# Caustic (optics)

In optics, a caustic or caustic network[1] is the envelope of light rays reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface.[2] The caustic is a curve or surface to which each of the light rays is tangent, defining a boundary of an envelope of rays as a curve of concentrated light.[2] Therefore, in the adjacent image, the caustics can be the patches of light or their bright edges. These shapes often have cusp singularities.

## Explanation

Concentration of light, especially sunlight, can burn. The word caustic, in fact, comes from the Greek καυστός, burnt, via the Latin causticus, burning. A common situation where caustics are visible is when light shines on a drinking glass. The glass casts a shadow, but also produces a curved region of bright light. In ideal circumstances (including perfectly parallel rays, as if from a point source at infinity), a nephroid-shaped patch of light can be produced.[3][4] Rippling caustics are commonly formed when light shines through waves on a body of water.

Another familiar caustic is the rainbow.[5][6] Scattering of light by raindrops causes different wavelengths of light to be refracted into arcs of differing radius, producing the bow.

## Computer graphics

In computer graphics, most modern rendering systems support caustics. Some of them even support volumetric caustics. This is accomplished by raytracing the possible paths of a light beam, accounting for the refraction and reflection. Photon mapping is one implementation of this. Volumetric caustics can also be achieved by volumetric path tracing. Some computer graphic systems work by "forward ray tracing" wherein photons are modeled as coming from a light source and bouncing around the environment according to rules. Caustics are formed in the regions where sufficient photons strike a surface causing it to be brighter than the average area in the scene. “Backward ray tracing” works in the reverse manner beginning at the surface and determining if there is a direct path to the light source.[7] Some examples of 3D ray-traced caustics can be found here.

The focus of most computer graphics systems is aesthetics rather than physical accuracy. This is especially true when it comes to real-time graphics in computer games[8] where generic pre-calculated textures are mostly used instead of physically correct calculations.

## Caustic engineering

Caustic engineering describes the process of solving the inverse problem to computer graphics. That is, given a specific image, one must determine a surface whose refracted or reflected light forms this image.

In the discrete version of this problem, the surface is divided into several micro-surfaces which are assumed smooth, i.e. the light reflected/refracted by each micro-surface forms a Gaussian caustic. The position and orientation of each of the micro-surfaces is then obtained using a combination of Poisson-integration and so-called simulated annealing.[9]

For the continuous problem there have been many different approaches to solving it. One approach uses an idea from transportation theory called ‘optimal transport’[10] to find a mapping between incoming light rays and target surface. After obtaining such a mapping, the surface is optimized by adapting it iteratively using Snell's law of refraction.[11][12]

But there are several other approaches using different methods.

## References

1. Lynch DK and Livingston W (2001). Color and Light in Nature. Cambridge University Press. ISBN 978-0-521-77504-5. Chapter 3.16 The caustic network, Google books preview
2. Weinstein, Lev Albertovich (1969). Open Resonators and Open Waveguides. Boulder, Colorado: The Golem Press.
3. Circle Catacaustic. Wolfram MathWorld. Retrieved 2009-07-17.
4. Levi, Mark (2018-04-02). "Focusing on Nephroids". SIAM News. Retrieved 2018-06-01.
5. Rainbow caustics
6. Caustic fringes
7. Guardado, Juan (2004). "Chapter 2. Rendering Water Caustics". In Fernando, Randima (ed.). GPU Gems: Programming Techniques, Tips and Tricks for Real-Time Graphics. Addison-Wesley. ISBN 978-0321228321.
8. "Caustics water texturing using Unity 3D". Dual Heights Software. Retrieved May 28, 2017.
9. Marios Papas (April 2011). "Goal Based Caustics". Computer Graphics Forum (Proc. Eurographics). 30 (2).
10. Villani, Cedric (2009). Optimal Transport - Old and New. Springer-Verlag Berlin Heidelberg. ISBN 978-3-540-71049-3.
11. Philip Ball (February 2013). "Light tamers". New Scientist. 217 (2902): 40–43. Bibcode:2013NewSc.217...40B. doi:10.1016/S0262-4079(13)60310-3.
12. Choreographing light: New algorithm controls light patterns called 'caustics', organizes them into coherent images
• Born, Max; Wolf, Emil (1999). Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (7th ed.). Cambridge University Press. ISBN 978-0-521-64222-4.
• Nye, John (1999). Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations. CRC Press. ISBN 978-0-7503-0610-2.
• Ferraro, Pietro (1996). "What a caustic!". The Physics Teacher. 34 (9): 572–573. Bibcode:1996PhTea..34..572F. doi:10.1119/1.2344572.
• Dachsbacher, Carsten; Liktor, Gábor (February 2011). "Real-time volume caustics with adaptive beam tracing". Symposium on Interactive 3D Graphics and Games. ACM: 47–54.