Bruno Paun's caustic, 26th of September 2011.

caustic, cup, coffee

I already wrote many times about caustic on the pages of "Construction of Reality". And, no, it is not caustic soda or encaustic, or something else that sounds similarly. It is a (natural) focusing of light, i.e. formation of inhomogeneities in an, initially homogeneous, light beam after it refracts of reflects from objects. These inhomogeneities can be seen on some screen.

So, why am I, after all that, writing again about caustic? Because there is a happy reason for it, and that is that my student Bruno Paun defended successfully today his diploma work "Investigation of caustic by raytracing and comparison with experiments". With Bruno's permission >> HERE you can download his diploma work in PDF format (it is in Croatian).

The images above show Bruno's simulations of reflection caustic in a coffee cup, depending on the incident angle of light beam. As the incident angle changes, so does the look of caustics, but also the size and shape of the shadow on the coffee surface. The images below show how the shape of caustic changes for fixed position of the light source, but variable level of coffee in the cup. So, as you drink your coffee, do expect to see the changes in caustic.

caustic, cup, coffee

Let us not forget that there are no coffee cups... The "real" cup is shown in the photograph below, which represents the experimental determination of reflection caustic. On the basis of this cup Bruno made PovRay models that he used for modeling the caustic by method of raytracing (plus photon mapping).

caustic, coffe, cup, photograph

Bruno made PovRay simulations to model the experiments with caustic on a metal pipe with a near, spotlight-like light source (Grace Weir and Brendan Guilfoyle, 2005). The comparison of experiments and simulations is shown below (the top row is experiment and the bottom row contains PovRay simulation results).

caustic, rings, experiment
caustic, rings, PovRay

In addition to reflection caustic, Bruno also studied caustic in transmitted light, in refraction. Of course, the most beautiful example of such caustic can be seen in a shallow see, on that special "place of ours", hidden from the people and inaccessible to boats and sails, where two grebes compete daily in freediving. Eh, now I am overboard a bit, so I quickly return to Bruno's diploma work. The images below show Bruno's simulation of a refraction caustic in a pool.

caustic, pool

Bruno shows how the look of the caustic network on the bottom and the sides of the pool directly depends on the shape of the water surface and on the depth of the pool. The images below show caustic which occurs when the water surface is a sine wave in one coordinate only, i.e. when the height of the water is constant in the direction perpendicular to the wave propagation, and changes sinusoidally along the wave propagation direction.

caustic, pool

Somewhat more complex water surface is given by the sum and product of sine functions along two perpendicular directions, and the caustics in these two cases are shown in the image below.

caustic, pool

And in the end (the image below), the caustic that results from the use of PovRay's f_noise3d function which sufficiently well represents the surface of water. This caustics look like a "real one". Nice.

caustic, pool

A lot of additional interesting information on caustic can be found in >> Bruno's diploma work, and its first half represents a good introduction to PovRay (in Croatian).

My contribution to this post is shown in the video below. Click on it to start streaming from YouTube. The video shows caustic in shallow water that I recorded on Krk island on 18th of September this year, on a special place where two grebes compete daily in freediving. But for real.

Last updated on 26th of September 2011.