I have no idea how these cats got wedged into acrylic squares, or why.
August 25, 2021 7:29 AM   Subscribe

Hiding Images in Plain Sight: The Physics Of Magic Windows. Engineer Matt Ferraro shows how to make transparent acrylic squares with holographic images embedded in them.
posted by Cash4Lead (24 comments total) 35 users marked this as a favorite
 
This man knows how to make me care about physics by using cats. Bravo, sir.
posted by Kitteh at 7:39 AM on August 25 [3 favorites]


I've discovered a truly marvelous proof of this, which this website's margin is unfortunately too narrow to contain

Love everything about this!
posted by riverlife at 7:42 AM on August 25 [1 favorite]


Wheh! We went from cats to math pretty quick there.
posted by Don.Kinsayder at 7:56 AM on August 25 [3 favorites]


I had to nope out of the math for reasons, but... did he 3D print something to holograph a cat, or did it actually take on the image of a cat by virtue of viewing a cat through the lens with the right kind of light? Does it reset and he can capture different images? If so, how does the reset work?
posted by Grither at 9:17 AM on August 25


@Grither: I was similarly confused by the initial description. It sadly isn't a magic create-a-cat-hologram device. It's more of a 3d printed (carefully! with lots of math!) really fancy lens that shows an image when you shine light through it.
posted by vernondalhart at 9:32 AM on August 25 [3 favorites]


It's not 3D printed. It's machined to the target shape using a CNC router. Very cool.
posted by cron at 9:47 AM on August 25 [4 favorites]


It's more of a 3d printed

Unfortunately it's CNC milled. And then very carefully post processed with sandpaper and automotive polish.

I wonder if you could get reasonable results out of clear resin and a SLA printer, or if clear resin is still milky. Formlabs has some suggestions, but ... still. oof.

(on preview: jinx!)
posted by Kyol at 9:48 AM on August 25


All the photons that don't pass directly through the object are what form the object's shadow.

Well that's... one way to think about it. It quirky stuff like this kept me reading. Fun article.

It's machined to the target shape using a CNC router. Very cool.

And he designed and built his router.
posted by Avelwood at 9:55 AM on August 25


This is way neat and would make amazing keepsakes for all kinds of things. Also good for secret messages?? And: lenses for cool effects for light shows, maybe?
posted by wemayfreeze at 1:23 PM on August 25


I have a CNC router that a friend built and didn't have a use for, and so now it's hanging from the ceiling in my shop. I am super intrigued by this project and want to make a couple, and, yeah, like wemayfreeze it's got me thinking about custom lenses: Are there places where weirdly shaped lenses that don't have to be super precise but could be relatively large would be useful? If I can cut a foot and a half diameter aspherical lens in a few hours, does that let me make like a big refractor telescope that's useful in any way?

At the very least, just making some cat shadows seems like something I should do.
posted by straw at 2:09 PM on August 25 [1 favorite]


I have on my bookshelf a Chinese "magic mirror" that does a similar thing based on reflected light rather than passed-through light. Wikipedia. The method is over 2000 years old -- presumably originally practiced by delicate etching and polishing while observing the result, rather than by clever math. The Wikipedia article references a physics journal that provides a mathematical explanation of the Chinese magic mirror, which I have not read but I presume is not too unsimilar to Matt Ferraro's explanation.

Anyways, it's all lovely!
posted by brambleboy at 2:53 PM on August 25 [3 favorites]


did he 3D print something to holograph a cat, or did it actually take on the image of a cat by virtue of viewing a cat through the lens with the right kind of light?

AFAICT, he took a 2d picture of a cat, did a bunch of math and used some machines and then sandpaper to grind a funny shaped lens that focuses normal light into a picture of a cat instead of into a point.

My hunch is that this looks good because he filmed it at the focal length where it looks amazing, and if you put the piece of paper further or closer to it the image would become blurry (which in this particular case I consider distinct from it being fuzzy).
posted by aubilenon at 4:10 PM on August 25 [1 favorite]


And he designed and built his router.

You know... as one does.
posted by hippybear at 6:07 PM on August 25 [1 favorite]


My hunch is that this looks good because he filmed it at the focal length where it looks amazing, and if you put the piece of paper further or closer to it the image would become blurry (which in this particular case I consider distinct from it being fuzzy).

The distance is specified in the calculations ('d') and is necessary to calculate the appropriate surface normal field. As you move away from the optimal distance the image will naturally blur, just like a more conventional lens shapes a beam of light into a double cone so as you move away from the focal plane you get circles of increasing diameter, rendered into Gaussians by diffraction...
posted by memetoclast at 8:57 PM on August 25 [4 favorites]


MetaFilter: as you move away from the focal plane you get circles of increasing diameter
posted by hippybear at 9:05 PM on August 25


I don't get where the 'hologram' part fits in unless it's an effect of moving from a man-made light source (narrow frequency range) to sunlight (wide frequency range)... and it's just a bit of woo that's due to the different refraction values for different frequencies of light. So it becomes a bit of a 2d fuzzed into 3d.

I was surprised that they could get enough resolution out of the bit they used in the CNC machine. Have to read through again, but the actual calculation part is pretty cool. Just my sort of backwards math. It's usually the other way around, here's this thing, figure out what comes out the other side with maths, this way it's make the thing that produces this result. Nice.

See also: Chinese magic mirror - Wikipedia. In sunlight it magically reflects an image onto a surface. The secret is akin to lens grinding. It's bronze and the reflecting side is flat and the back has is casted with an image. When polising the slight differences in pressure due to the thickness tend to influence the 'flat' surface being polished. Shine a bright enough light on it and it will reflect those differences onto the wall. A variant of these was used in Japan by the Christians during the period where Christianity was forbidden. A simple mirror (the back now enclosed) that if you use it right projects the cross or the Virgin Mary, or even really any other diety.

Technically, people were doing things like this (though much simpler) long ago.
posted by zengargoyle at 12:11 AM on August 26


I wonder if you could get reasonable results out of clear resin and a SLA printer, or if clear resin is still milky. Formlabs has some suggestions, but ... still. oof.

You can definitely 3d print transparent resin with a cheap resin DLP printer (I've done it with 28mm minis), though it will also need polishing and/or clear coat varnishing to eliminate the surface frosting. You can easily get down to a resolution of 0.01mm in the z axis (0.035 in x/y with the new elegoo mars 3 f.ex) so that should be sufficient to print the lens detail.

Doing the math to create an STL from an image... uh, I'll let someone else tackle that.
posted by Absolutely No You-Know-What at 1:00 AM on August 26


Their diagram is wrong. They left out a part of the equations. The part left out doesn't really matter but the diagram is wrong and the glossing over is slight-of-hand.

Snell's law is disregarded on the flat side. Wrong, it applies on both sides the same way. The only ray of light that goes straight line through the air-lens-air transition with no angle change is the middle ray because it's the only one that is perpendicular to both surfaces of the lens (so to speek). They draw the change of angle the rays experience coming in the curved side according to Snell's law (all but the center get bent)... but then draw the the non-center rays as going straight through the intersection of the lens back to air in a straight line. That is false, Snell's law still applies, the non-perpendicular to the surface ray crossing a medium still has it's angle changed. All but the center ray on that diagram should have 2 bends in them, one when they enter the lens and one when they exit the lens (the transition from one medium of transport to another with differing refractive indexes). As diagrammed and implied it's implied that Snell's law only applies to the curved side of the lens.

Doesn't really matter though (I think so far as I have thought) within reason. But were you to make it too thick, the resulting image would be upside down.

Pendant mode off.
posted by zengargoyle at 2:47 AM on August 26


I don't get where the 'hologram' part fits in unless it's an effect of moving from a man-made light source (narrow frequency range) to sunlight (wide frequency range)..

I suspect it's just a variant of the hollow face illusion - as they move the caustics around (towards the end of the video), there's a mask-like distortion and your brain makes some assumptions.
posted by Kyol at 6:35 AM on August 26 [1 favorite]


Doesn’t really matter, within reason, but it’s “pedant.”
posted by fantabulous timewaster at 4:35 PM on August 26 [1 favorite]


but it’s “pedant.”

It took me a second to realize you were correcting a typo, and not doing a bit my friend does where whether you say pedant with a long or short e* , he'll put on his most condescending voice and "correct" you "Actually it's pronounced [the other way]".

* or perhaps I should say: /pidn̩t/ or /pɛdn̩t/
posted by aubilenon at 7:25 PM on August 26 [1 favorite]


You know what, I think I'm misremembering and it's in fact patronizing vs pātronizing he does that with. Never mind.
posted by aubilenon at 9:06 PM on August 26 [1 favorite]


The image of a lens that neglects Snell’s Law on the flat side seems to have come from a company that sells parabolic-mirrored lights to photographers, rather than from the author. I have seen images with that error in textbooks.

A simple fix to the convex-lens stock image is to draw the parallel light rays interacting with the flat side, so that they stay parallel in the glass. Then you can invoke the “thin lens approximation” to say that the focal length should be symmetric if the light approaches from either side.

For the magic window, the thin-lens approximation is probably good but not great. If the model assumes a single refraction at the engineered surface, the caustic image will probably look more like the calculation if the light interacts with the flat side first: Snell’s law says that parallel light rays interacting with a flat surface remain parallel on the other side.

The part of me that overspecifies problems and gets lost in the weeds is now wondering whether you could engineer both surfaces to make an asymmetric magic window, which displays different images when the light approaches from opposite directions.
posted by fantabulous timewaster at 5:18 AM on August 27 [1 favorite]


Yeah, I went searching for better images and found very few. I think most drawings are small enough so that it would be hard to tell anyway so why not just draw the lines inside the lens straight from the focal point to the outer surface.

Does the picture change if we turn a thin lens around | Physics Forums has a better diagram (for flavors of better).

Chromatic aberration - Wikipedia is where I think there might be some wonky going on with the man-made-light vs sunlight thing. Also maybe just brightness (depending on man-made-source) if not the spectrum. Also the sunlight would be more on the imagined distant source rays are taken as coming in parallel.

Lens - Wikipedia has some good images and animations.
posted by zengargoyle at 10:44 PM on August 27


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