12
$\begingroup$

This nice paper contains a neat demonstration of the fact that optical caustics, when seen from a wave-optics perspective, contain a bunch of interesting interference terms which can be calculated nicely using the integrals with coalescing saddles of catastrophe theory. Moreover, they showcase this with experiments that have clear optical implementations of those functions, which reportedly look much like this:

Image source

I would like to be able to reproduce this sort of behaviour, as a home experiment and as a lecture demonstration, ideally in a configuration that doesn't require anything much fancier than a laser pointer and some household items or office equipment, and ideally in a procedure that is simple, robust, stable, and easily reproducible. It doesn't have to be all that clean ─ it just has to reliably produce images with the Airy fringes and the Pearcey-like behaviour at the tips of the caustics.

What are good ways to do this, or good resources that explain the procedure?

$\endgroup$
  • $\begingroup$ a white porcelain cup and a laser pointer, the caustic is a nephroid $\endgroup$ – hyportnex Jan 26 '18 at 20:15
  • 1
    $\begingroup$ @hyportnex I had a go with a porcelain cup and a laser pointer but failed to get the fringes. Any practical tips? $\endgroup$ – Farcher Jan 26 '18 at 22:19
18
+200
$\begingroup$

This may be easier than you think. I took this photo (with my iPhone) of a cusp caustic which I generated by darkening the bathroom, wetting the mirror, and angling the laser pointer so it hit a water drop and then reflected off the mirror onto a convenient spot on the wall:

enter image description here

It's extremely close to the Pearcey integral.

The wall was literally covered in these things. Here's a shot zoomed out slightly so you can see the spidery networks connecting the cusps:

enter image description here

Here is a diagram of the "apparatus": enter image description here

$\endgroup$
  • $\begingroup$ I was gonna down vote you for stealing this from Wikipedia, but I of course checked the references first. $\endgroup$ – JEB Apr 6 '18 at 0:27
  • $\begingroup$ @JEB :-) AFAICT There isn't a lot of interest in this stuff so the same names tend to pop up. $\endgroup$ – Dan Piponi Apr 6 '18 at 0:55
  • $\begingroup$ Which Wikipedia page is this? $\endgroup$ – Emilio Pisanty Apr 6 '18 at 5:22
  • $\begingroup$ @EmilioPisanty en.wikipedia.org/wiki/Pearcey_integral $\endgroup$ – Dan Piponi Apr 6 '18 at 13:42

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.