I have shadowgraphs of plasma filament formed in air by focusing a femtosecond laser and I am trying to solve for refractive index change in the region using the shadowgraph. The contrast value at each pixel is a source term for 2D-Poisson equation.
I can apply the Dirichlet boundary condition at the top and bottom of the image. But the left and right corners contain sections modulated by the filament.
What type of boundary conditions should I use in this case?
You can see the following:
1. http://graphics.cs.cmu.edu/courses/15-463/2019_fall/lectures/lecture9.pdf
2. http://dev.ipol.im/~coco/website/docs/simpois.pdf
3. https://www.math.kth.se/na/SF2568/parpro-16/F4.pdf
You have three possibilities:
- Dirichlet b.c. - specifies the value of the function at the boundary: if the boundary is sufficiently extended from the source/filament you can use Dirichlet b.c. assuming no signal there (e.g. n=1).
- Neumann b.c. (specifies derivative of the function, so at boundary you would like to have no change in the processed value, so d(n)=0;
- Cauchy b.c. (specifies both: value e.g. n=1 and its derivative (d(n)=0).
It depends on the geometry of your imaging system, the field of view, known information (maybe you have specific values at the boundary?). The simplest case is for D.b.c. (1st point), if you can assume an environmental index of refraction equal to 1 for a sufficiently large distance from the source. Hope this helps.
- Badges
- Science topic
- Similar topics
- Geoscience
- Atmospheric Sciences
- Atmosphere
- Air