the astigmatism mode of deformation. This plane is the COG for flat mirrors with small sagitta. I do not know if this rule holds also for more concave mirrors and meniscus.

The SC tapered mirrors have also stiffening ribs. They are clever designs clearly optimized (or better optimized) than constant cross section shapes.


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mark cowan
Vendor (Veritas Optics)
*****

Reged: 06/03/05

Loc: salem, OR
Re: How many points for a primary cell ? new [Re: Mauro Da Lio]
      #5291812 - 06/27/12 04:17 PM Attachment (7 downloads)

Quote:

As far as I know random variations can be applied to the design variables. Tat means that if you use the same variable (eg the radius of a circle of support points) a random variation results into correlated variation of all the radiuses (when one point moves out the other do).

To achieve a real sensitivity analysis every point must have its own independent variation and that seem to be very lengthy to carry out.




Yes, that's the way it's implemented. Changes in radius of the support circles and angles are all that's allowed. I ran some comparisons between about 5000 iterations and 500,000 and there was little variation in maximum error.

There's nothing to prevent you SFAIK from setting up a ring for every support point except the time it would take to define the cell.

Regarding the use of (solid) pads, no it doesn't affect the support much at all so long as they're centered. Pads will have to conform to the glass though. You can get an idea of this by running the 3D PLOP option after you do a cell, it models the glass more accurately and generally returns lower overall errors by about 50%.

Quote:

Intuition is not a reliable guide, but... I would imagine that a deep meniscus mirror would be far more resistant than a flat mirror to spherical aberration, but I very much doubt that it would be more resistant to astigmatism (low order "potato chipping", trefoil or higher order terms).
It would be interesting to know the results of a finite element simulation (you know if you can do it!). Maybe a solution would be 9 or 12 support points on one circle?




Cell induced astig, yes. But for multi-point support I doubt the front/back curves matter much (see below).

Quote:

The "flat" mirror, according to PLOP would be 81 nm PV and 20 nm rms. So there is an improvement but not that huge.




Hmm, I got 14.6nm RMS surface. Same specifications for size, modeling an f/100 plate in PLOP. 3D PLOP shows 11nm RMS surface (see below), and it's nearly identical to Mauro's FEM result for the meniscus! Something is not correct somewhere in this line of thought then.

Unless (of course) there is in reality negligible surface change due to the shape itself - which was my original hypothesis and one that I still mark as the winner for actual mirror support.

This is why I was going to deploy a 27-point cell on the 1/3" 14.7" mirror in my first design (well more than good enough, 1.6nm RMS surface at least). But to test Mel's observation I'd put it on a simple fixed-angle 9-point first, planning to upgrade to 27-point as a further experiment, which would bring me back to my original design. The cost of doing the experiment is pretty small, and I'll know the cell isn't doing any harm by the end. Also note that the error on the 9-point should be easily visible in star testing, if it performs as expected. And by building two interchangeable cells (they just bolt to the back of the collimation supports I can field test one against the other as needed.

So a tentative conclusion here is that Mel's reasoning is incorrect somehow - either the observation, the actual effect of cell support on thin mirrors (how many people TRY a 3-point cell on a 13.2x1"?), or the conclusion based on equivalent thickness.

But since the primary error afflicting thin mirrors on multi-point supports is sag not shear my thinking was that (on the small scale between support points) the overall curve of the glass can play only a small role. And that's why I modeled the f/100 mirrors in the first place, and am prepared to build 81-point supports (or beyond) for much larger versions.

Uhm, one final point. Tapered mirrors (Mauro's suggestion) have been around forever. I've seen some horrible FEM modeling on such, but in practice they seem to work well enough. Which could just mean many of the considerations involved in support and thermal analysis are a level beyond real world performance - or that real world "performance" tends to be a level beneath what is theoretically possible. Not really wanting to go there on those.

Best,
Mark

Edited by mark cowan (06/28/12 04:58 PM)


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kfrederick
Carpal Tunnel


Reged: 02/01/08

Re: How many points for a primary cell ? new [Re: mark cowan]
      #5292940 - 06/28/12 10:01 AM

Mark that is very thin I would think it hard to make with out getting astig

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