Classics revisited: Parabolic reflectors in high resolution

This is a remake, in much higher resolution and with an improved color shading, of the video • A wave traveling betwe... , showing how parabolic reflectors (also known as parabolic antennae or satellite dishes) work. A circular wave is emitted at the focal point of the left reflector. The reflected wave becomes linear, and can therefore travel long distances with hardly any loss of power. When hitting the right-hand reflector, the wave is turned into a circular wave again, which concentrates at the right-hand focal point, where one would put a receiver. Part of the non-reflected wave also hits the right-hand reflector, but it has lost power, and it not concentrated on the focal point. Its power decreases like distance between the parabolic reflectors in two dimensions, and like its square in three dimensions. In practice, one typically only emits energy towards the left reflector, which suppresses the non-reflected wave altogether.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Wave energy: 1:44
In the first part, the color hue depends on the height of the wave. In the second part, it depends on the energy of the wave. The contrast has been enhanced by a shading procedure, similar to the one I have used on videos of reaction-diffusion equations. The process is to compute the normal vector to a surface in 3D that would be obtained by using the third dimension to represent the field, and then to make the luminosity depend on the angle between the normal vector and a fixed direction.
There are absorbing boundary conditions on the borders of the simulated rectangle. They do not work perfectly, as shown by slight reflections on the boundaries, with are made more visible by the chosen lighting.
Render time: 47 minutes 28 seconds
Compression: crf 23
Color scheme: Part 1 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Missing Persons" by Jeremy Blake‪@RedMeansRecording‬
See also images.math.cnrs.fr/des-ondes... for more explanations (in French) on a few previous simulations of wave equations.
The simulation solves the wave equation by discretization. The algorithm is adapted from the paper hplgit.github.io/fdm-book/doc...
C code: github.com/nilsberglund-orlea...
www.idpoisson.fr/berglund/sof...
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!
#wave #diffraction #grating

[@marioeuler8814]

Love myself some classic parabolic reflectors in high resolution! Immediately brightens my day

[@kylebowles9820]

I just started learning about differential geometry; so glad smarter people than me have figured this stuff out, super fun to play with!
(Sorry for jargon salad: In differential geometry the wavefront (2nd part of video) is roughly speaking the immersion of the orthotomic of the surface and the point light source along its evolute first derivative (then successively apply each next optical element on the resulting parametric envelope. If you know of a simpler way, please comment)

[@NilsBerglund]

This is also known as the Huygens-Fresnel principle. Each point in a wavefront acts as the source for the wavefront at a later time, and it is the interference of these elementary waves that builds the evolving front.

[@Dr-Zed]

I love the patterns

[@annoyannoy]

2:21 That is so beautiful....................

[@blas5i]

One of your best

[@Pillow_Cat]

Whish to see with emitter/receiver part being simulated too

[@lodkathree]

Nice. It would be interesting to see with one half of the target reflector being slightly more curved. That would give an asymmetrical reflection pattern.

[@SpeakMouthWords]

Yooooo it's the HD remake

[@MDNQ-ud1ty]

There are strange reflections off the "walls" which shouldn't exist. I imagine this is having to setup some type of boundary conditions in the solver? Can you not setup free boundary conditions then?

[@float32]

Maybe it’s the impedance mismatch between the pixels at the edge of your screen and free space?

[@NilsBerglund]

There is no simple way to get "free" boundary conditions. What I'm using here is a form of absorbing, or perfectly matched layer, boundary conditions. They are not quite perfect, and the reflections are made more visible by the used lighting.

[@nikolaiturcan6963]

In my biophotonics course they taught us that an effective way with which they managed to reduce the effect of the boundary conditions is by creating a diffuse boundary region with increasing absorption(a gradient of absorbance over 10-20 "pixels") , and also by computing for a slightly larger area and then recording values only for a smaller region inside ( takes longer but the effect has time to spread out and not be as evident) (maybe there is some publication by my professor regarding this method.. his name is Alwin Kienle ) hope it helps :)

[@danamulter]

This one was super cool. Can you give it some permeability, like a low % for the front and back wall of the lenses going both ways, so I can see where the stuff that makes it all the way through lands?

[@user-vt4bz2vl6j]

Niel : HIGH RESOLUTION
My Phone : 220p take it or leave it