Скачать или смотреть Classics revisited: A linear wave crossing a Fresnel lens

Fresnel lenses have appeared before on this channel, see for instance    • A Fresnel lens   . This is a remake in high definition, when a linear wave gets focused upon crossing the lens.
A Fresnel lens is obtained by taking a usual lens, in this case with one straight and one circular boundary, cutting it into slices, and only keeping the outermost parts of each slice. This allows saving space in the horizontal direction, by keeping similar properties as the original lens. This design is often used in projectors, for instance in lighthouses. The page https://www.parabolixlight.com/fresne... gives more details on their working.
See the video    • Comparison of a Fresnel lens and a circula...   for a comparison between a Fresnel lens and an ordinary semi-circular lens.
This video has two parts, showing the same simulation with two different color gradients.
Wave height: 0:00
Average wave energy: 1:04
In part 1, the color hue depends on the wave height. In part 2, it depends on the wave energy, averaged from the beginning of the simulation. The plot at the right shows these quantities averaged over a short time interval. The boundary conditions are absorbing on the right boundary, and periodic between the top and bottom boundary.

Render time: 25 minutes 58 seconds
Compression: crf 23
Color scheme: Part 1 - Twilight by Bastian Bechtold
https://github.com/bastibe/twilight
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
https://github.com/BIDS/colormap

Music: "Plaidness" by Francis Preve‪@francispreve‬

See also
https://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 https://hplgit.github.io/fdm-book/doc...
C code: https://github.com/nilsberglund-orlea...
https://www.idpoisson.fr/berglund/sof...
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!

#wave #refraction #lens #fresnel