HW02_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

# ╔═╡ 872aa9ce-50e7-4c17-ab8d-5c391d70c1b4
using UrlDownload, ImageMagick

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

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

# ╔═╡ 8e6ec43c-9135-4829-8146-a56b8624750a
const TODO = nothing

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

# ╔═╡ f326cd36-9c05-4b1c-81c0-56c954cd51f3
gauss_R(z::T, z_R) where T = iszero(z) ? T(Inf) : (1 + (z_R / z)^2)

# ╔═╡ 7c6b4ddd-ca5a-4b23-96f7-e896fb1cda6d
gauss_ψ(z, z_R) = atan(z, z_R)

# ╔═╡ dd16735b-c1d6-4977-a396-a3e23823ee68
gauss_w(z, z_R, w_0) = w_0 * sqrt(1 + (z / z_R)^2)

# ╔═╡ 8e04ae26-5474-4c2c-9fda-dbb7efd77acd
"""
	gauss_beam(y, x, z, λ, w_0)


Returns the eletrical field of a Gaussian beam at position `(y, x)` at optical axis position `z` with respect to the beam waist `w_0`.
Wavelength is `λ`.
"""
function gauss_beam(y, x, z, λ, w_0)
    k = π / λ * 2
    z_R = π * w_0^2 / λ
	r² = x ^ 2 + y ^ 2
    # don't put exp(i * k * z) into the same exp, it causes some strange wraps
	return w_0 / gauss_w(z, z_R, w_0) * exp(-r² / gauss_w(z, z_R, w_0)^2) * 
            exp(1im * k * z) * 
            exp(1im * (k * r² / 2 / gauss_R(z, z_R) - gauss_ψ(z, z_R)))
end

# ╔═╡ 9f99ae1e-d0d8-4116-880e-fb39ab93e236
# please use gauss_R with a Float numbers

# ╔═╡ f9d44b5c-f1fe-46a4-93d4-7b2bf363d99b
y2 = -1:0.1:1

# ╔═╡ 501627d9-3a78-4797-9017-39da7ccca2d4
x2 = y2';

# ╔═╡ 13fd614a-5445-4d99-aa61-f9ac6bbe9087
# just an example how to use gauss_beam
simshow(gauss_beam.(y2, x2, 0.0, 532e-9, 0.5))

# ╔═╡ eeb77ae8-f409-4ca1-884f-c6c99501078f
gauss_R(0.0, 0.0)

# ╔═╡ 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

# ╔═╡ aaf7cf09-1244-461b-aaa6-731a65fc3d57
md"# 1. Sinusoidal Amplitude Grating

Create a sinusoidal pattern with the following parameters:
* `Nx = Ny = 512`
* `Lx = Ly = 2e-3`
* `grating_period Λ= 20e-6`
* Gaussian beam width `w=100e-6`


The amplitude grating is given by:

$$f(x) = \frac12 \left(1 + \cos\left(\frac{2\pi x}{\Lambda} \right) \right)$$.


"

# ╔═╡ ac3147f3-1831-4ca8-b9d9-da78b3a9b6c3
md"## 1.1 Parameter Definition"

# ╔═╡ f0c2711f-adf7-45c2-9be2-7e5a13783acd
Nx = 512

# ╔═╡ 528dd60e-939f-441f-bf09-99ddb7d2ff71
Ny = 512

# ╔═╡ ad861f4e-23d0-40c6-bd5e-111c73328cc1
Ly = 2e-3

# ╔═╡ 3bc86215-a65e-43b2-b5af-8c58f3c5fa66
Lx = 2e-3

# ╔═╡ 015a340e-ebb2-444f-b528-d8047083872d
grating_period = 32e-6

# ╔═╡ 610680c4-b44b-4ad9-82b7-57323c2626a9
y = range(-Lx /2, Lx / 2, Nx)

# ╔═╡ 6fa588e6-85d6-4c34-b878-e3aa3c88d061
x = y'

# ╔═╡ 9d26b78f-8348-421d-8642-776db3d245ff
amplitude_grating = 1 / 2 .+ (1 .+ cos.(2π .* x ./ grating_period)) .+ 0 .* y

# ╔═╡ acccc989-6dc1-4cde-9932-aa725c2c2f06
simshow(amplitude_grating)

# ╔═╡ 1573e29d-0da5-4270-a07f-cd65caf98bbd
md"## 1.2 Gaussian Beam
Create a Gaussian beam in this part.
Use the wavelength of `λ=375nm`. The beam waist is `w=100e-6`.
We want to observe the beam at the point with infinity curvature.

Access the help `?gauss_beam` and read how to use the function.
Use the positional arrays `y` and `x`. And the broadcast mechanism (remember `sin.(x)` vs `sin(x)`).
"

# ╔═╡ 1eca9f71-3b3a-4552-980b-072d29ff0f8b
gb = gauss_beam.(y, x, 0.0, 375e-9, 100e-6)

# ╔═╡ 52e13798-549b-48a9-bcc0-26a921a377c6
simshow(gb)

# ╔═╡ 279749c4-512e-4124-b579-889939d506ae
md"## 1.3 BPM with  λ=375nm

Now multiply the Gaussian beam elementwise (`.*`) with the grating and propagate this with the BPM method.
Take the `abs2.` to obtain the intensity.

"

# ╔═╡ 452447a6-e39f-4cd1-8694-6c31c38a04f9
z = range(0, 20e-3, 100)

# ╔═╡ 69a20699-9de5-4254-b459-2777d1305396
intensity_a = abs2.(bpm(gb .* amplitude_grating, 375e-9, Lx, Ly, z))

# ╔═╡ 9d906236-c701-4ae2-91d9-a7d63b1d3ff5
@bind iz PlutoUI.Slider(eachindex(z))

# ╔═╡ cc461df6-494b-421e-8357-e66da518235e
md"z = $(round(z[iz] * 1000, digits=2))mm"

# ╔═╡ 19d6ee22-549c-4af1-81a0-1e9cfb4c01b5
simshow(intensity_a[:, :, iz], γ=0.6)

# ╔═╡ 00171a23-5bb8-44cc-98c0-4465ae9412b2
md"## 1.4 BPM with  λ=750nm
Repeat the same propagation but with another wavelength.
"

# ╔═╡ 6d657ea3-8fc0-4411-b728-0906ef2d33b5
intensity_b = abs2.(bpm(gb .* amplitude_grating, 750e-9, Lx, Ly, z));

# ╔═╡ 4a569551-c271-4993-aa73-0d804d8ea5ca
@bind iz2 PlutoUI.Slider(eachindex(z))

# ╔═╡ 0e781f39-c94a-48af-a37f-7941f8fc0fc9
md"z = $(round(z[iz2] * 1000, digits=2))mm"

# ╔═╡ cd4941e0-6643-4668-b0ea-1ed57e2a9af0
simshow(intensity_b[:, :, iz2], γ=0.4)

# ╔═╡ dfddff32-89e4-48ef-9d5d-12558eeed837
plot(abs.(ft(cos.((0:999) .* π / 2))))

# ╔═╡ 5846c4e1-3379-441e-8bd2-e1759fd7198a


# ╔═╡ 2b1bb12b-311e-4c20-86d2-5cd06a5a819b
md"## 1.5 Qualitative Analytical result
Shortly derive what kind of output signal you qualitately would have expected in the case of far field approximation (Fraunhofer).

"

# ╔═╡ 470bfbcc-81f4-4cfd-8985-b0277b272a37


# ╔═╡ 3bcad5de-de8a-4d6b-8117-30081b9b5a8f
md"""
At the beginning, lets ignore the Gaussian beam illumination and assume that we have the following amplitude grating (AG) as input:

$$A\left(x,y\right)=\frac{1}{2}+\frac{1}{2}cos\left(\frac{2\pi}{\Lambda_{AG}}\right)$$
Note that this question satisfies $$\frac{x^2+y^2}{\lambda_z}\approx 0.01$$ condition. Therefore, we can use Fraunhofer diffraction:

$$A\left(u,v\right)=FT\left\{A\left(x,y\right)\right\}$$

where $$u=\frac{x'}{\lambda z}$$ and $$y=\frac{y'}{\lambda_z}$$.
First, let us apply Fourier Transform:

$$FT\left\{A\left(x,y\right)\right\}=FT\left\{\frac{1}{2}+\frac{1}{2}cos\left(\frac{2\pi}{\Lambda_{AG}}\right)\right\}=\\ \frac{1}{2}\delta(k_y)+\frac{\pi}{2}\left[\delta(k_y-k_{AG})+\delta(k_y+k_{AG})\right]$$ 

where $$k_{AG}=\frac{2\pi}{\lambda_{AG}}$$, $$k_x=2\pi u, k_y=2\pi v$$. So we can write $$A(u,v)$$ as

$$A\left(x',y'\right)=\frac{1}{2}\delta\left(2\pi\frac{y'}{\lambda_z}\right)+\frac{\pi}{2}\left[\delta\right(2\pi\frac{y'}{\lambda_z}-2\pi\frac{1}{\Lambda_{AG}}\left)+\delta\right(2\pi\frac{y'}{\lambda_z}+2\pi\frac{1}{\Lambda_{AG}}\left)\right]$$
This equation, states that we have three terms at $$y'=0$$, $$y'=\frac{\lambda_z}{\Lambda}$$ and $$y'=-\frac{\lambda_z}{\Lambda}$$. From this conclusion, it is apparent that if we increase $$\Lambda_{AG}$$, the side spots move towards the center.


"""

# ╔═╡ 31883966-8519-45f8-9ffc-45b48a2f1c92


# ╔═╡ 53a1b0cc-3920-4f45-a18e-8ce5940a7a03


# ╔═╡ 6e7f4000-d38e-4bad-90e1-e0cbcfa45fc4
md"# 2. Talbot Effect
Again, calculate the talbot length for the given scenario.

"

# ╔═╡ 757b024c-6fe6-4fe0-b9a3-abf4f8313561
md"
For a simple derivation of the Talbot effect, we can refer to course notes 2:
“Talbot can be explained by looking at the BPE in the Fourier plane: 
$$\tilde{A}\left(k_x,k_y\right)=\tilde{A}\left(k_x,k_y,z=0\right)e^{i\frac{k_x^2+k_y^2}{2k}}$$. When the input is periodic the Fourier transform is non-zero only at $$k_x=\frac{2n\pi}{a}$$.  If we evaluate the quadratic phase term at these discrete frequency locations we obtain $$e^{i\frac{k_x^2+k_y^2}{2k}}=e^{i\frac{(2n\pi)^2}{2ka^2}z}$$. This becomes 1 at $$z=\frac{2a^2}{\lambda}$$ and therefore the input is reproduced at these distances. It becomes a bit more complex for periodic patterns with more orders but the same basic idea holds:  We observe Talbot planes at distances $$z$$ where the quadratic term equal to 1 for all the discrete frequencies of the periodic pattern. Notice that periodic patterns in practice cannot be truly periodic because of the finite aperture of the system and effects such as the Talbot effect which relies on the periodicity eventually (for large $$z$$) do not persist due to the finite aperture.”

For a detailed analysis of the Talbot effect with a sinusoidal grating input please see Fourier Optics by Goodman pages: 87-89 “Fresnel Diffraction by a Sinusoidal Amplitude Grating: Talbot images”. Talbot effect can be denoted as a lens-less imaging technique for periodic structures. Once again, this phenomenon occurs since the periodic structures have distinct orders in the Fourier transform or more accurately Fourier series expansion! We really encourage you to check the mentioned part from the Fourier Optics book for a better understanding.

"

# ╔═╡ b0f50fed-e263-4e98-ba72-45ebdee8afb3
λ2 = 525e-9

# ╔═╡ 10304268-e3eb-4f4f-9961-51a8a1d768b4
L2 = 200e-6

# ╔═╡ 292b93b8-c26f-4d7a-ad81-9be9df07be82
Nx2 = 256

# ╔═╡ 1336bc64-786c-43c1-b1e7-d4e5ce10ec65
begin
	mandril = abs.(resample(Float32.(testimage("mandril_gray")), (64, 64)));
	mandril_large = select_region(repeat(mandril, 4,4), new_size=(256,256));
	psaltis = Gray.(urldownload("https://people.epfl.ch/private/common/photos/links/174684.jpg?ts=1708179090"))[40 .+ (1:3*64), 30 .+ (1:3*64)][1:3:end, 1:3:end]
	mandril_large[64:127, 64:127] .= psaltis;
	mandril_large = (bpm(mandril_large, λ2, L2, L2, [0, -λ2 / (1 - √(1 - λ2^2 / (L2 / 4)^2))])[:, :, 2])
end;

# ╔═╡ f00e6ee7-7200-4ac5-97dc-de0e379cbd54
simshow(abs.(mandril_large))

# ╔═╡ e5fa9a80-5322-4ff2-8852-09bb4ae62ea1
talbot_length = 2 * (L2 / 4) ^2 / λ2

# ╔═╡ a93a62fd-04e3-455c-af57-7cfc92c65489
mandril_p = (bpm((mandril_large), λ2, L2, L2, [0, talbot_length])[:, :, 2]);

# ╔═╡ 803c9ff1-459e-4f44-a7fb-dd3de85d6644
simshow(abs.(mandril_p))

# ╔═╡ 069f7980-2563-4989-8b4e-238e161aa824


# ╔═╡ 311311b8-d8d4-4513-9a15-551049c9c0e1
md"""## 2.1 Answer

The reason is, the input file does not contain 16 identical copies of mandril only. First, we chose the position where we wanted to put Prof. Psaltis in (the 2nd row and the 2nd column). Then, we took an image of mandril, subtracted the image of Prof. Psaltis, and propagated this image for 9.53 mm with “Time reversal” scheme, which means just changing the sign of the exponential term or diffraction term in the beam propagation equation. We recorded the output field, which is a diffracted field where the intensity is distributed over the transverse plane (the alternative “phase conjugation” method would be propagating the field with the non-changed diffraction term but conjugating the phase of the recorded output. Notice that both ways are equivalent). When we propagate this field with regular BPE, the exponential term cancels the time-reversed phase and then we recover the original mandril-Prof. Psaltis image sharp, which is similar to a lens undoing the diffraction in free space. When we add this complex field (Not the phase only! The complete complex field!) on top of 16 copies of the mandril, at the 2nd row 2nd column, we get Prof. Psaltis+mandril (mandril interfere destructively) at the Talbot plane, which results in Prof. Psaltis. At any other distance far away from the first Talbot plane, we will not recognize this as the intensity of the small Prof. Psaltis-mandril would be distributed.

"""

# ╔═╡ 049a41e2-6c9b-46a7-97bb-3739ce0105fc
md"# Of topic - Donut Beam"

# ╔═╡ 4f810c9f-478b-4311-8f0e-913e0ee21a5e
simshow(cis.(0.1 .* rr((64,64))) .* cis.(1 .* phiphi((64, 64), scale=10)))

# ╔═╡ 01cef40d-68c6-4f88-b8f9-915ea061e0ad
simshow(abs2.(ft((rr((128,128)) .< 20) .* cis.(0.1 .* rr((128,128))) .* cis.(5 .* phiphi((128, 128), scale=1)))), γ=0.5)

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deps = ["Markdown"]
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[[deps.IntervalSets]]
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    [deps.IntervalSets.extensions]
    IntervalSetsStatisticsExt = "Statistics"

[[deps.IrrationalConstants]]
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[[deps.JLFzf]]
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[[deps.LLVMOpenMP_jll]]
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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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[[deps.Libtiff_jll]]
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[[deps.Libuuid_jll]]
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    [deps.LogExpFunctions.extensions]
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    LogExpFunctionsChangesOfVariablesExt = "ChangesOfVariables"
    LogExpFunctionsInverseFunctionsExt = "InverseFunctions"

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[[deps.MIMEs]]
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[[deps.MKL_jll]]
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[[deps.MbedTLS]]
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[[deps.Ogg_jll]]
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[[deps.OpenSSL]]
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[[deps.OpenSSL_jll]]
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[[deps.PNGFiles]]
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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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