Caustic (optics)

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Typical "coffee cup caustic"
The light entering from the left is focused by reflection on the inner wall of the cup .

As caustic (from ancient Greek καυστός kaustos , German , burned ' ), and focal line or focal surface is referred to in the technical optics an area in which light rays tangent to an arc or a curved surface. The arch limits the light space. The intensity increases towards the arch and drops off steeply there. With caustic only this wing tip or the enveloping face is sometimes meant.

Collecting lenses and concave mirrors focus only approximately on one point . Due to imaging errors (spherical aberration, coma) the light is collected in a finite caustic.


A distinction is made between catacoustics and diacaustics , depending on whether the bundling occurs through reflection or refraction . In addition, a distinction is sometimes made between first and second type caustics , depending on whether the light rays to be collected are incident parallel ( coming from a point light source that is very far away ) or divergent (from a relatively close point light source).


The beam is deflected by specular reflection on a hollow surface. A well-known example is the "coffee cup caustic": When light falls at an angle into a cup with a shiny inside, you can observe a heart-shaped concentration of light on the bottom of the cup or in a somewhat cloudy cup, an extreme form of spherical aberration. In special cases, the sharp boundary surface is described mathematically by a cardioid or nephroid .


The beam is deflected by refraction. For example, the play of light at the bottom of a water basin shows diacaustics if the waves are so steep or the water is so deep that rays of light cross. Coma shows the light concentration on the delimiting arc in its pure form.


Beam path in a drop of water for monochromatic light: the parallel incident light (upper half of the image) is refracted when entering, reflected on the back and refracted again when exiting.

A rainbow is based on the caustic of the catadioptric beam path in water droplets. The dependence of the exit angle from the axis distance of the incident beam passes through a maximum. In the direction of the maximum the intensity is particularly high and then drops off steeply. The maximum angle depends on the wavelength , which gives the rainbow its color.

Significance in laser beams

The envelope of a beam waist, in particular a laser beam, is also called caustic, even if the beam optics are no longer valid there and the radial intensity distribution does not have a maximum at the edge, but in the beam axis.

Importance in computer graphics

In 3D computer graphics , caustics have long been the most difficult phenomenon to simulate because they occur in a concentrated manner and can only be simulated well using methods that work from the light sources. Methods for calculating the global illumination also have to simulate caustics, which the photon mapping algorithm developed in 1995 was able to achieve for the first time in a general and efficient manner . In the light path notation , catacaustics correspond to the paths of the type LS + DE, i.e. at least one specular and one subsequent diffuse reflection.

Individual evidence

  1. Georg Glaeser: Geometry and its applications in art, nature and technology . Springer-Verlag, April 2, 2014, ISBN 978-3-642-41852-5 , p. 185.
  2. ^ Dieter Meschede: Gerthsen Physics . Springer-Verlag, February 27, 2015, ISBN 978-3-662-45977-5 , p. 519.
  3. Max Born: Optics: A textbook of electromagnetic light theory . Springer Berlin Heidelberg, March 13, 2013, ISBN 978-3-662-00058-8 , p. 52.
  4. ^ E. Alberts, W. Arndt, A. Beckmann: Manual of lighting technology: first part . Springer Berlin Heidelberg, April 17, 2013, ISBN 978-3-642-50693-2 , p. 952.


  • John F. Nye: Natural Focusing and Fine Structure of Light. Caustics and Wave Dislocations. Institute of Physics Publishing, Bristol et al. 1999, ISBN 0-7503-0610-6 .

Web links

Commons : caustic  - album with pictures, videos and audio files