Scratch Holograms

thingiverse

Recently I visited a museum in Los Angeles where they displayed metal discs, approximately the size of vinyl records, etched with numerous scratches and illuminated from above. As you gaze at these objects, the scratches conspire to create the image of a polyhedron floating in space! And what's more, when you walk around, you can see this virtual polyhedron from different angles. After some online research, I discovered that these things have been rediscovered at various times and studied in detail somewhat recently (1990s) by William Beaty. The basic idea is this: when you scratch metal, the scratch acts a little bit like a very thin reflective tube. If you illuminate this with a point source of light, each eye sees the point source as a bright spot somewhere along the scratch. If the scratch is curved, then each eye sees the bright spot at a slightly different angle. Your brain's depth-perception algorithms interpret what you see as a point of light floating in space. It turns out that the radius of the scratch curve corresponds to how deep you see the point of light. This means you can take a polyhedron, and place a bunch of virtual points of light along each edge, and then put a bunch of appropriate scratches on metal (or plastic), and when illuminated from above, the light scatters off the collection of scratches in just such a way that you see the polyhedron, and what's more, it's like a hologram in that you can move left and right and see the polyhedron rotating. Anyway, I was curious if these things could be done with 3D printing. The result is this, and while the effect isn't as good as what I saw in the museum, it's not bad for a few grams of plastic! I included the Python script I used to make these objects, as well as two designs: a tetrahedron and a cube.