Large mirrors can't achieve theoretical resolution, due to surface flaws?

On Thu, 23 Jul 2009 18:39:23 +0100, Androcles wrote:

The way to make a larger mirror:
http://tinyurl.com/m24thr

Close. This how the ESO does it in Paranal:
http://en.wikipedia.org/wiki/Very_Large_Telescope
-- four 8m mirrors, optically linked for better resolution.

---(kaimartin)---
--
Kai-Martin Knaak
Öffentlicher PGP-Schlüssel:
http://pgp.mit.edu:11371/pks/lookup?...rch=0x6C0B9F53

"Marco" wrote in message news:4a68c04a$1@darkstar...
Additionally, large telescopes 8m are segmented and made of many
mirrors each ~1m in size. Each is then aligned to form the larger
mirror surface. So when polishing, you are always dealing with a
mirror of ~1m not 30m.

Marco
UCO Lick Observatory
Laboratory for Adaptive Optics

"Phil Hobbs" wrote in message
...
Neil B. wrote:
"Kai-Martin Knaak" wrote in message
news On Thu, 23 Jul 2009 12:54:41 -0400, Neil B. wrote:

if they are simply accurate to within a given standard like 1/8
wave.
They are a lot better.

It's the principle of the thing as the trends converge, not any
particular level of accuracy.
But consider that as a mirror gets larger, the tiny variations
in orientation of portions of the mirror should eventually cause
errors greater than the ever-decreasing diffraction spot.
The trick is not to allow "tiny variations" on a small scale. This
is
called "polishing". The result is a surface that is smooth over the
whole
range of lengths from the diameter down to the size of the
wavelength.

Thanks, but you miss the point (in effect, at least.) You cannot
prevent "tiny variations" since nothing is perfect. It's just a
matter of how far we push the given surface standards. Given any
particular level of tiny variations, the geometric effect of
variation in directing the average pencil of light will eventually
outgrow the size of the ideal diffraction spot.
But application of geometric optics to the surface irregularities
should
mean, a circle of confusion 0.01 arcsec diameter.
You better apply wave optics here.
...
I question whether that is good enough. There is still a variation
in the direction the light is sent, from various parts of the
mirror. The waves still have a propagation vector that must
correspond to the orientation at various places (if the variations
occur at distances further from each other than the wavelength.)
Just imagine a mirror that you would say worked fine. OK, if I
tilted part of that by 0.01 arcsec, and then more, and then more
.... how could it not be a continuous shifting of some part of the
concentrated spot? Then multiply that by various portions.

IOW we are not talking about effectively resolving features on the
mirror closer together than a certain distance. Instead, it's about
the directed nature of the wave, given angular uncertainty in the
orientation of portions at various scales. Like I said, given a
certain orientation standard like "0.01 arcsec" (or whatever it is),
the sending of PVs to slightly different spots should eventually
overcome the ideal resolution as the mirror gets bigger. But if you
are right, then we really could get better resolution in some cases
from using longer-wave light! (Because, in the short-wave case,
there is no possible excuse that wave properties could compensate
for the unevenness.)



Even ordinary 1-metre class telescopes fail to achieve the
diffraction limit, due to atmospheric irregularities. The big news
in astronomical instruments since Hubble has been adaptive optics,
where the waveform errors are sensed and corrected in real time.

The same systems can correct for errors that are static (mirror
figure) or slowly varying (e.g. sag under gravity as the telescope
tracks).

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal
ElectroOptical Innovations
55 Orchard Rd
Briarcliff Manor NY 10510
845-480-2058
hobbs at electrooptical dot net
http://electrooptical.net


Yes, interesting points but don't address the point of interest. I don't
care about whether we can correct for the surface irregularities except
as a practical hope we can get pretty pictures. The point of the post is
the theoretically interesting question, of whether visible resolution of
a single large mirror, as is; would start to be limited by surface
irregularities as the aperture grew larger.

"Jim Black" wrote in message
...
On Thu, 23 Jul 2009 12:54:41 -0400, Neil B. wrote:

Maybe I misunderstand the implications of applying a "1/8 wave" etc.
standard to different apertures, but I can't imagine that as
mirrors/lenses were made larger we'd be able to proportionately
reduce
the magnitude of orientation flaws.

As you have stated yourself, the position of the mirror surface is
accurate
to within a fraction of a wavelength. That implies that errors in
orientation are, in fact, being reduced as the mirrors are made
larger.

--
Well, maybe then we really couldn't do that. I can't imagine that we can
make the relations of patches of a mirror, endlessly fixed to smaller
and smaller angular tolerances. Just consider the problem of
manufacture. So I'm working on a palm-sized patch of a mirror. Because
the rest of the mirror is huge like 30m, somehow I can make the local
region match another one some meters away in orientation to some very
tiny angle? How? And if the mirror was even bigger, then I'd have to try
even harder at my local patch to finish the surface, etc. That doesn't
match my expectation of what is done, or is possible, with very large
mirrors.

In any case, that brings up the question: what's roughly the biggest
mirror can we make, that really does achieve theoretical resolution if
in space and no gravity/temperature issues? I can't believe we can
endlessly reduce the orientation errors down the line, one order of
magnitude after another.

On Jul 23, 1:35 pm, "Neil B." wrote:

Thanks, but you miss the point (in effect, at least.) You cannot
prevent "tiny variations" since nothing is perfect. It's just a matter
of how far we push the given surface standards. Given any particular
level of tiny variations, the geometric effect of variation in directing
the average pencil of light will eventually outgrow the size of the
ideal diffraction spot.

No, tis you who miss the point. First of all get geometric optics out
of your pointy little head! Your ideas simply do no compute! And the
mirror IS perfect. If it is a small one it is polished to a fraction
of a wavelength AT THE WAVELENGTH it is intended to be used so it IS
accurate! And it DOES have resolving power close to theoretical (but
not through the atmosphere obviously).

When mirrors are made larger the very weight, temperture expansion,
and changing forces cause it to deflect and lose accuracy even as you
move it from pointing at one part of the sky to another. So for a long
time telescopes made with mirror polished into perfect figure had a
size limit. But the new idea was the "rubber mirror". Basically you
build a mirror as good as you can and then use a series of electronic
jacks to bend it back where it belongs when it sags. Using this idea
one can actually create imaging telescopes out of multiple mirrors
that are all jacked into perfect alignment to a fraction of a
wavelength. [Which, let me note is NOT what is going on in Andro's
boiler picture which as usual has absolutely nothing to do with what
we are talking about here. ]

To elaborate, the relationship between the mirror and the far field
resolving power is as in any antenna namely where the angular pattern
in the far field is the Fourier transform of the light distribution
across the aperture. If for example the mirror were square, the far
field angular pattern that is used to resolve point sources would be
the familiar sin x/x function. If you have multiple mirrors then they
act as classic arrays. The advantage to an array is the that you get
angular patterns related to he spacing of the elements rather than the
size of a single mirror. And the is obviously more because it is
possible to adjust the far field pattern to make it sharper by
modulating the intensity on the receiving miror. And the ultimate is
the "synthetic aperture" antenna where gigantic equivalent mirrors are
created by moving smaller ones. The telescope guys can tell you more,
but I'd guess that only the miltary spooks are using that technology
at optical wavelengths presently. For Sonor it's SOP.

The bottom line is that you are SO far behing state of the art, that
it's hard to tell you where to begin to catch up.

On Jul 23, 8:54*pm, "Neil B." wrote:
"Marco" wrote in messagenews:4a68c04a$1@darkstar...
Additionally, large telescopes 8m are segmented and made of many
mirrors each ~1m in size. *Each is then aligned to form the larger
mirror surface. So when polishing, you are always dealing with a
mirror of ~1m not 30m.

Marco
UCO Lick Observatory
Laboratory for Adaptive Optics

"Phil Hobbs" wrote in message
...
Neil B. wrote:
"Kai-Martin Knaak" wrote in message
news On Thu, 23 Jul 2009 12:54:41 -0400, Neil B. wrote:

if they are simply accurate to within a given standard like 1/8
wave.
They are a lot better.

It's the principle of the thing as the trends converge, not any
particular level of accuracy.
But consider that as a mirror gets larger, the tiny variations
in orientation of portions of the mirror should eventually cause
errors greater than the ever-decreasing diffraction spot.
The trick is not to allow "tiny variations" on a small scale. This
is
called "polishing". The result is a surface that is smooth over the
whole
range of lengths from the diameter down to the size of the
wavelength.

Thanks, but you miss the point (in effect, at least.) *You cannot
prevent "tiny variations" since nothing is perfect. It's just a
matter of how far we push the given surface standards. Given any
particular level of tiny variations, the geometric effect of
variation in directing the average pencil of light will eventually
outgrow the size of the ideal diffraction spot.
But application of geometric optics to the surface irregularities
should
mean, a circle of confusion 0.01 arcsec diameter.
You better apply wave optics here.
...
I question whether that is good enough. *There is still a variation
in the direction the light is sent, from various parts of the
mirror. The waves still have a propagation vector that must
correspond to the orientation at various places (if the variations
occur at distances further from each other than the wavelength.)
Just imagine a *mirror that you would say worked fine. OK, if I
tilted part of that by 0.01 arcsec, and then more, and then more
.... how could it not be a continuous shifting of some part of the
concentrated spot? *Then multiply that by various portions.

IOW we are not talking about effectively resolving features on the
mirror closer together than a certain distance. *Instead, it's about
the directed nature of the wave, given angular uncertainty in the
orientation of portions at various scales. *Like I said, given a
certain orientation standard like "0.01 arcsec" (or whatever it is),
the sending of PVs to slightly different spots should eventually
overcome the ideal resolution as the mirror gets bigger. *But if you
are right, then we really could get better resolution in some cases
from using longer-wave light! (Because, in the short-wave case,
there is no possible excuse that wave properties could compensate
for the unevenness.)

Even ordinary 1-metre class telescopes fail to achieve the
diffraction limit, due to atmospheric irregularities. *The big news
in astronomical instruments since Hubble has been adaptive optics,
where the waveform errors are sensed and corrected in real time.

The same systems can correct for errors that are static (mirror
figure) or slowly varying (e.g. sag under gravity as the telescope
tracks).

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal
ElectroOptical Innovations
55 Orchard Rd
Briarcliff Manor NY 10510
845-480-2058
hobbs at electrooptical dot net
http://electrooptical.net

Yes, interesting points but don't address the point of interest. I don't
care about whether we can correct for the surface irregularities except
as a practical hope we can get pretty pictures. The point of the post is
the theoretically interesting question, of whether visible resolution of
a single large mirror, as is; would start to be limited by surface
irregularities as the aperture grew larger.- Hide quoted text -

- Show quoted text -

The answer is that the frequency response of the mirror is a function
of the autocorrelation of the pupil function. The pupil function is
the wavefront error of the converging (imaging) light. If a larger
mirror is made to the same specification in terms of wavefront errors
then the pupil fuction will remain constant.

www.richardfisher.com

"Benj" wrote in message
...
On Jul 23, 1:35 pm, "Neil B." wrote:

Thanks, but you miss the point (in effect, at least.) You cannot
prevent "tiny variations" since nothing is perfect. It's just a matter
of how far we push the given surface standards. Given any particular
level of tiny variations, the geometric effect of variation in directing
the average pencil of light will eventually outgrow the size of the
ideal diffraction spot.

No, tis you who miss the point. First of all get geometric optics out
of your pointy little head! Your ideas simply do no compute! And the
mirror IS perfect. If it is a small one it is polished to a fraction
of a wavelength AT THE WAVELENGTH it is intended to be used so it IS
accurate! And it DOES have resolving power close to theoretical (but
not through the atmosphere obviously).

When mirrors are made larger the very weight, temperture expansion,
and changing forces cause it to deflect and lose accuracy even as you
move it from pointing at one part of the sky to another. So for a long
time telescopes made with mirror polished into perfect figure had a
size limit. But the new idea was the "rubber mirror". Basically you
build a mirror as good as you can and then use a series of electronic
jacks to bend it back where it belongs when it sags. Using this idea
one can actually create imaging telescopes out of multiple mirrors
that are all jacked into perfect alignment to a fraction of a
wavelength. [Which, let me note is NOT what is going on in Andro's
boiler picture which as usual has absolutely nothing to do with what
we are talking about here. ]

You wouldn't know a mousetrap from a dog's jaw if it bit you on
the arse, Jocaby.
http://en.wikipedia.org/wiki/File:US...geArray.02.jpg





To elaborate, the relationship between the mirror and the far field
resolving power is as in any antenna namely where the angular pattern
in the far field is the Fourier transform of the light distribution
across the aperture. If for example the mirror were square, the far
field angular pattern that is used to resolve point sources would be
the familiar sin x/x function. If you have multiple mirrors then they
act as classic arrays. The advantage to an array is the that you get
angular patterns related to he spacing of the elements rather than the
size of a single mirror. And the is obviously more because it is
possible to adjust the far field pattern to make it sharper by
modulating the intensity on the receiving miror. And the ultimate is
the "synthetic aperture" antenna where gigantic equivalent mirrors are
created by moving smaller ones. The telescope guys can tell you more,
but I'd guess that only the miltary spooks are using that technology
at optical wavelengths presently. For Sonor it's SOP.

The bottom line is that you are SO far behing state of the art, that
it's hard to tell you where to begin to catch up.

"Kai-Martin Knaak" wrote in message
news
On Thu, 23 Jul 2009 18:39:23 +0100, Androcles wrote:

The way to make a larger mirror:
http://tinyurl.com/m24thr

Close. This how the ESO does it in Paranal:
http://en.wikipedia.org/wiki/Very_Large_Telescope
-- four 8m mirrors, optically linked for better resolution.


The difference is the focal point is shared as I've shown it, whereas at
Paranal each individual dish has its own focal point and is used for radio
wavelengths. Don't be fooled by "optically linked", fibre optics are used
everywhere these days. My phone is "optically linked" in journalist speak.

On Jul 23, 10:26*pm, "Androcles"
wrote:
"Benj" wrote in message

...



On Jul 23, 1:35 pm, "Neil B." wrote:

Thanks, but you miss the point (in effect, at least.) *You cannot
prevent "tiny variations" since nothing is perfect. It's just a matter
of how far we push the given surface standards. Given any particular
level of tiny variations, the geometric effect of variation in directing
the average pencil of light will eventually outgrow the size of the
ideal diffraction spot.

No, tis you who miss the point. First of all get geometric optics out
of your pointy little head! Your ideas simply do no compute! *And the
mirror IS perfect. If it is a small one it is polished to a fraction
of a wavelength AT THE WAVELENGTH it is intended to be used so it IS
accurate! And it DOES have resolving power close to theoretical (but
not through the atmosphere obviously).

When mirrors are made larger the very weight, temperture expansion,
and changing forces cause it to deflect and lose accuracy even as you
move it from pointing at one part of the sky to another. So for a long
time telescopes made with mirror polished into perfect figure had a
size limit. But the new idea was the "rubber mirror". Basically you
build a mirror as good as you can and then use a series of electronic
jacks to bend it back where it belongs when it sags. Using this idea
one can actually create imaging telescopes out of multiple mirrors
that are all jacked into perfect alignment to a fraction of a
wavelength. [Which, let me note is NOT what is going on in Andro's
boiler picture which as usual has absolutely nothing to do with what
we are talking about here. ]

You wouldn't know a mousetrap from a dog's jaw if it bit you on
the arse, Jocaby.
*http://en.wikipedia.org/wiki/File:US...geArray.02.jpg

To elaborate, the relationship between the mirror and the far field
resolving power is as in any antenna namely where the angular pattern
in the far field is the Fourier transform of the light distribution
across the aperture. If for example the mirror were square, the far
field angular pattern that is used to resolve point sources would be
the familiar sin x/x function. If you have multiple mirrors then they
act as classic arrays. The advantage to an array is the that you get
angular patterns related to he spacing of the elements rather than the
size of a single mirror. And the is obviously more because it is
possible to adjust the far field pattern to make it sharper by
modulating the intensity on the receiving miror. And the ultimate is
the "synthetic aperture" antenna where gigantic equivalent mirrors are
created by moving smaller ones. The telescope guys can tell you more,
but I'd guess that only the miltary spooks are using that technology
at optical wavelengths presently. For Sonor it's SOP.

The bottom line is that you are SO far behing state of the art, that
it's hard to tell you where to begin to catch up.

I think what he is talking about is surface roughness. Although the
average overall surface may be accurate to within 1/8 wave, it has
some overall surface roughness. Roughness on long spatial dimensions
becomes a variation in figure. Roughness on a much smaller scale is a
problem EVEN FOR SPATIAL WAVELENGHTS SMALLER THAN THE DESIGN photon
wavelength of the mirror. That is, this micro-roughness which may be
on the order of a few angstroms in height will scatter light. The
degree of scatter (fractions of photons removed from the desired beam)
is given roughly by the Debye -Waller factor. For visible wavelengths
it is ussually not a problem because such micro-roughness can be
reduced to below a few nanometers in height. It CAN be a problem for
very sensitive measurements where it reduces overall contrast.
Mirrors for IR military space based sensors are often superpolished to
get roughness of roughly 5 angstroms rms. There is an equation that
escapes me right now for the angle into which half of the scattefred
photons will be scattered inside of. I do know this equation is in a
paper by Susini et. al in Optical Engineering. The paper is about x-
ray optics where such roughness is a major problem.

"Neil B." wrote in
maker:

In any case, that brings up the question: what's roughly the biggest
mirror can we make,

There are plans for a 100m telescope.

http://www.eso.org/sci/facilities/eelt/owl/

It must work, or else why would they do it?

Or..... maybe it's all a big conspiracy. Telescopes don't
really work. All those pretty pictures are just CGI.

Anyway, I think you are simply missunderstanding the concept
of surface accuracy. As long as the entire mirror surface,
whether it be one piece or segments, is held to an accuracy
of less than the wavelength of light it observes at, it is
for all intents and purposes, "perfect". This is simple wave
theory. As other have tried to point out, you can't look at
this problem as rays and beams of light.

Just to give an example I think you'll understand, the door
on your microwave. Obviously the screen on the door has holes
in it, but as far as the microwaves are concerned, it's solid.
The wavelength of the microwaves is larger than the holes,
therefore they can't "see" the holes. It's like they just
aren't there. However, light that we see with has a much smaller
wavelength and therefore "sees" the holes, in this case passing
through them.

It's the same with optical mirrors. As long as any imperfections
are sufficiently smaller than the wavelength of the light,
the light simply doesn't "see" the errors.

Microwaves and light waves are both electromagnetic waves
and both follow the same rules of wave theory.

Brian
--
http://www.skywise711.com - Lasers, Seismology, Astronomy, Skepticism
Seismic FAQ: http://www.skywise711.com/SeismicFAQ/SeismicFAQ.html
Quake "predictions": http://www.skywise711.com/quakes/EQDB/index.html
Sed quis custodiet ipsos Custodes?

"Frogwatch" wrote in message
...
On Jul 23, 10:26 pm, "Androcles"
wrote:
"Benj" wrote in message

...



On Jul 23, 1:35 pm, "Neil B." wrote:

Thanks, but you miss the point (in effect, at least.) You cannot
prevent "tiny variations" since nothing is perfect. It's just a matter
of how far we push the given surface standards. Given any particular
level of tiny variations, the geometric effect of variation in
directing
the average pencil of light will eventually outgrow the size of the
ideal diffraction spot.

No, tis you who miss the point. First of all get geometric optics out
of your pointy little head! Your ideas simply do no compute! And the
mirror IS perfect. If it is a small one it is polished to a fraction
of a wavelength AT THE WAVELENGTH it is intended to be used so it IS
accurate! And it DOES have resolving power close to theoretical (but
not through the atmosphere obviously).

When mirrors are made larger the very weight, temperture expansion,
and changing forces cause it to deflect and lose accuracy even as you
move it from pointing at one part of the sky to another. So for a long
time telescopes made with mirror polished into perfect figure had a
size limit. But the new idea was the "rubber mirror". Basically you
build a mirror as good as you can and then use a series of electronic
jacks to bend it back where it belongs when it sags. Using this idea
one can actually create imaging telescopes out of multiple mirrors
that are all jacked into perfect alignment to a fraction of a
wavelength. [Which, let me note is NOT what is going on in Andro's
boiler picture which as usual has absolutely nothing to do with what
we are talking about here. ]

You wouldn't know a mousetrap from a dog's jaw if it bit you on
the arse, Jocaby.
http://en.wikipedia.org/wiki/File:US...geArray.02.jpg

To elaborate, the relationship between the mirror and the far field
resolving power is as in any antenna namely where the angular pattern
in the far field is the Fourier transform of the light distribution
across the aperture. If for example the mirror were square, the far
field angular pattern that is used to resolve point sources would be
the familiar sin x/x function. If you have multiple mirrors then they
act as classic arrays. The advantage to an array is the that you get
angular patterns related to he spacing of the elements rather than the
size of a single mirror. And the is obviously more because it is
possible to adjust the far field pattern to make it sharper by
modulating the intensity on the receiving miror. And the ultimate is
the "synthetic aperture" antenna where gigantic equivalent mirrors are
created by moving smaller ones. The telescope guys can tell you more,
but I'd guess that only the miltary spooks are using that technology
at optical wavelengths presently. For Sonor it's SOP.

The bottom line is that you are SO far behing state of the art, that
it's hard to tell you where to begin to catch up.

I think what he is talking about is surface roughness. Although the
average overall surface may be accurate to within 1/8 wave, it has
some overall surface roughness. Roughness on long spatial dimensions
becomes a variation in figure. Roughness on a much smaller scale is a
problem EVEN FOR SPATIAL WAVELENGHTS SMALLER THAN THE DESIGN photon
wavelength of the mirror. That is, this micro-roughness which may be
on the order of a few angstroms in height will scatter light. The
degree of scatter (fractions of photons removed from the desired beam)
is given roughly by the Debye -Waller factor. For visible wavelengths
it is ussually not a problem because such micro-roughness can be
reduced to below a few nanometers in height. It CAN be a problem for
very sensitive measurements where it reduces overall contrast.
Mirrors for IR military space based sensors are often superpolished to
get roughness of roughly 5 angstroms rms. There is an equation that
escapes me right now for the angle into which half of the scattefred
photons will be scattered inside of. I do know this equation is in a
paper by Susini et. al in Optical Engineering. The paper is about x-
ray optics where such roughness is a major problem.

========================================
Jokaby still wouldn't know a mousetrap from a dog's jaw if it bit
him on the arse.
The way to build a large mirror is a collection of small mirrors
individually actuated and computer controlled.

See: http://tinyurl.com/lvh6dd