Transmission of a Gaussian Beam through a Lens

7-01-2021

About:

Exploration of Julia 1.6.1 for simple optical simulations

• Using FFTW v1.4.3 and GLMakie v0.4.2
• Platform: Windows 10 Pro

VS Code:

• Navigate to the "GaussianBeamLens" folder, Right-click > Open with VS Code
• Start a Julia REPL with ALT + J + O or Option + J + O in Mac
• Create a Julia environment for the scripts in this folder as follows:
  Go to the package manager from Julia REPL with ], then
  (@v1.6) pkg> activate .
(@v1.6) pkg> add GLMakie, FFTW
(@v1.6) pkg> status -- this should show only two packages, GLMakie and FFTW
  Note that Manifest.toml and Project.toml are generated in this folder after the above steps

Verdict:

• The interactive plot generated with GLMakie is nice. However, I've found that it takes a long time not only to initialize GLMakie, but once it's precompiled, the code itself takes a considerable amount of time to generate the output (2 minutes+ on my machine). Even the simple Test_GLMakie_Plots.jl took 2+ minutes.
  GaussianBeamLens + GLMakie heatmap + GLMakie labelslidergrid!
3.239748 seconds (4.75 M allocations: 441.220 MiB, 4.99% gc time, 17.12% compilation time)
59.421104 seconds (92.34 M allocations: 5.453 GiB, 4.02% gc time, 65.05% compilation time)
9.986559 seconds (17.61 M allocations: 1.021 GiB, 4.72% gc time, 99.67% compilation time)

• Since this code only needs to run once, the performance benefit of re-running it (numbers below) is practically irrelevant.
  0.463848 seconds (258.34 k allocations: 157.616 MiB, 7.76% gc time, 28.38% compilation time)
0.125093 seconds (158.68 k allocations: 11.320 MiB, 26.83% gc time)
0.237762 seconds (448.46 k allocations: 26.290 MiB, 94.47% compilation time)\

• Hopefully, GLMakie and the overall visualization landscape in Julia will improve in the future, thereby making a switch to Julia from MATLAB/Python/Mathematica for these types of tasks more compelling.

rc

Updated timings after some optimization by @mkitti

Loading core functionality

julia> @time using GaussianBeamLens
  0.376621 seconds (368.81 k allocations: 40.561 MiB, 0.93% compilation time)

julia> @time GaussianBeamLens.GaussianBeamLensPropagateUncached(0, 25, 1000, 1000);
  0.283066 seconds (832.55 k allocations: 110.724 MiB, 6.95% gc time, 77.52% compilation time)

julia> @time GaussianBeamLens.GaussianBeamLensPropagateUncached(0, 25, 1000, 1000);
  0.063783 seconds (46.21 k allocations: 64.539 MiB, 13.68% gc time)

Displaying a static image using GR v0.57.3

julia> @time using GR
  0.106745 seconds (50.41 k allocations: 3.768 MiB)

julia> @time GR.heatmap(GaussianBeamLens.GaussianBeamLensPropagateUncached(0, 25, 1000, 1000))
  3.199314 seconds (4.19 M allocations: 237.825 MiB, 1.40% gc time, 21.84% compilation time)

julia> @time GR.heatmap(GaussianBeamLens.GaussianBeamLensPropagateUncached(0, 25, 1000, 1000))
  0.160951 seconds (3.12 M allocations: 174.922 MiB, 13.37% gc time)

julia> @time GR.heatmap(GaussianBeamLens.z, GaussianBeamLens.x, GaussianBeamLens.GaussianBeamLensPropagateUncached(0, 25, 1000, 1000)')
  2.803033 seconds (5.90 M allocations: 188.710 MiB, 0.96% gc time, 6.35% compilation time)

julia> @time GR.heatmap(GaussianBeamLens.z, GaussianBeamLens.x, GaussianBeamLens.GaussianBeamLensPropagateUncached(0, 25, 1000, 1000)')
  3.518419 seconds (7.33 M allocations: 273.173 MiB, 1.21% gc time, 25.10% compilation time)

julia> @time GR.heatmap(GaussianBeamLens.z, GaussianBeamLens.x, GaussianBeamLens.GaussianBeamLensPropagateUncached(0, 25, 1000, 1000)')
  0.302649 seconds (5.58 M allocations: 170.225 MiB, 6.66% gc time)

Interactive simulation using GtkReactive.jl

julia> @time include("src/GtkGUI.jl")
  7.177190 seconds (17.21 M allocations: 1.096 GiB, 6.74% gc time, 0.04% compilation time)
Main.GtkGUI

julia> @time using .GtkGUI
  0.000004 seconds (19 allocations: 1.203 KiB, 55445.45% compilation time)

julia> @time gui()
  1.769222 seconds (2.44 M allocations: 208.761 MiB, 2.90% gc time, 86.39% compilation time)

Interactive simulation using GLMakie.jl

julia> include("GLMakie_GaussianBeamLens.jl")
  1.519261 seconds (6.40 M allocations: 433.387 MiB, 6.65% gc time, 4.79% compilation time) # @lift
 34.037748 seconds (94.64 M allocations: 5.542 GiB, 4.08% gc time, 64.77% compilation time) # heatmap
  5.783349 seconds (17.83 M allocations: 1.035 GiB, 4.66% gc time, 99.59% compilation time) # labelslidergrid!

Pluto with GR

See a static HTML version of the notebook.

PC: D13