5 ms·

Hiding Images in Plain Sight: The Physics of Magic Windows

272 points by Amorymeltzer 5y ago

sapphire_tomb 5y ago
Absolutely love the Fermat reference at the end!
constantform 5y ago
https://michaelberryphysics.files.wordpress.com/2013/07/berry383.pdf https://michaelberryphysics.files.wordpress.com/2013/07/berr...
- duffmancd 5y ago
  For more information, the parent PDF describes a similar process using reflection discovered in China. If you cast and polish a bronze mirror with raised letters/shapes on the back, the very slight deformations caused by polishing over the different thicknesses will create an image in the reflected caustics, despite the fact that the mirror appears smooth when using it as a mirror.
etaioinshrdlu 5y ago
Meanwhile I spent all day debugging a mess of React code, ultimately getting nowhere. Life choices questioning intensifies.
- wlesieutre 5y ago
  If you want to code up some holograms try a Looking Glass Portrait
- giovannibonetti 5y ago
  You might be interested in learning Elm [1] to escape React hell. [1] https://elm-lang.org/ https://elm-lang.org/
- mferraro89 5y ago
  Author here. At my day job I spend lots of hours debugging messy React code! The key is to have side projects too :)
  - etaioinshrdlu 5y ago
    You actually made me feel a lot better about this.
newpavlov 5y ago
While the described window is not a hologram per se and I think the hologram-like effect can easily break for other images (i.e. it can not reliably represent depth), it should be noted that it has a certain relation to holograms. Holograms modify plane wave in a way which reproduces wavefront from a recorded scene. Usually it's done by capturing interference pattern, but alternatively hologram can introduce phase shifts by varying thickness (ideally it's worth to use both phase shift and absorption). I think it should be possible to create hologram with the same setup by changing optimization function. Although I am not sure if you will be able to perform precise enough carving with your setup for reproducing complex enough scenes. Try to start with representing several dots at different distance from hologram plane each radiating radial wave. Thinking about diverging lens as of hologram representing one such point should help with intuition.
- tobr 5y ago
  That brings to mind this description of a technique for hand-engraved holograms[1]. > The required tools are so simple that ancient peoples could have drawn these images in hardened sooty resin pools with wooden tools, had they but known the trick. 1: http://amasci.com/amateur/holo1.html http://amasci.com/amateur/holo1.html
  - enriquto 5y ago
    This is incredibly awesome!
  - 123pie123 5y ago
    many thanks for this great nugget of information This could be used as a great art project, even young kids could do
- plutonorm 5y ago
  You can form this hologram trivially by considering each pixel as a source of rays in a variety of directions. You might then expect a series of hemispherical shapes on the surface, with areas of the dome missing where rays should not be fired. In this case you hit the age old problem of holograms - the sheer volume of information that needs to be encoded onto the surface for a hologram of reasonable resolution to be formed. Whether there is some more subtle surface that reproduces the light field but exploits its compressibility to reduce the surface complexity, I don’t know. Would be fun to try to optimise for it, but alas I have too many things to do already. How does one get grad students?
woko 5y ago
This is another amazing blog post by Matt Ferraro. You may remember his post last month about Poisson's Equation. For the past 2 blog posts, see: https://news.ycombinator.com/from?site=mattferraro.dev https://news.ycombinator.com/from?site=mattferraro.dev
alecst 5y ago
This is fucking awesome.
dekhn 5y ago
Fun stuff, I really like the intersection of modern CAM and mathematics with making.
thhkmth 5y ago
I also got quite interested some times ago ! A nice paper published about this magic : https://infoscience.epfl.ch/record/201509/files/caustics.pdf https://infoscience.epfl.ch/record/201509/files/caustics.pdf
- mferraro89 5y ago
  yep that paper is extremely impressive! I would love to implement that approach as well, but it is much more computationally expensive. In the Q&A after a talk from that paper's author, he mentions that it takes about 6 hours for the algorithm to run. The approach I took, modeled off of Yue et al, takes about 30 seconds. The trade-off is that the Schwartzburg paper is capable of much more general purpose remapping. It does not require continuity, which is why that paper results in ray folding which you can see as creasing in the lens.
mkoryak 5y ago
Ok, but can I buy one of these? I would pay money for a cat magic window that's not even my cat!
deleted 5y ago
[deleted]
kmm 5y ago
I've thought about it for an hour now, but I don't understand how the given algorithm works. I understand Step 1, growing and shrinking the cells such that the area of the cell on the window is proportional to the brightness of the corresponding cell on the image plane. Intuitively this feels like the cells on the window represent the total light budget, and growing a cell means taking a larger proportion of the incoming light to aim towards a given point. But I'm stuck at Step 2. If a window cell has a single normal, i.e. if it's a flat plane, I don't see how it would increase the brightness. Like the author previously describes, the brightness is dependent on the second derivative of the height, not the first. A larger flat window cell will not make for a brighter image cell, it'll simply make the image cell larger. Brightness could be increased by having more window cells aimed at the same point, not larger cells. The way I understand this could work is if the second step of converting the window cells into normals is done at a much higher resolution than the given map, and the target point is fixed for each cell. That way, the normal could vary over the course of a window cell, and every cell would function as a tiny lens, where now bigger lenses would in fact lead to brighter spots. I assume I'm missing something, can anyone tell me where I go wrong?
- contravariant 5y ago
  Yeah I think that part is a bit iffy, and if you look at the resulting image it does seem to have some fringes around the outside of the cat, indicating that it's showing something related to the curvature of the heightmap, rather than the intended image. It's probably a good enough approximation to at least generate a recognizeable image. Especially if you use a point source because then each 'window' will reflect all its light in more or less the right direction which will converge on a single point as well. Not sure if they'll all focus on the same plane but it's probably close enough.
  - mferraro89 5y ago
    yep I think you're exactly right, as evidenced by the fringes.
- mferraro89 5y ago
  Author here. That's a fantastic question! I think you're right that a better solution would include adding curvature to the individual "pixels" in the lens mesh. Unfortunately I don't know how to manufacture anything with microstructure that small! The microlenses would need to be of order .2mm by .2mm square and have curvature that is very slight, because the image plane pixel is about 20 cm away. Perhaps this could be achieved by choosing a ball-nose machine tool of the exact right radius and sweeping it back and forth in the channels formed between the "pixels"? It would leave a grid of tiny features that might just get the job done! As is I just gloss over that completely and I don't address it. So tiny, lone, bright pixels end up more smeared than I'd like.

272 points by Amorymeltzer 5y ago

Absolutely love the Fermat reference at the end!

https://michaelberryphysics.files.wordpress.com/2013/07/berry383.pdf https://michaelberryphysics.files.wordpress.com/2013/07/berr...

duffmancd 5y ago
For more information, the parent PDF describes a similar process using reflection discovered in China. If you cast and polish a bronze mirror with raised letters/shapes on the back, the very slight deformations caused by polishing over the different thicknesses will create an image in the reflected caustics, despite the fact that the mirror appears smooth when using it as a mirror.

etaioinshrdlu 5y ago

Meanwhile I spent all day debugging a mess of React code, ultimately getting nowhere. Life choices questioning intensifies.

wlesieutre 5y ago
If you want to code up some holograms try a Looking Glass Portrait
giovannibonetti 5y ago
You might be interested in learning Elm [1] to escape React hell. [1] https://elm-lang.org/ https://elm-lang.org/
mferraro89 5y ago
Author here. At my day job I spend lots of hours debugging messy React code! The key is to have side projects too :)
- etaioinshrdlu 5y ago
  You actually made me feel a lot better about this.

newpavlov 5y ago

While the described window is not a hologram per se and I think the hologram-like effect can easily break for other images (i.e. it can not reliably represent depth), it should be noted that it has a certain relation to holograms. Holograms modify plane wave in a way which reproduces wavefront from a recorded scene. Usually it's done by capturing interference pattern, but alternatively hologram can introduce phase shifts by varying thickness (ideally it's worth to use both phase shift and absorption). I think it should be possible to create hologram with the same setup by changing optimization function. Although I am not sure if you will be able to perform precise enough carving with your setup for reproducing complex enough scenes. Try to start with representing several dots at different distance from hologram plane each radiating radial wave. Thinking about diverging lens as of hologram representing one such point should help with intuition.

tobr 5y ago
That brings to mind this description of a technique for hand-engraved holograms[1]. > The required tools are so simple that ancient peoples could have drawn these images in hardened sooty resin pools with wooden tools, had they but known the trick. 1: http://amasci.com/amateur/holo1.html http://amasci.com/amateur/holo1.html
- enriquto 5y ago
  This is incredibly awesome!
- 123pie123 5y ago
  many thanks for this great nugget of information This could be used as a great art project, even young kids could do
plutonorm 5y ago
You can form this hologram trivially by considering each pixel as a source of rays in a variety of directions. You might then expect a series of hemispherical shapes on the surface, with areas of the dome missing where rays should not be fired. In this case you hit the age old problem of holograms - the sheer volume of information that needs to be encoded onto the surface for a hologram of reasonable resolution to be formed. Whether there is some more subtle surface that reproduces the light field but exploits its compressibility to reduce the surface complexity, I don’t know. Would be fun to try to optimise for it, but alas I have too many things to do already. How does one get grad students?

woko 5y ago

This is another amazing blog post by Matt Ferraro. You may remember his post last month about Poisson's Equation. For the past 2 blog posts, see: https://news.ycombinator.com/from?site=mattferraro.dev https://news.ycombinator.com/from?site=mattferraro.dev

alecst 5y ago

This is fucking awesome.

dekhn 5y ago

Fun stuff, I really like the intersection of modern CAM and mathematics with making.

thhkmth 5y ago

I also got quite interested some times ago ! A nice paper published about this magic : https://infoscience.epfl.ch/record/201509/files/caustics.pdf https://infoscience.epfl.ch/record/201509/files/caustics.pdf

mferraro89 5y ago
yep that paper is extremely impressive! I would love to implement that approach as well, but it is much more computationally expensive. In the Q&A after a talk from that paper's author, he mentions that it takes about 6 hours for the algorithm to run. The approach I took, modeled off of Yue et al, takes about 30 seconds. The trade-off is that the Schwartzburg paper is capable of much more general purpose remapping. It does not require continuity, which is why that paper results in ray folding which you can see as creasing in the lens.

mkoryak 5y ago

Ok, but can I buy one of these? I would pay money for a cat magic window that's not even my cat!

deleted 5y ago

[deleted]

kmm 5y ago

I've thought about it for an hour now, but I don't understand how the given algorithm works. I understand Step 1, growing and shrinking the cells such that the area of the cell on the window is proportional to the brightness of the corresponding cell on the image plane. Intuitively this feels like the cells on the window represent the total light budget, and growing a cell means taking a larger proportion of the incoming light to aim towards a given point. But I'm stuck at Step 2. If a window cell has a single normal, i.e. if it's a flat plane, I don't see how it would increase the brightness. Like the author previously describes, the brightness is dependent on the second derivative of the height, not the first. A larger flat window cell will not make for a brighter image cell, it'll simply make the image cell larger. Brightness could be increased by having more window cells aimed at the same point, not larger cells. The way I understand this could work is if the second step of converting the window cells into normals is done at a much higher resolution than the given map, and the target point is fixed for each cell. That way, the normal could vary over the course of a window cell, and every cell would function as a tiny lens, where now bigger lenses would in fact lead to brighter spots. I assume I'm missing something, can anyone tell me where I go wrong?

contravariant 5y ago
Yeah I think that part is a bit iffy, and if you look at the resulting image it does seem to have some fringes around the outside of the cat, indicating that it's showing something related to the curvature of the heightmap, rather than the intended image. It's probably a good enough approximation to at least generate a recognizeable image. Especially if you use a point source because then each 'window' will reflect all its light in more or less the right direction which will converge on a single point as well. Not sure if they'll all focus on the same plane but it's probably close enough.
- mferraro89 5y ago
  yep I think you're exactly right, as evidenced by the fringes.
mferraro89 5y ago
Author here. That's a fantastic question! I think you're right that a better solution would include adding curvature to the individual "pixels" in the lens mesh. Unfortunately I don't know how to manufacture anything with microstructure that small! The microlenses would need to be of order .2mm by .2mm square and have curvature that is very slight, because the image plane pixel is about 20 cm away. Perhaps this could be achieved by choosing a ball-nose machine tool of the exact right radius and sweeping it back and forth in the channels formed between the "pixels"? It would leave a grid of tiny features that might just get the job done! As is I just gloss over that completely and I don't address it. So tiny, lone, bright pixels end up more smeared than I'd like.