Back in 2017, an oil painting called Salvator Mundi (Savior of the World) sold for $450.3 million at Christie’s auction house in New York. That made it the world’s most expensive by some margin. The painting is one of fewer than 20 thought to be by Leonardo da Vinci, although there is still some dispute over this attribution.
There is also another puzzle. The picture depicts Christ holding a glass orb representing the celestial sphere of the heavens. Such a sphere ought to act like a convex lens, magnifying and inverting the robes behind it. However, Christ’s robes are not inverted or magnified but appear with minimal distortion.
Leonardo was well aware of the way glass refracts light. Indeed, his notebooks are filled with depictions of the way light bounces off and refracts from various objects. And this raises the question of why he drew the orb in this way.
Today, we get an answer thanks to the work of Marco Liang and colleagues at the University of California, Irvine. This group has used computer graphics software to reproduce the scene in three dimensions and then studied how light would be refracted through orbs of different kinds.
After comparing their renderings with the original, they have concluded that the orb is not solid at all. Instead, they show that the painting is a realistic physical representation of a hollow sphere with a diameter of 6.8 centimeters but a thickness of just 1.3 millimeters.
First some background. Inverse rendering is a computer graphics technique originally developed to produce physically realistic renderings of virtual scenes by simulating the physics of light flow. One goal of this technique is to better simulate the appearance of transparent and semi-transparent objects made of glass or water.
The technique begins by creating a 3D representation of the scene, incorporating the texture and structure of all the objects that light interacts with. The scene must also include a source of light and a viewpoint. Then a ray-tracing algorithm maps out the way light illuminates the scene, as seen from the viewpoint.