I’d like to do simulation and optimization of optical caustics. The basic phenomenon is that caustics can have a very high dynamic range and project a reasonable distance, and in particular can produce divergence-limited-brightness lines in the projected image.
Fundamentally the simplest idea is that if you take a single pencil of a collimated beam impinging on a nearly-flat mirrorlike reflector surface and look at the pattern it makes on a target — whether an interface between optical media or a metallic surface — the point where the pencil lands on the target is a continuous function of its position on the reflector, and can be computed using Heron’s law of reflection. However, the pencil may be deformed to be convergent, divergent, or both, by the curvature of the reflector at that point. If it is converged to a point or a line, then there is a singularity of infinite brightness in the caustic.
The derivative of the point to which the pencil is directed with respect to the point where it’s reflected may go through zero at these points, in X, Y, or both. The product of the two derivatives gives, in some sense, the size of the spot.
Probably the most sensible thing to do is actually to compute a bunch of reflected rays from different points, then calculate some kind of spline joining them. The area of each square of the spline grid provides a local brightness, but the grid may fold back on itself through the aforementioned lines of singularity. This is close to the approach taken by Evan Wallace in WebGL-Water.
(Of course the bright lines are limited in brightness both by the divergence of the incident light and diffraction over the focusing zone.)
See also Gauzy shit.