Caustic (optics)

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Caustics produced by a glass of water

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.

Nephroid caustic at bottom of tea cup
Caustics made by the surface of water

Explanation[edit]

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[edit]

Photograph of a typical wine glass caustic
Computer rendering of a wine glass caustic

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[edit]

Caustic engineering describes the process of solving the inverse problem to computer graphics. Given a specific shape or image one wants to find a surface such that the light refracted 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.

See also[edit]

References[edit]

  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. ^ a b 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

Further reading[edit]

  • 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.