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In a recent idea I proposed using an array of Luneburg
lenses as a 3D display. Luneburg lenses are not easy
to
make. It requires a gradient of refractive index from
the
centre to the surface of a sphere.
I have been pondering methods of forming uniform
thickness spherical layers.
An
added level of difficulty is making very small lenses
(500µm diameter).
The best method I can think of is using a process
called
'hot flocking' wherein the object to be coated is heated
so
that when the powder contacts the object the powder
melts thus forming a layer. This process would be
repeated to epitaxially form the lens.
To ensure the layer growth is uniform, the lens would
need to be not contacting any support. This could be
done in zero-gravity or using magnetic levitation, but
the
simplest way would be to drop the seed lens in a
vacuum.
The seed lens is dropped and heated with radiation
(microwave or IR laser). As the seed lens falls, a first
blast
of ultra-fine glass powder (diameter of about 2µm) is
fired
at the seed lens from all directions. The powder only
attaches to the seed lens (and not the glass powder),
thus forming a uniform layer. As the powder melts, the
surface tension keeps the melted layer at a uniform
depth.
The lens continues to fall and be heated, and then
passes
a second blast of ultra-fine glass powder of slightly
lower
refractive index.
The processes continues about 100 times; the lens
having fallen a few hundred meters. The lens is then
cooled and then gently decelarated in a low-density
material.
Luneburg microlens array
[xaviergisz, Jan 09 2020]
Spaceframe Mountain
Spaceframe_20Mountain
"mfd - redundant (see [Vernon]'s <link>) - kept only for the smartass remarks." [8th of 7, Jan 10 2020]
Wikipedia: Cold spraying
https://en.wikipedi.../wiki/Cold_spraying
Mentioned in my anno. A thermal spraying process [notexactly, Jan 15 2020]
Wikipedia: Inkjet printing § Continuous inkjet
https://en.wikipedi...g#Continuous_inkjet
Mentioned in my anno. Could be adapted to "continuous powder jet" [notexactly, Jan 15 2020]
Link 1
https://www.advance...-transparent-glass/
3D printed glass [bhumphrys, Jan 15 2020]
Link 2
https://3dprint.com...-lens-radar-system/
3D printed RF Luneburg lens [bhumphrys, Jan 15 2020]
Wikipedia: Robocasting
https://en.wikipedia.org/wiki/Robocasting
MIMA. 3D printing of pastes that then get sintered to make hard objects [notexactly, Feb 27 2020]
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Annotation:
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//fired at the seed lens from all directions// |
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Without compromising the vacuum? |
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Oh, right; you're doing this in space, aren't you? |
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Why can't you just leave the hot glass on a flat surface and
drop the glass powder onto it in a regular atmosphere? |
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//Without compromising the vacuum?
Oh, right; you're doing this in space, aren't you?// |
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This would be terrestrial; in a tall tower or deep
mineshaft. |
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All the ultra-fine powder which didn't stick to the lens
would fall to the bottom. Because it's a vacuum, the
powder should fall. The tube might need to be cleaned
regularly with a shuttle. |
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//Why can't you just leave the hot glass on a flat surface
and drop the glass powder onto it in a regular
atmosphere?// |
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I don't think the hot glass would remain spherical, nor
would it get coated uniformly. |
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Alternatively, you could try rolling the hot glass lens on a
bed of glass powder, but again it's not going to be pretty. |
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Keeping it uniform at each stage is very important. Even
small imperfections will grow bigger with each layer
added. |
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Neither technique will place a drop of near-molten glass
directly upon each previously-deposited hardening drop. |
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In light of pertinax's comment I realise that I haven't
explained the idea very well. |
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The seed lens would be dropped in a very high tube.
Along the tube would be radially placed: a) powdered
glass blasters, and b) heaters. The spacing (and size) of
these would increase down the tube to account for the
acceleration of the lens, so that each iteration would be
the same length of time. |
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The bottom could have a series of quick-opening doors
so that the lens could fall into a deceleration chamber
without losing the vacuum in the tube. |
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What does a radially-placed powdered glass blaster look like? |
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If I were inadvisedly riding the seed lens down the tube, would I
see a series of rings of orifices out of which powdered glass
would be blasted? In that case, the blasting would be
asymmetrical in the vertical dimension. Or would I see a
uniform coating of glass powder backed by an explosive
substrate, whose detonation would somehow propagate down
the tube at an accelerating rate? Or what? |
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The blasters would be angled and timed so the powder
would hit the seed lens at the same speed and
approximately from an angle perpendicular to the
surface of the seed lens. As the speed of the lens
increases down the tube, the angles and spacing of the
blasters would be more exaggerated. |
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The propulsion mechanism would be some kind of
precisely controlled linear motor (piezoelectric or
solenoid). The powder would be held in place on the end
of the linear motor by a mesh with holes the same size
as the powder diameter. |
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Alternatively the powder could be kept in thousands of
tubes. An impact at one end sends a shock wave
through the spherical powder particles so that the last
one is ejected (like a Newton's cradle). |
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There are a few other ways I can envisage, e.g. similar to
electrospraying. |
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Instead of the seed lens falling past the powder
blasters, the seed lens and blasters and heater could all
be in self-contained shuttle. The seed lens would initially
be held in the centre by a releasable mechanism. When
the shuttle drops and everything in the shuttle
experiences zero-g, the seed lens is released and then
heated and then the powder is blastered at the lens
iteratively. At the end of the process the lens is cooled
and captured by the mechanism, and then the whole
shuttle gently decelarated. The tower could be relatively
small so the shuttle would do the first 10% of the layers
in the first drop, then raised back up to do the next 10%
and so on. |
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hmmm Would a Prince Rupert drop qualify as a Luneburg lens with a fiber optic focal point or is the shape not spherical enough to lens properly? |
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It has been proposed to make a perfectly spherical
version of a Prince Rupert's Drop. This could be done by
rapidly cooling a blob of molten glass in a zero-g
environment. Such a Prince Rupert's Drop would have a
gradient of stress from the centre to the surface. It is a
tantalizing possibility that (with a carefully chosen
material) the gradient of stress could affect the gradient
of refractive index such that it forms a Luneburg lens. |
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What about molecular beam epitaxy ? |
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// The tube might need to be cleaned regularly with a shuttle. // |
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You might have a job borrowing one of the retired ones. Museums can be pretty reluctant to lend out their prize exhibits, no matter how politely they're asked. Even if you only want a small part as a souvenir, they can cut up really rough. It's not like they even paid for the damn thing, the Wrights donated it ... petty, we call it. |
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//It has been proposed to make a perfectly spherical version of a Prince Rupert's Drop. This could be done by rapidly cooling a blob of molten glass in a zero-g environment.// |
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I proposed it in my Prince Rupert Spheres posting... that's what made me think of it. You might be able to do away with the enormous tower and a bunch of steps by making your lenses in microgravity. |
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// the enormous tower and a bunch of steps // |
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<Fondly recalls all-time-favourite anno, in "Spaceframe Mountain" <link>/> |
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This seems like a thermal spraying-based process whereby the glass powder is sprayed on and then melted by
the heat that the nascent lens already has. What about the kinetic energy of the powder, though? Cold
spraying [link], despite the name, is a thermal spraying process where the kinetic energy of the powder is
what's used to melt it. It generally produces incomplete melting and therefore voids in the coating, but that
could theoretically be controlled as a means of varying the refractive index, as long as the powder particles
and voids are considerably smaller than the wavelengths the lens will be used with. |
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What about suspending the nascent lenses in an upward hot gas jet? You can shoot glass powder at them from
the side, and the imbalance will cause rotation to allow even coverage. You'll have to shoot from multiple
sides in a carefully planned sequence to ensure they rotate in such a way that all points on the surface can
be blasted. Also, to compensate for recoil, the gas jet could be at an angle to vertical, or an additional gas
jet can be added that provides horizontal wind (in pulses timed to coincide with glass powder blasts, if those
are intermittent). |
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What about using the method used for manufacturing glass marbles? Those are made with a pair of screws
that roll the marble along between them as it cools down. Instead of just dropping a full-size blob of glass on
straight screws and using them to form it into a sphere, you could use tapered screws that grow from the size
of the seed to the size of the finished lens, and set up blasters for each grade of glass powder along their
length. The lens would grow as it goes along the screws, and the size of the screws would increase at the
same rate. The two screws might need to be slightly different in size, and/or have different surface
materials or textures (or maybe even different surfaces between the forward- and backward-facing sides of
the thread), to ensure the lenses rotate in a way that results in even coverage. The screws would need to be
very long in total, but you could easily break them up into multiple stages that you could stack. Also, either
the screws need to be either made of or coated with something that the glass powder won't stick to, or the
blasters need to produce very narrow streams. (Yes, that sentence has "either" twice. It's grammatically
correct.) |
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What I thought of for producing very narrow streams of glass powder was something like continuous inkjet
technology [link] (not to be confused with a drop-on-demand inkjet printer with a continuous ink supply
system). Basically, a CIJ printer shoots a stream of electrically charged ink droplets and controls their
trajectory similarly to how a CRT monitor controls its electron beam's trajectory. (This technology is one of
the ones commonly used on packaging lines, for printing best before dates, lot numbers, etc., along with
drop-on-demand inkjet and laser marking. That's why those markings often have letters made of dots of
black ink, that can be scraped off if the substrate isn't porous, on a white background that's incorporated
into the main label printing, which is done in advance of packaging.) |
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That would also enable easy control of when it's blasting glass powder and when it isn't, as well as fine
aiming control. You could also, maybe, charge the nascent lenses to attract the glass powder, and the
gas/screws to repel it, but it would be difficult to achieve that because glass is generally a dielectric, and
the nascent lenses are in direct contact with the gas/screws. Maybe a beam of positive ions aimed at the top
of each nascent lens as it goes along? Or a gas/surface on the screws that charges the lenses
triboelectrically? |
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There are many manufacturing possibilities indeed. |
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I'm attracted to the super precise methods. For example,
imagine a geodesic arrangement of hundreds of
thousands of needles and lasers. The molten seed lens
is held in place in the centre (with zero-g or mag-lev).
The needles simultaneously fire individual glass powder
spheres; the first layer only requiring 1,000 powder glass
spheres, progressing to the last layer requiring hundreds
of thousands. Each needle would contain a series of
progressively lower refractive index glass powder
spheres, and ejected with a Newton' s Cradle impulse. |
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The glass powder spheres could be made with
electrospray techniques. |
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Simply 3D print a structure in glass (link 1) consisting of an appropriately spaced matrix of filaments in accordance with the eventual ly required spatial distribution of refractive indea required to form the Luneburg lens (link 2). Place the matrix thus formed inside a spherical mould. Fill the mould containing the matrix with powder of a different refractive index. Sinter it. Remove the sintered sphere and polish it: pronto. |
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You won't be able, with current technology, to 3D print a structure small enough, I think. It would have to be on the scale of tens to hundreds of nanometers to be transparent to visible light, and Wikipedia [link] says "Robocasting has also been used to deposit polymer and sol-gel inks through much finer nozzle diameters (<2μm) than is possible with ceramic inks." (The article you linked mentions it's a "direct ink writing" process, and doing a Google search for that tells me it's the same as "robocasting", which is just 3D printing of shear-thinnable pastes that then get sintered.) |
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