Controlling Caustics Choreographs Light

A new algorithm based on a well-known natural optical phenomenon called the caustic effect makes it possible to “paint” images using light and a curved surface. The technique holds potential for automobile headlights, projectors and architectural applications.

The scientists at Ecole Polytechnique Fédérale de Lausanne (EPFL) who developed the algorithm tested it by transforming a simple transparent acrylic plate into a molded surface that, when a light is directed through it, produces a coherent image of the face of Alan Turing, a British mathematician and the father of modern computer science.

Researchers at EPFL found a way to control caustics — patterns that appear when light hits a water surface or a transparent material. Thanks to an algorithm, investigators can shape a transparent object so that it reflects a coherent image. Courtesy of ©Alain Herzog.

“With the technique that we developed, we can compose any image we want, from a simple form such as a star to complex representations such as faces or landscapes,” said EPFL professor Mark Pauly, who conducted the study with four other scientists.

It isn’t magic — the only thing at work is the relief on the plaque’s surface and the caustic effect, which the scientists succeeded in bending to their will. This effect is easy to observe and can be explained by light refraction.

When light rays hit a transparent surface, they continue their trajectory but are bent as a function of the surface geometry and optical properties of the material. The light passing through does not distribute uniformly, but rather gets concentrated in certain points, forming some zones that are more intense and others that are more shaded.

Pauly and his colleagues studied these distribution principles, identifying the curves and undulations they would need to give the surface to direct the beams of light to a desired area. From this, they developed an algorithm to precisely calculate the trajectories to form specific images.

On auto headlights, the technique could be used to direct light toward a specific direction. With applications in architecture, the method could be applied to display cases, windows, fountains and ornamentations on monuments or in museums.

The research was presented in September at the Advances in Architectural Geometry Conference in Paris.

For more information, visit: www.epfl.ch