TWO men walk onto a darkened stage carrying a thick slab of transparent plastic. They hold it up and Mark Pauly shines a torch through it. The audience gasps in surprise: on the screen at the back of the stage is an image of computer pioneer Alan Turing, every thread of his tweed jacket picked out clearly in light and shade.
It is not the clarity of the image that amazed the audience. What really impressed them is the fact that Pauly, a specialist in computational geometry, achieved this trick by taking control of a seemingly chaotic optical phenomena known as caustics.
Best known for causing the bright lines of light that dance on the bottom of a swimming pool, caustics are patterns created by the reflection or refraction of light by curved surfaces, in this case by the ripples on the water’s surface. The key to taming them lies in the precise way that Pauly and his colleagues shaped the surface of the perspex (plexiglass) so it refracts light in a specific way to form the image of Turing.
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Since the curves on the surface are only just perceptible – if anything the slab resembles a piece of antique glass – this kind of “caustic engineering” has already attracted architects who want to create windows that are also cryptic projectors, summoning ghostly images from sunlight. But it has other uses too. Caustic “lenses” should be just the thing for all kinds of optical and lighting technologies, from smarter car headlights to improved lithographic manufacturing, as well as new forms of art, toys or security devices on credit cards. It might even be possible to control caustic images in real time, creating a new generation of high-contrast projection systems. The way we see the world is about to change.
Pauly’s fascination with the way light interacts with three-dimensional shapes began a decade ago, when he was a postdoc at Stanford University in California. “I spent hours wandering through the university’s Rodin sculpture garden, admiring how the sun played on the bronze,” he recalls.
Later Pauly moved to the Swiss Federal Institute of Technology in Lausanne, where he put this interest to work by developing “shadow art”. He devised an algorithm that allowed him to design objects which cast shadows in different shapes when illuminated from different angles. One , made in glass, threw a shadow of Andy Warhol when lit from above, Marilyn Monroe when lit from one side and Warhol’s soup tin image when lit from the other.
In 2010, Pauly was introduced to , an architect with Paris-based company RFR. Bompas, too, had long been fascinated by the unintentional light shows produced by the reflection and refraction of light from curved mirrors or glass structures. In the late 1990s he began to manipulate these caustics to generate striking, random patterns of light.
Once Pauly and Bompas realised they shared a similar interest, they started thinking about using caustics in architecture and came up with a plan to mould light as Pauly had previously moulded shadows. Working with Pauly’s former student Michael Eigensatz, now at Austrian architectural design company Evolute, they began experiments to create images from reflected light.
Magic mirrors
The possibility of using mirrors to create complex patterns of light was first recognised by Chinese metal smiths of the Han dynasty, around 2000 years ago. They made “magic mirrors” from discs of bronze, which had a smooth, reflective surface on one side and a pattern cast on the other. Light shining off the reflective side created a projection of the image embossed on the reverse side, as though the mirror had become transparent. Such mirrors became popular in Japan in the 16th century where they were known as makyoh, or “wonderful mirrors”, but the secret of how they were made was subsequently lost.
It wasn’t until 1932 that English physicist William Bragg came up with an explanation for how they work. He suggested that the mirror surface is not perfectly smooth. Instead, subtle stresses in the metal produced as the casting cools replicate the embossed image as an imperceptible pattern on the mirrored side of the disc. Though too slight to be noticed with the naked eye, this pattern changes the shape of the mirror enough to show up in the reflection. In 2006 physicist Michael Berry of the University of Bristol, UK, published a detailed study of how the reflected images form ().
Although the Han smiths didn’t actually make use of caustics to produce their images, Pauly, Bompas and their colleagues also chose polished metal to make their first images, since this material is relatively easy to turn into complex forms using milling machines. But that meant they had to figure out how the material must be shaped to direct the light where it is needed.
Having worked with computer graphics, Pauly was already familiar with the maths needed to determine how light interacts with a mirror or glass lens. Yet he now faced the inverse problem: working backwards from a pattern of light to deduce the structure needed to create it. The trick would be to mould a uniform light field into a two-dimensional image in which some regions are brighter and some darker. Where the target image is brighter, for instance, light must be collected from a larger area and directed onto that point (“see diagram”).
Making the wave
As a target image, Pauly, Bompas and their collaborators chose The Great Wave off Kanagawa, the famous engraving of a tidal wave by 19th-century Japanese artist Katsushika Hokusai. Then they made a digital model of a mirror and adjusted its shape until the reflection it produced matched the patterns of light and dark in Hokusai’s print.
When the reflection looked about right, the team were amazed to see that the surface of their virtual mirror was surprisingly flat and smooth. It was almost impossible to tell from its appearance what the target image was, or that it could even make patterns in light.
That worried them. If the mirror was so featureless, could it really produce an image with any detail? Would tiny errors in fabrication distort the image out of all recognition? The only way to find out was to make the mirror for real.
Using a computer-controlled milling machine, the team shaped the mirror from a slab of aluminium. When it emerged looking like the mildly dented bodywork of a car, it was hard to be optimistic. And when the researchers shone a flashlight onto the surface, the reflection didn’t look promising – they could just make out bright and dark regions in the image but little else. Then they polished the metal. The result was astonishing. Suddenly they could see all the tendrils and flecks of the breaking wave. The idea was going to work.
At this point the pair decided to go for broke: they would make a large, transparent plate capable of generating a high-resolution image when a light was shone through it. This time their target image was a portrait of Alan Turing, since 2012 was the centenary of his birth. The researchers chose to make the plate in perspex, which is easier to shape than glass.
Their Turing plate worked better than they had dared hope. Pauly and Eigensatz demonstrated it at the in Paris last year. Now they hope that the technique will be used in architectural design, to create windows that mould sunlight and throw images or patterns onto walls or floors, for example. “Incredible detail can be achieved even with very crude production methods like standard milling,” says Pauly. “This is crucial for cost-effective application to architecture or art installations.”
“Incredible detail can be achieved, even with very crude production methods like standard milling”
Yet Pauly admits that he still doesn’t fully understand why it works as well as it does – why, despite the apparent sensitivity of the image to fine details of the surface topography, the surface doesn’t have to be shaped with an impossible degree of precision. “It might be a feature of our particular way of computing the surface,” he says. “We’re still puzzled.”
It also turns out that the patterns the team make are not wholly created from caustics. Some genuine caustics, where the light seems “folded”, do lace through the images, but they also contain light that has been reflected or refracted in the same manner as the Chinese magic mirrors.
Caustic or not, the idea of sculpting light in this way has attracted the attention of other researchers. Wojciech Jarosz at the Zurich-based Disney Research lab, with a team including computer graphics specialist Tim Weyrich at University College London, has created similar images by milling the surface of a glass plate into a series of curved lenses so that the plate resembles a fly’s compound eye (newscientist.com/article/dn20280).
When light passes through the plate, each lens directs a fuzzy ellipse of light onto a screen, and these overlapping patches produce an image. The crispness of the image depends on how small the patches are, but because each lens must be milled individually, the fabrication process can be very slow. So far Jarosz and his colleagues have made plates 10-centimetres across, each with more than 1000 lenses, but these take up to three days to craft and still make pixellated images.
In contrast, the surface of Pauly’s perspex slab is relatively smooth – which is very important for the visual quality of the image, he says, and means that the slab itself can potentially act as a window. On the other hand, Weyrich points out, Pauly’s method can’t reproduce areas of uniform light intensity as well as their pixellated system.
The potential for caustic engineering is also being explored at the Fraunhofer Institute for Technical and Industrial Mathematics in Kaiserslautern, Germany, where Norbert Siedow and his team are developing what they call ““. They have devised an algorithm that, in just a few seconds, can solve the inverse problem to calculate the lens shape needed to produce a target image – essentially tackling the same problem as Pauly but more efficiently. Though they have yet to manufacture a lens for real, they foresee uses in advertising and graphic art.
Freeform lenses could also prove useful for domestic lighting. Say you want to illuminate a room with an uneven pattern of light, with brighter areas over tables or your favourite armchair, for instance, and darker spots around the TV. You could use several spotlights, or place a mask and lens system over a single light source, but both would waste light and energy.
Alternatively a freeform lens placed on a single, central light source could do the job. Since the patterns are formed by focusing and refracting light rather than blocking it, the result should be brighter given the same light source, and provide better contrast than conventional lighting. “One of the main ideas of freeform optics is to conserve light and energy, to bring all the light to the place where it is needed without any wastage,” says Siedow – just a single source could give both general illumination and spotlights, he says.
Controlling lighting in this way would be useful in museums and theatres, as well as for car headlights, Siedow says, providing bright illumination on the road ahead while reducing glare for oncoming drivers. There could be other benefits too, says Miguel Alonso of the Institute of Optics at the University of Rochester in New York. Freeform optics should allow more versatile lens designs, he says, “which in turn will lead to better, more compact systems for imaging and illumination”.
Jarosz, meanwhile, can’t reveal whether the Walt Disney company is planning to commercialise the technology for toys, but says that if their pixellated approach can be miniaturised and reproduced in plastic, it could be used to make difficult-to-forge security windows on credit cards. Whatever the eventual applications, the creative use of caustics appeals to Berry, who has extensively. “I admire the ingenuity and the beauty of these schemes,” he says.
As far as architecture is concerned, using caustics in windows depends on whether the effects can be created in large plates of glass. Here, Pauly is optimistic. One window manufacturer he approached is confident that glass milling would work. “We’ll do some glass milling soon, and also glass casting with a mould,” he says. But, he adds, even in perspex there might be applications in architecture, if the material can be protected from degradation by UV light.
One of the aspects that appeals to Pauly is how the projected image changes as the light source moves. So could we take this further and generate moving images? Certainly it should be possible to create a transparent plate containing several overlayed caustics that become visible as an animation as the light source moves, says Pauly. Jarosz has tested a similar idea to create simple animations ().
Even the idea of caustic movies isn’t implausible, in principle. After all, mirrors with computer-controlled, reconfigurable surfaces are already used by astronomers. These adaptive optics are built into telescopes to compensate for distortions in light from distant stars, produced by fluctuations of the Earth’s atmosphere. “It might be hard to manufacture and control,” says Pauly, “but I think something like this should be possible with a flexible membrane.”
Whether or not we ever watch movies projected using caustics, it’s not hard to imagine buildings with genuine picture windows. In fact you may never look at a humble pane of glass in the same light again – the possibilities, says Pauly, are endless. “That is what makes the project so exciting.”
