HW01_solution.jl

### A Pluto.jl notebook ###
# v0.19.37

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ d1980bd2-babf-11ee-1dbb-dfefbdbdb36d
using PlutoUI, Plots, ImageShow, TestImages, FFTW, NDTools, IndexFunArrays, FileIO, FourierTools

# ╔═╡ 7d8a9001-31cd-4e57-ae24-b76c0f423193
using PlutoTest

# ╔═╡ 17adc747-9822-42be-91c1-ad8a2e1532bc
md"# 0. Load packages"

# ╔═╡ d2c6102c-7a62-4899-9c5c-b08ce9a5baa8
FFTW.set_num_threads(4)

# ╔═╡ 7331d6a5-dd03-42c7-9ab3-c84a641296bc
TableOfContents()

# ╔═╡ 67d711ec-a6ab-4b8a-b5aa-7342531fd6bb
md"""
# 1.Beam propagation method - Notebook

This first notebook presents the general concepts and the numerical implementation of beam propagation method (BPM) in free space. 
The propagation of a monochromatic wave in an homogeneous medium is described by the scalar Helmoltz equation (wave equation):

$$\frac{\partial^2E}{\partial x^2} + \frac{\partial^2E}{\partial y^2} + \frac{\partial^2E}{\partial z^2} + k^2E=0$$


where $E$ is the scalar field and $k=\frac{2\pi \cdot n}{\lambda}$ is the wavenumber in the propagation medium with refractive index $n$.

In the BPM we assume that the wave is propagating along a specific axis, in the following $z$, and we factorize the field as a product of an enveloppe $A(x,y,z)$ and a fast oscillating term along the propagation direction $\exp(-jkz)$. By plugging $E=A\exp(-jkz)$ in the wave equation we can write in the wave equation we get:

$$
2jk\frac{\partial A}{\partial z} = \frac{\partial^2A}{\partial x^2} + \frac{\partial^2A}{\partial y^2} + \frac{\partial^2A}{\partial z^2}
$$

If we now consider that the dependence of $A$ on $z$ is slow because the fast variation along this axis is taken into account by the fast oscillating term $\exp(-jkz)$ we can neglect the second order derivative along $z$, better knwon as slowly varying envelope (SVE) approximation. We finally get to the BPM equation in free space

$$\frac{\partial A}{\partial z} = \hat{A}A$$

where we labelled with $\hat{A}$ the diffraction operator:

$$\hat{A} = \frac{j}{2k}\left(\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}\right)$$

In practice it is more convenient to solve this first order partial differential equation in the spatial frequency domain. Indeed if we take the Fourier transform of $A$ with respect to $x$ and $y$, labelled $\tilde{A}$ hereafter, we get:

$$\frac{\partial \tilde{A}}{\partial z}=-\frac{j}{2k} \left(K_x^2+K_y^2\right)\tilde{A} $$

This is a differential equation in $z$ with general solution:

$$\tilde{A}(x,y,z+\Delta z) = \tilde{A}(x,y,z)\exp(D\Delta z)$$

with 

$$D = -\frac{i}{2k} \left(K_x^2+K_y^2\right) $$

being the diffraction operator in the frequency domain. 
In summary, the SVE propagation describing diffraction can be solved in the inverse space and then transformed back in the direct space:

$$A(x,y,z+\Delta z) = \text{IFT}\left\{\text{FT}[A(x,y,z)]\exp(D\Delta z)\right\}$$

where $\text{FT}$ and $\text{IFT}$ denote Fourier transform and its inverse operation, respectively.

Note that this is an approximation, and a rigorous solution is the angular spectrum method of plane waves.
"""

# ╔═╡ 43ae81bb-8a6b-47be-8e64-129c19f045be
md"# 2. Load Initial Field"

# ╔═╡ fb52f064-67d6-4771-8d81-5e7226c32910
testimage("mandril_gray")

# ╔═╡ ed2480ca-0c0b-490d-b470-97760f976d71
field = 0im .+ select_region(Float64.(testimage("mandril_gray")[begin:4:end, begin:4:end]), new_size=(300, 300));

# ╔═╡ d9f1e0c0-a815-419f-a3d3-4611a28a4e38
md"#
This is a complex image. The phase is encoded as color (here constant) and the amplitude as brightness of the image
"

# ╔═╡ 7d659569-4bc3-44cb-8366-7c0a737200d8
md"We can also just plot it as a heatmap. The y axis is swapped in this case"

# ╔═╡ 664fabff-7205-47e0-b076-6f26824d0cad
heatmap(abs.(field))

# ╔═╡ cf3f3ec0-4c9c-4089-ba0a-bbca193ad3f7
heatmap(angle.(field))

# ╔═╡ a015a2af-557e-442f-b92a-37455b93e393
md"# 3. Define Helper Variables"

# ╔═╡ 237ce060-85ba-4bde-b08c-b29425ae95ac
# points along the optical axis
Nz = 100 

# ╔═╡ 9d02e310-287d-48a1-b172-1de96b9a9107
Nx = size(field, 2)

# ╔═╡ 6e88f054-7ce5-454b-97ee-b3841636a4dc
Ny = size(field, 1)

# ╔═╡ c89a2539-58d1-4639-88f1-5166a8ef6283
# width of field
Lx = 200e-6

# ╔═╡ 5b4648b6-4d41-4581-91fe-de0e10fe8565
Ly = Lx

# ╔═╡ 77c5991f-5bd5-410b-ac29-055717af6280
# propagation distances
Lz = 1000e-6

# ╔═╡ 7fcb26f9-1fea-4ec0-ba63-e2f0b70ea7c8
y  = range(-Ly /2, Ly / 2, Ny)

# ╔═╡ 13c6547f-42cc-49b6-a748-e65422180eae
x  = range(-Lx /2, Lx / 2, Nx)

# ╔═╡ a0303640-8adf-468f-85f2-a6a12ec85107
# background refractive index
n0 = 1

# ╔═╡ 90f4e2b0-8d71-4a0d-9be4-2f2b713fea17
# free space wavelength
λ = 532e-9

# ╔═╡ 116286e2-6787-4ce9-b2cd-40b1a9317894
z = range(0, Lz, Nz)

# ╔═╡ 0cebf599-48cd-4d86-a3e6-0bf9eaae4bdb
md"# 4. BPM Function"

# ╔═╡ 5f21a849-0272-4bca-9659-54cd38068e09
"""
	bpm(field, λ0, Lx, Ly, z)

Propagates the array `field` with wavelength `λ0` and in meter size
`(Lx, Ly)`. The propagation distance `z` is a vector of distances.
.
The returned array is a three dimensional array where `size(arr, 3) == size(z, 1)`.
"""
function bpm(field, λ0, Lx, Ly, z, n=1)
	# free space wavenumber in m-1
	k0 = 2 * π / λ0
	# medium wavenumber m-1
	k = n * k0
	# medium in m
	dz = z[2] - z[1]

	# field parameters
	Nx = size(field, 1)
	dx = Lx / Nx
	x  = range(-Lx/2, Lx/2, Nx)
	kx = 2π .* reshape(fftfreq(Nx, 1 / dx), (1, Nx))

	Ny = size(field, 1)
	dy = Ly / Ny
	y  = range(-Ly/2, Ly/2, Ny)
	ky = 2π .* fftfreq(Ny, 1 / dy)

	# important step, this calculates the Fourier space kernel
	H = exp.(-1im .* (kx.^2 .+ ky.^2) ./ (2*k) * dz)

	# 3d output fields we save
	# third dimensions stores the different z propagation distances
	out_field = zeros(ComplexF64, (Ny, Nx, size(z, 1)))
	# first entry corresponds to z[1] = 0
	out_field[:, :, 1] = field

	# FFT plan for calculating FFTs
	# It's a more efficient sytanx: p * x == fft(x)
	p = plan_fft(field, (1,2))
	
	# inverse FFT
	invp = inv(p)
	for z_index in 2:size(out_field, 3)
		u0 = out_field[:, :, z_index - 1]
    	u1 = invp * ((p * u0) .* H)
		out_field[:, :, z_index] .= u1
	end
	return out_field
end

# ╔═╡ 5d095823-5b49-4f0e-994e-70b4600f5db5
md"# 5. Experiments"

# ╔═╡ 8a1ac052-66ed-4388-8769-034f15f3d950
out_field = bpm(field, λ, Lx, Ly, z);

# ╔═╡ 3ed0d447-0cbd-480c-8517-6714265e0778


# ╔═╡ d5c7d05c-0080-4ee9-84ab-c4738a641df5
@bind iz PlutoUI.Slider(eachindex(z))

# ╔═╡ f2427112-dc6b-4345-a3ec-ec6dbb297428
heatmap(x[:] .* 1000, y[:] .* 1000, abs2.(out_field[:, :, iz]), xlabel="x in mm", ylabel="y in mm", title="intensity of the propagated field by distance $(round(z[iz] * 1000, digits=3))mm")

# ╔═╡ 60de432a-dded-4f6c-b5c2-6316d0a35028
heatmap(z .* 1000, x[:] .* 1000, abs2.(out_field[:, 150, :]), xlabel="z in mm", ylabel="y in mm")

# ╔═╡ 273d6dae-ffc8-4d35-afd6-6307ef7228d3
md"# Homework"

# ╔═╡ f08de158-f6e6-4766-b9af-6af7c400e2a2
md"## 1.1. Talbot effect"

# ╔═╡ 37f4c7da-1b3b-4ddc-a5e1-b03539892769
mandril = abs.(resample(Float32.(testimage("mandril_gray")), (64, 64)));

# ╔═╡ 940600d3-5632-4aa2-b1d2-96842020d305
mandril_large = select_region(repeat(mandril, 4,4), new_size=(256,256));

# ╔═╡ d3a1dfc1-f480-4b43-ae88-10104ceaa185
simshow(mandril_large)

# ╔═╡ 7c4e702a-6292-47f6-b475-9d2d3aafe649
z2 = range(0, 10f-3, 300)

# ╔═╡ df5870c1-78a4-4f04-9fec-40bbc311a8e0
mandril_prop = bpm(mandril_large, λ, Lx, Ly, z2);

# ╔═╡ 4d7453b1-66d9-4b58-a361-dcacc52610e9
x2 = range(-Lx/2, Lx/2, size(mandril_large, 1))

# ╔═╡ bc28ee52-22fa-4dc0-a0fd-b58b196c346d
y2 = range(-Ly/2, Ly/2, size(mandril_large, 1))

# ╔═╡ 1c1d36b2-1d2d-4b81-af44-34951569628c
@bind iz2 PlutoUI.Slider(eachindex(z2), default=282)

# ╔═╡ 19822b65-a4c8-4e11-8607-1009fb180f4c
md"
propagation distance z = $(round(z2[iz2] * 1000, digits=3))mm
"

# ╔═╡ 45a4261b-f8b0-4c1b-b65d-4f9e0e62c91e
heatmap(y2, x2, abs.(mandril_prop[:, :, iz2]), xlabel="in mm", ylabel="in mm")

# ╔═╡ 2a03a775-e930-47e7-b228-9f0a8202b801
size(mandril_prop)

# ╔═╡ 829baabc-1462-480f-b879-b0ca453d0e9f
md"## 1.2 Talbot length"

# ╔═╡ 8ba00f7c-13a1-49ac-8a91-6cf21bceb787
dx = Lx / size(mandril_large, 1)

# ╔═╡ 008388f4-4096-41e3-8ba5-11329f139098
2 * dx^2 / λ

# ╔═╡ e25f5105-e5d1-494f-8709-d265138dc176
λ / (1 - √(1 - λ^2 / (64 * dx)^2))

# ╔═╡ 05be96ef-6e66-4972-98b4-8241d6eec4c1
md"""## 2. Propagation through aperture

Use BPM to propagate a plane wave that goes through the input apertures described below 

- A rectangular aperture of $20\mathrm{\mu m} \times 200\mathrm{\mu m}$

Note: For the BPM code use a window of $2\mathrm{mm} \times 2\mathrm{mm}$, propagation distance 40 mm and λ=532nm

Provide the amplitude x-z plot and comment on your results.

Hint: use the `box` function
"""

# ╔═╡ f48628e5-1825-486b-9ced-03fede0da7a9
# access the help with typing ?box

# ╔═╡ 0b4d696e-8218-413f-be22-eab08829efbf
Lrec = 2e-3

# ╔═╡ 4c7096ad-8b6d-4808-938c-9d5cc5b272cb
Nrec = 500

# ╔═╡ 1b223678-2328-408c-a152-12fb955c7224
yrec = range(-Lrec / 2, Lrec / 2, Nrec)

# ╔═╡ 0dd4c703-4eee-4a59-b03c-393606855f00
xrec = yrec

# ╔═╡ a49957f5-b120-4e7f-a6fb-c562e0aebd80
aperture_size = (20e-6, 200e-6) ./ 2e-3 .* Nrec

# ╔═╡ fef13208-7aad-4e9f-9140-ccc59e91d9ae
aperture = box((Nrec, Nrec), aperture_size);

# ╔═╡ 6095b2ae-b516-47ba-8301-159749f659d9
simshow(aperture)

# ╔═╡ 8ce4e662-1143-4fd8-98b8-ba0df79335ae
z_aperture = range(0, 80e-3, 100)

# ╔═╡ c3b363ee-5489-4e86-8849-14fbcac80a19
aperture_p = bpm(aperture, λ, Lrec, Lrec, z_aperture);

# ╔═╡ 4b703f6f-7bfd-4c07-8011-696b4a0f5731
@bind iz3 PlutoUI.Slider(eachindex(z))

# ╔═╡ 7b478e05-c748-48bf-9037-d499474968e9
md"
propagation distance z = $(round(z_aperture[iz3] * 1000, digits=3))mm
"

# ╔═╡ 27d270b9-5f3a-48eb-b5c8-79602bcbf25b
heatmap(xrec .* 1000, yrec .* 1000, abs.(aperture_p[:, :, iz3]), xlabel="x in mm", ylabel="y in mm")

# ╔═╡ 48073d7a-2257-4134-aead-aa9e5238f60e
md"""## 3. Grating

Repeat the above question with 5 rectangular apertures (20 μm by 200 μm) with a spacing of 50 μm each in x-axis. What do you observe?
Then, repeat this experiment for 200-μm separation as well. Comment on your results.


Hint: use again the `box` function. And then use `circshift`.
"""

# ╔═╡ 32e786fc-681c-4328-9db2-4affc68c93f8
md"### 3.1 Solution
For short propagation distances first we see diffraction happening across the first dimension (y axis).
The light spreads across y with longer propagation distance.

For very long distances, diffraction also across x impacts and spreads the light across x.
"

# ╔═╡ dec9d570-8759-4455-bec6-52660cac36da
spacing_N = round(Int, 50e-6 / Lrec * Nrec)

# ╔═╡ 8eacfde4-935f-457b-92fe-5cd84edc3857
grating = aperture .+ circshift(aperture, (spacing_N,0)) .+ circshift(aperture, (-spacing_N, 0)) .+ circshift(aperture, (2*spacing_N, 0)) .+ circshift(aperture, (-2 * spacing_N, 0));

# ╔═╡ d18e9f18-d523-401f-8cca-fe9251656e09
grating_p = bpm(grating, λ, Lrec, Lrec, z_aperture);

# ╔═╡ e87820dd-b62b-4e08-81b6-abb97540e07d
@bind iz4 PlutoUI.Slider(eachindex(z))

# ╔═╡ bd98a76d-9dd0-456a-b257-818e55108a06
Lrec

# ╔═╡ a8588063-bcfb-44d3-8617-ad7bf79bef37
md"
propagation distance z = $(round(z_aperture[iz4] * 1000, digits=3))mm
"

# ╔═╡ 7496534a-54b7-4a8a-b09d-72eb5efa7835
heatmap(xrec .* 1000, yrec .* 1000, abs.(grating_p[:, :, iz4]), xlabel="x in mm", ylabel="y in mm")

# ╔═╡ 835114d1-c642-4b51-8b4d-52849265d39e
md"### 3.2 Solution
Similar to before.

But since the spacing between the stripes is bigger, the distance needs to be longer that we see the impact of the interference of the individual apertures.

"

# ╔═╡ b299f4e2-7d1e-4420-a67a-df81b58635bc
spacing_N2 = round(Int, 200e-6 / Lrec * Nrec)

# ╔═╡ 6f5f05fb-acf6-4d20-b1af-7bbd622a58b6
grating2 = aperture .+ circshift(aperture, (spacing_N2,0)) .+ circshift(aperture, (-spacing_N2, 0)) .+ circshift(aperture, (2*spacing_N2, 0)) .+ circshift(aperture, (-2 * spacing_N2, 0));

# ╔═╡ 26aa49ea-570a-411e-bdc4-c6115c4953ab
grating_p2 = bpm(grating2, λ, Lrec, Lrec, z_aperture);

# ╔═╡ ba341031-5535-40cf-a44d-7fb149349467
@bind iz5 PlutoUI.Slider(eachindex(z))

# ╔═╡ 8be506a3-cbd6-4198-9b36-357ec987e7fb
Lrec

# ╔═╡ be7662a6-8c47-4f96-8358-413720ed479d
md"
propagation distance z = $(round(z_aperture[iz4] * 1000, digits=3))mm
"

# ╔═╡ 38915ff7-a8f7-4cfe-ba71-deee0d45413b
heatmap(xrec, yrec, abs.(grating_p2[:, :, iz5]), xlabel="x in mm", ylabel="y in mm")

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[[deps.IntelOpenMP_jll]]
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[[deps.InteractiveUtils]]
deps = ["Markdown"]
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[[deps.IntervalSets]]
deps = ["Dates", "Random"]
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    [deps.IntervalSets.extensions]
    IntervalSetsStatisticsExt = "Statistics"

[[deps.IrrationalConstants]]
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[[deps.IteratorInterfaceExtensions]]
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[[deps.JLFzf]]
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[[deps.JLLWrappers]]
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[[deps.JSON]]
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[[deps.JpegTurbo]]
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[[deps.JpegTurbo_jll]]
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[[deps.JuliaVariables]]
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[[deps.LAME_jll]]
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[[deps.LERC_jll]]
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[[deps.LLVMOpenMP_jll]]
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[[deps.LZO_jll]]
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[[deps.LaTeXStrings]]
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[[deps.Latexify]]
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[[deps.LazyModules]]
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[[deps.LibCURL]]
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[[deps.LibCURL_jll]]
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[[deps.LibGit2]]
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[[deps.LibGit2_jll]]
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[[deps.LibSSH2_jll]]
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[[deps.Libdl]]
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[[deps.Libffi_jll]]
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[[deps.Libgcrypt_jll]]
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[[deps.Libglvnd_jll]]
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[[deps.Libgpg_error_jll]]
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[[deps.Libiconv_jll]]
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[[deps.Libmount_jll]]
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git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
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[[deps.Libtiff_jll]]
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git-tree-sha1 = "3eb79b0ca5764d4799c06699573fd8f533259713"
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[[deps.Libuuid_jll]]
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[[deps.LinearAlgebra]]
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[[deps.LogExpFunctions]]
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    [deps.LogExpFunctions.extensions]
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    LogExpFunctionsChangesOfVariablesExt = "ChangesOfVariables"
    LogExpFunctionsInverseFunctionsExt = "InverseFunctions"

    [deps.LogExpFunctions.weakdeps]
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[[deps.Logging]]
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[[deps.LoggingExtras]]
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[[deps.MIMEs]]
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[[deps.MKL_jll]]
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[[deps.MLStyle]]
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[[deps.MacroTools]]
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[[deps.MappedArrays]]
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[[deps.Markdown]]
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[[deps.MbedTLS]]
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[[deps.MbedTLS_jll]]
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[[deps.Measures]]
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[[deps.Memoize]]
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[[deps.MicroCollections]]
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[[deps.Missings]]
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[[deps.Mmap]]
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[[deps.NDTools]]
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[[deps.NFFT]]
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[[deps.NaNMath]]
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[[deps.NameResolution]]
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[[deps.Netpbm]]
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[[deps.OffsetArrays]]
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    [deps.OffsetArrays.extensions]
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[[deps.Ogg_jll]]
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[[deps.OpenBLAS_jll]]
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[[deps.OpenEXR]]
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[[deps.OpenEXR_jll]]
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[[deps.OpenSSL]]
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[[deps.OpenSSL_jll]]
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[[deps.OpenSpecFun_jll]]
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[[deps.Opus_jll]]
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[[deps.PCRE2_jll]]
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[[deps.PNGFiles]]
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[[deps.PaddedViews]]
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[[deps.Parsers]]
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[[deps.Pixman_jll]]
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[[deps.PkgVersion]]
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[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.1+0"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "b4bfde5d5b652e22b9c790ad00af08b6d042b97d"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.15.0+0"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "730eeca102434283c50ccf7d1ecdadf521a765a4"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.2+0"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.6+0"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.39.0+0"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.5.0+0"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+1"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.5+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "a68c9655fbe6dfcab3d972808f1aafec151ce3f8"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.43.0+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.8.0+1"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "93284c28274d9e75218a416c65ec49d0e0fcdf3d"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.40+0"

[[deps.libsixel_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "libpng_jll"]
git-tree-sha1 = "d4f63314c8aa1e48cd22aa0c17ed76cd1ae48c3c"
uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
version = "1.10.3+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.52.0+1"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+1"
"""

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