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womiller
member
Reged: 10/05/09
Posts: 27
Loc: Bay Area, CA
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Hello All,
I will welcome the group wisdom on how to interpret the various types of geometric error on a mirror surface, and their relative importance in telescope design. So far I have learned about two types of geometric error, and they appear to differ by about three orders of magnitude. For discussion, let's consider 500 nm light, which has a 1/10 wavelength of 50 nm (2 micro inches)
(1) Figure tolerance, which is a gross measure of the mirror curve. See here starting at Fig B (an equation for tolerance X). For the representative optic in this article, this tolerance is on the order of 0.01", or about 500 wavelengths in round numbers. As I understand this article, if the mirror figure is within this tolerance band, then the mirror really cannot be focused any better as the focal plane is actually a focal zone defined by the Airy disk. I think this is also one definition of a diffraction limited optic.
(2) Surface roughness, a.k.a. peak-to-valley. Now the local polish of the mirror comes in to play, and variations in surface roughness are measured in fractions of a wavelength, so for a 1/10 wavelength metric, the surface roughness would need to be under 50 nm/ 2 microinches. This is 5000 times smaller than the allowable figure error (500 wavelengths vs 0.1 wavelength).
So there is the rub. If the larger figure error really does define a reasonable physical limit of what the mirror can achieve, then why are we concerned with sub wavelength surface finish at all? Doesn't that sub-wavelength super polish just end up being in the Airy disk fuzz?
OK, here's a follow-up question. What tolerance does the mirror cell need to hold? Surely it must maintain the mirror surface within the figure error (500 wavelength tolerance). Can we ignore deflections that are below this figure limit, or do we really need to be concerned with sub-wavelength distortions from the mirror cell, gravity orientation, etc.?
Thanks for your guidance on this!
Regards
Wayne Miller
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Orion Argonaut 150mm Mak-Cass
Vixen GP mount
Livermore, CA viewing conditions
Edited by womiller (10/28/09 01:18 PM)
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perfessor
sage
Reged: 12/30/07
Posts: 499
Loc: Northern Illinois
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Some other experts will give more details. But I think you have conflated two completely different measurements.
In (1), the quantity being measured (to within 0.010") is the radius of curvature - i.e. the knife edge position.
In (2), you are measuring surface defects at the mirror itself. Very different. Don't expect the numbers to line up - of course the orders of magnitude will be different!
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Tom
"Don't always know what I'm talkin about"
8" f/7
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womiller
member
Reged: 10/05/09
Posts: 27
Loc: Bay Area, CA
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Hi Tom,
I sort of agree with you, but I don't grasp the importance of sub-wavelength surface finish if all the light ends up in the right place just by the relatively loose tolerances on the radius of curvature.
The figure error I referred to is the tolerance on the radius of curvature, more or less. To stick with the example, the radius of curvature can vary by +/-500 wavelengths.
I think it is pretty well described here in Figure B(a), which shows that the focal zone along the optical axis is defined by region between two spot sizes of the Airy disk diameter. There really isn't just a single point of perfect focus on the optical axis. A mirror that can focus light along the optical axis and within this range is doing it's job, and that figure tolerance is how that focus range is defined.
Cheers,
Wayne
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Orion Argonaut 150mm Mak-Cass
Vixen GP mount
Livermore, CA viewing conditions
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mark cowan
Vendor (Obsidian Optics)
Reged: 06/03/05
Posts: 2159
Loc: salem, OR
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The distance you can move the ground glass (as in the illustration) at the paraxial focus (ROC) for any zone on the mirror is vastly larger than the tolerance required for the accuracy of the same zone. This may be what's got you confused.
Also it's incorrect that:
Quote:
There really isn't just a single point of perfect focus on the optical axis.
Of course there is, for a paraboloidal mirror working at infinity there is one and only one point of perfect focus on the optical axis. The same mirror at ROC produces a caustic horn where only zones along the diameter focus at one point along the longitudinal axis, this is inevitable, but it's not how the mirror is used just one of the ways it's tested, as shown in fig B(a).
Hope that helps.
Use this code:
Quote:
[image]http://cleardarksky.com/c/LvrmrCAcs0.gif?1[/image]
Best,
Mark
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Luigi
Post Laureate
Reged: 07/03/07
Posts: 4938
Loc: MA
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To form a "perfect" image, the figure of the surface must be perfect. It is generally not too important what the focal length is so a tolerance on the focal length can be many millimeters. However, with respect to whatever that focal length happens to be, the mirror surface must have a very high degree of perfection. It's kind of like specifying a work bench to be 46 +/- 2" tall. You wouldn't want the surface of the workbench to have +/- 2" irregularities in height.
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17.5" f/5 Dob. IM-715 MCT. 120ED. Lunt 60mm Ha.
Zeiss, Leica, Fujinon, Nikon, Pentax, Bushnell bins
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womiller
member
Reged: 10/05/09
Posts: 27
Loc: Bay Area, CA
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OK, I'm starting to get the idea. There is a big tolerance on the radius of curvature (ROC) but a fine tolerance on the surface finish, but the interplay between them is still unclear to me (no pun intended). The ROC tolerance can be big because diffraction limited optics, even parabolas, have no precise focal plane. I'll provide an edited quote from the same reference that is illustrated in Fig B(a):
Quote:
...the physical properties of light decree a range of ambiguity in the location of the plane of focus for any given bundle of rays of light being focused into a point in the focal plane. In fact, no lens or mirror can actually focus light into an infinitesimally small point of light in its focal plane. Rather, when examined up close, we find the tip of the cone of a focused bundle of light not to be a tiny sharp point, but rather a very small disk with a measurable diameter. This little disk of light is the so-called Airy disk (sometimes also referred to as the "diffraction disk").
...The size of the Airy disk is a function of the focal ratio of the mirror or lens. If we move slightly inwards along the OA (towards the mirror) from one of these disks in the focal plane for a cone of focused light, we will finally come to a place along the cone where a cross section of it will be a disk having the same diameter as the Airy disk at its tip. Conversely, if we move outwards along the OA (farther away from the mirror or lens) from the Airy disk in the focal plane, we will again come to a point where the re-expanding cone of light has a circular cross section that again equals the diameter of the Airy disk. If we inserted a small square of finely ground glass in the focal plane and moved it back and forth through the focal plane between these two locations we would not see the little focused dot of light on the glass change diameter.
In short, it is quite impossible for us to find a precisely defined focal plane for any mirror or lens. Rather, we will have this very short region in which the focus will be found to be acceptable. Thus, we require to figure our mirror only accurately enough that the tip of the cone of light focused by any given zone on the mirror will fall somewhere between these two locations along its optical axis. This range of locations for the center of curvature of any zone constitutes our allowed (tolerance) error for its location.
So it seems that light focused in this range on the optical axis, as defined by the large ROC tolerance, is "in focus" as much as it is possible to be so in terms of diffraction limits. Given that, what does the sub wavelength mirror surface tolerance provide? I'm sure my simple concept of focus is missing something.
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Orion Argonaut 150mm Mak-Cass
Vixen GP mount
Livermore, CA viewing conditions
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womiller
member
Reged: 10/05/09
Posts: 27
Loc: Bay Area, CA
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Mark,
EDIT: Problem solved (Thanks for the [image]...[/image] code. Still not working for me though)
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Orion Argonaut 150mm Mak-Cass
Vixen GP mount
Livermore, CA viewing conditions
Edited by womiller (10/28/09 01:19 PM)
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womiller
member
Reged: 10/05/09
Posts: 27
Loc: Bay Area, CA
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Regarding mirror cells, I think the answer is emerging for me that the cell need only support the mirror sag within the rather large ROC figure tolerance (many hundreds of wavelengths). I'm certain that a mirror support could not affect surface finish at sub wavelength features anyway. The sagging and draping of a mirror across it's supports would simply carry the surface finish along with it.
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Orion Argonaut 150mm Mak-Cass
Vixen GP mount
Livermore, CA viewing conditions
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mark cowan
Vendor (Obsidian Optics)
Reged: 06/03/05
Posts: 2159
Loc: salem, OR
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Quote:
OK, I'm starting to get the idea. There is a big tolerance on the radius of curvature (ROC) but a fine tolerance on the surface finish, but the interplay between them is still unclear to me (no pun intended). The ROC tolerance can be big because diffraction limited optics, even parabolas, have no precise focal plane. I'll provide an edited quote from my above reference that is illustrated in Fig B(a):
This is still wrong. You're confusing what a mirror does at COC with what a mirror does at focus. Not at all the same thing.
Works for this (without the spaces below). Don't know why it doesn't work for your clear dark sky...sorry!
[i m a g e]http://raddobs.com/atm/LvrmrCAcs0.gif[/ i m a g e]
Best,
Mark
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womiller
member
Reged: 10/05/09
Posts: 27
Loc: Bay Area, CA
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Mark,
Can you recommend a reference text to define and explain these issues?
Cheers,
Wayne
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Orion Argonaut 150mm Mak-Cass
Vixen GP mount
Livermore, CA viewing conditions
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mark cowan
Vendor (Obsidian Optics)
Reged: 06/03/05
Posts: 2159
Loc: salem, OR
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The one you're reading (by Dave Harbour) is a good one. Texereau's book on "How to make a telescope" covers all this stuff quite lucidly, easy to find. Other people might make some suggestions?
Best,
Mark
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Galaxyhunter
Pooh-Bah
Reged: 01/02/06
Posts: 1251
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Do you have this part of your code also? This goes ahead of what you have. ( this is the first part for my CSC.)
[url=http://cleardarksky.com/c/HwkyObILkey.html]
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Carl
My lousy skies at Hawkeye Observatory
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womiller
member
Reged: 10/05/09
Posts: 27
Loc: Bay Area, CA
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OK, after your tip and a trip to the Feedback forum I found a link to the archives that described the trick needed to show the CSC clock. It's a rather nonintuitive nesting of [url] and [image] tags. Thanks for the help.
Edited by womiller (10/28/09 01:17 PM)
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Mark Harry
Post Laureate
Reged: 09/05/05
Posts: 3125
Loc: Northeast
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Wayne, I glossed over the link you mentioned in your first post, and it's a fairly good basic description of what you're asking about.
As far as microfinish goes, if you can figure the mirror to 1/10th PVW, with good transition between the zonal values, your microfinish -SHOULD- be at least 10-100x finer.(estimated) This allows not only the basic shape of the mirror to focus the light reasonably well, but will also be a nice dark, contrasty mirror. It will have a sharp characteristic to the view.
(Should beat the pants off any mass produced scopes)
Mark
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So many projects, so little time!
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