# Math, Optics, And CNC Combine To Hide Secret Images In Acrylic

Magic mirrors, with an LCD panel hidden behind a partially reflectively mirror, are popular for a reason — they’re a good-looking way to display useful information. A “Magic Window,” however, is an entirely different thing — and from the look of it, a far cooler one.

If you’ve never seen a Magic Window before, don’t worry — it’s partially because you’re not supposed to see it. A Magic Window appears to be a clear piece of glass or plastic, one with a bit of a wave in it that causes some distortion when looking through it. But as [Matt Ferraro] explains, the distortion encodes a hidden image, visible only when light passes through the window. It looks a bit like a lithophane, but it’s projected rather than reflected, and it relies on an optical phenomenon known as caustics. If you’ve ever seen the bright and dark patches cast on the bottom of a swimming pool when sunlight hits the surface, you’ve seen caustics.

As for how to hide an image in a clear window, let’s just say it takes some doing. And some math; Snell’s Law, Fermat’s Theorem, Poisson’s Equation — all these and more are mentioned by [Matt] by way of explanation. The short story is that an image is morphed in software, normalized, and converted into a heightmap that’s used to generate a toolpath for a CNC router. The design is carved into a sheet of acrylic by the router and polished back to clarity with a succession of sandpaper grits. The wavy window is then ready to cast its hidden shadow.

Honestly, the results are amazing, and we marvel at the skills needed to pull this off. Or more correctly, that [Matt] was able to make the process simple enough for anyone to try.

# Create An Aurora Of Your Own

Throughout our day-to-day experiences, we come across or make use of many scientific principles which we might not be aware of, even if we immediately recognize them when they’re described. One such curiosity is that of caustics, which refers not only to corrosive substances, but can also refer to a behavior of light that can be observed when it passes through transparent objects. Holding up a glass to a light source will produce the effect, for example, and while this is certainly interesting, there are also ways of manipulating these patterns using lasers, which makes an aurora-like effect.

The first part of this project is finding a light source. LEDs proved to be too broad for good resolution, so [Neuromodulator] pulled the lasers out of some DVD drives for point sources. From there, the surface of the water he was using to generate the caustic patterns needed to be agitated, as the patterns don’t form when passing through a smooth surface. For this he used a small speaker and driver circuit which allows precise control of the ripples on the water.

The final part of the project was fixing the lasers to a special lens scavenged from a projector, and hooking everything up to the driver circuit for the lasers. From there, the caustic patterns can be produced and controlled, although [Neuromodulator] notes that the effects that this device has on film are quite different from the way the human eye and brain perceive them in real life. If you’re fascinated by the effect, even through the lens of the camera, there are other light-based art installations that might catch your eye as well.