matrix_method_optical_systems.jl

### A Pluto.jl notebook ###
# v0.19.41

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, SpecialFunctions, UrlDownload, ImageMagick

# ╔═╡ f1abb608-c56e-4a88-84ef-0d1cf3d97050
using LinearAlgebra

# ╔═╡ 637745b4-3d94-4407-997f-cddfd953271c
using RadonKA, DiffImageRotation

# ╔═╡ a7a9946e-0013-4cfe-aaf7-0c19da075abd
using Noise

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

# ╔═╡ 50cf4730-3a0e-44a6-b3c0-b85281bac209
BLAS.set_num_threads(4)

# ╔═╡ 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

# ╔═╡ 5f21a849-0272-4bca-9659-54cd38068e09
"""
	bpm(field, λ0, Lx, Ly, z, n; window=true, paraxial=true, amplitude_array)

Propagates the array `field` with wavelength `λ0` and the filed size in meter size
`(Lx, Ly)`. The propagation distance `z` should be a vector of distances.
`n` is the average refractive index of the propagation medium.

The returned array is a three dimensional array where `size(arr, 3) == size(z, 1)`.


If `window=true` we apply a Hann window function to dampen the boundaries.
A keyword `amplitude_array` can be provided, which multiplies with the field at each point. This allows to include obstacles or to shift the phase.

If `paraxial=true` the Fresnel approximation is applied.
"""
function bpm(field, λ0, Lx, Ly, z, n=1; window=true, amplitude_array=ones(size(field)..., length(z)), paraxial=true)
	# free space wavenumber in m-1
	k0 = 2 * π / λ0
	# medium wavenumber m-1
	k = n * k0
	λ = λ0 / n
	# medium in m
	dz = z[2] - z[1]

	# field parameters
	Nx = size(field, 2)
	dx = Lx / Nx
	x  = Nx > 1 ? range(-Lx/2, Lx/2, Nx) : zero(typeof(Lx))
	fx = reshape(fftfreq(Nx, 1 / dx), (1, Nx))

	Ny = size(field, 1)
	dy = Ly / Ny
	y  = range(-Ly/2, Ly/2, Ny)
	fy = fftfreq(Ny, 1 / dy)

	if paraxial
		# important step, this calculates the Fourier space kernel
		H = exp.(-1im .* k .* λ^2 .* (fx.^2 .+ fy.^2) ./ (2) * dz)
	else
		H = exp.(1im .* sqrt.(1 .+ 0im .- λ^2 .* fx.^2 .- λ^2 .* fy.^2) .* k .* dz) .* ((λ0^2 .* fx.^2 .+ λ0^2 .* fy.^2) .< 1)
	end
	# 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 syntax: p * x == fft(x)
	p = plan_fft(field, (1,2))
	window_f = window ? IndexFunArrays.window_hanning(size(out_field)[1:2], border_in=0.9) : 1
	# inverse FFT
	invp = inv(p)
	for z_index in 2:size(out_field, 3)
		u0 = out_field[:, :, z_index - 1] .* window_f .* amplitude_array[:, :, z_index - 1]
    	u1 = invp * ((p * u0) .* H)
		out_field[:, :, z_index] .= u1
	end
	return out_field
end

# ╔═╡ 1d6a9432-2784-4902-ba96-f082be62fa78
"""
	bpm(field, λ0, Lx, Ly, z, n_1, n_2; window=true, paraxial=true, amplitude_array)

Propagates the array `field` with wavelength `λ0` and the filed size in meter size
`(Lx, Ly)`. The propagation distance `z` should be a vector of distances.
`n_1` is the refractive index of region 1 and `n_2` the refractive index of region 2.
`n_array` is an array filled with either `n_1` or `n_2` and the algorithm stiches the regions together.

The returned array is a three dimensional array where `size(arr, 3) == size(z, 1)`.


If `window=true` we apply a Hann window function to dampen the boundaries.
A keyword `amplitude_array` can be provided, which multiplies with the field at each point. This allows to include obstacles.

If `paraxial=true` the Fresnel approximation is applied.
"""
function bpm_split(field, λ0, Lx, Ly, z, n1=1, n2=1; window=true, n_array=ones(size(field)..., length(z)), paraxial=true)
	# free space wavenumber in m-1
	k0 = 2 * π / λ0
	# medium wavenumber m-1
	k1 = n1 * k0
	k2 = n2 * k0
	λ1 = λ0 / n1
	λ2 = λ0 / n2
	# medium in m
	dz = z[2] - z[1]

	# field parameters
	Nx = size(field, 2)
	dx = Lx / Nx
	x  = Nx > 1 ? range(-Lx/2, Lx/2, Nx) : zero(typeof(Lx))
	fx = reshape(fftfreq(Nx, 1 / dx), (1, Nx))

	Ny = size(field, 1)
	dy = Ly / Ny
	y  = range(-Ly/2, Ly/2, Ny)
	fy = fftfreq(Ny, 1 / dy)

	if paraxial
		# important step, this calculates the Fourier space kernel
		H1 = exp(1im * k1 * dz) .* exp.(-1im .* k1 .* λ1^2 .* (fx.^2 .+ fy.^2) ./ (2) * dz)
		H2 = exp(1im * k2 * dz) .* exp.(-1im .* k2 .* λ2^2 .* (fx.^2 .+ fy.^2) ./ (2) * dz)
	else
		H1 = exp.(1im .* sqrt.(1 .+ 0im .- λ1^2 .* fx.^2 .- λ1^2 .* fy.^2) .* k1 .* dz) .* ((λ1^2 .* fx.^2 .+ λ1^2 .* fy.^2) .< 1)
		H2 = exp.(1im .* sqrt.(1 .+ 0im .- λ2^2 .* fx.^2 .- λ2^2 .* fy.^2) .* k2 .* dz) .* ((λ2^2 .* fx.^2 .+ λ2^2 .* fy.^2) .< 1)
	end
	# 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 syntax: p * x == fft(x)
	p = plan_fft(field, (1,2))
	window_f = window ? IndexFunArrays.window_hanning(size(out_field)[1:2], border_in=0.8) : 1
	# inverse FFT
	invp = inv(p)
	for z_index in 2:size(out_field, 3)
		u0_1 = out_field[:, :, z_index - 1] .* window_f
		
		u1_1 = invp * ((p * u0_1) .* H1)
		u1_2 = invp * ((p * u0_1) .* H2)

		out_field[:, :, z_index] .= u1_1 .* (n_array[:, :, z_index] .≈ n1) .+ u1_2 .* (n_array[:, :, z_index] .≈ n2)
	end
	return out_field
end

# ╔═╡ 66f6d122-3ab9-4f44-b702-4a526c0700db
"""
	free_space_propagation(field, z, λ, L)

Propagate a `field` with wavelength `λ` and field size `L` with free space bandlimited angular spectrum over a distance `z`.
"""
function free_space_propagation(field, z, λ, L)
	@assert size(field, 1) == size(field, 2) "Requires quadratic field"
	@assert ndims(field) == 2 "Requires a 2D array"
	# physical parameters
	Lp = 2 * L
	field_p = select_region(field, M=2)
	Np = size(field_p, 1)
	f_y = fftfreq(Np, inv(Lp / Np))
	f_x = f_y'
	k = 2 * π / λ

	# matsushima bandlimit
	Δu = 1 / Lp
	u_limit = 1 / (sqrt((2 * Δu * z)^2 + 1) * λ)
	W = ((abs2.(f_y) ./ u_limit .^2 .+ abs2.(f_x) * λ^2) .< 1) .*
        ((abs2.(f_x) ./ u_limit .^2 .+ abs2.(f_y) * λ^2) .< 1)

	# H is the Fourier space kernel
	H = W .* exp.(1im .* k .* z .* sqrt.(1 .+ 0im .- abs2.(f_x .* λ) .- abs2.(f_y .* λ)))

	# do wraparound free convolution
	field_propagated = select_region(fftshift(ifft(fft(ifftshift(field_p)) .* H)), M=0.5)

	return field_propagated
end

# ╔═╡ 83f49548-e22f-4bf4-9e22-235fdd8b0ad2
"""
	free_space_propagation(field, z, λ, L)

Propagate a `field` with wavelength `λ` and field size `L` with free space bandlimited angular spectrum over a distance `z`.
"""
function free_space_propagation_1D(field, z, λ, L)
	# physical parameters
	Lp = 2 * L
	field_p = select_region(field, M=2)
	Np = size(field_p, 1)
	f_y = fftfreq(Np, inv(Lp / Np))
	k = 2 * π / λ

	# matsushima bandlimit
	Δu = 1 / Lp
	u_limit = 1 / (sqrt((2 * Δu * z)^2 + 1) * λ)
	W = ((abs2.(f_y) ./ u_limit .^2 .+ abs2.(0) * λ^2) .< 1)

	# H is the Fourier space kernel
	H = W .* exp.(1im .* k .* z .* sqrt.(1 .+ 0im .- abs2.(f_y .* λ)))

	# do wraparound free convolution
	field_propagated = select_region(fftshift(ifft(fft(ifftshift(field_p)) .* H)), M=0.5)

	return field_propagated
end

# ╔═╡ 5bdc18e1-be5b-4f4e-a15b-cd9b637adaeb
md"# 1. Load Images"

# ╔═╡ 3051cffc-ff2b-4250-b930-15c5b9c0921f
img = Float32.(select_region(testimage("resolution_test_512"), center=(250, 320), new_size=(100, 100))[begin:2:end, begin:2:end]);

# ╔═╡ fba88879-6300-462f-bd64-e2fa844d467c
simshow(img)

# ╔═╡ f1c78448-5c13-490a-8dc2-945ab1ab6759
N = size(img, 1)

# ╔═╡ 9bf4273e-7b55-4cce-8ead-243f0e3e35c2
z = 200e-6

# ╔═╡ 0976061a-1720-4b9e-97da-5dae3b1e441c
λ = 633e-9

# ╔═╡ 13b20910-1952-4a46-8b48-3bc1d42185ff
L = 50e-6

# ╔═╡ b973b266-8993-4db0-9074-bf23a00e6cee
diffuser = conv_psf(cis.(2 .* randn(size(img)...)), gaussian(size(img), sigma=1.5));

# ╔═╡ 631cd34f-c3f6-42ee-8a6d-a922f3002948
simshow(diffuser);

# ╔═╡ 550365b8-75c9-46ff-bfd1-7aac851bbaef
fwd(x) = free_space_propagation(x, z, λ, L)

# ╔═╡ c7f55837-40bb-44c2-90f7-5cbffbad689b
md"# 2. Measure Linear Matrix


Usually optical systems are linear systems hence they can be described with matrices.
In practice this is used for complex systems such as fibres. Imaging systems are better described with more efficient approaches such as Fourier transforms.

To measure the system matrix $M$ experimentally, we probe the system with $K$ different inputs $\vec x$. Each $\vec x$ is one projected image, we just reshape as a vector.
Then, we assemble our input matrix $X$ where each column corresponds to one input vector.





So $X \in \mathbb{C}^{N^2 \times K}$. 
The system matrix is $M \in \mathbb{C}^{N^2 \times N^2}$.
The measurements are $Y \in \mathbb{C}^{N^2 \times K}$.  
$N^2$ because we reshape a image with size $N \times N$ into a vector of length $N^2$.


The connection between input $X$ and output matrix $Y$ is:

$$Y = M \cdot  X$$.


To obtain $M$ we invert $X$.
The inverse of $X$ is not possible since $X$ is not quadratic and also not of full rank.
We have to use the pseudoinverse for it.

$$M = Y \cdot X^{-1}$$.

$$M = Y \cdot \text{pinv}(X)$$

By choosing suitable inputs $X$ we hope to find a matrix $M$ which is able to represent the optical system.
"

# ╔═╡ b5cc0ed6-eb23-4908-bb50-492e67b74348
function make_measurements(fwd, N, K)
	
	Y = zeros(ComplexF64, N^2, K)
	X = zeros(ComplexF64, N^2, K)
	
	for c in 1:K
		# create a random direction Gaussian Beam
		dir1 = randn() / 10
		dir2 = randn() / 10
		xpos = fftpos(L, N)
		#diffuser2 = conv_psf(cis.(3 .* randn(size(img)...)), gaussian(size(img), sigma=1.5));
		# a single vector which we use to probe the matrix
		x = gaussian((N, N), sigma=15) .* exp.(2π .* 1im ./ λ .* (xpos .* sin(dir1) .+ xpos' * sin(dir2)))

		# save input x to X
		X[:, c] .= reshape(x, :)
		# use optical system to propgate x and save it to Y
		Y[:, c] .= reshape(fwd(x), :)
	end

	return X, Y
end

# ╔═╡ 60eb88aa-608d-4a0d-b862-6a7761f7ab1b
N

# ╔═╡ 6e5e42b6-7a81-400a-b325-fcc15c6051f8
N^2

# ╔═╡ f903a341-5d1f-4aa2-a3f8-dbbf1076d29e
K = 1000

# ╔═╡ d69fc6db-9747-4d4b-be12-2f162e350a49
X, Y = make_measurements(fwd, 50, K)

# ╔═╡ 20fc69f1-daaa-4074-8e0b-636f293231e1
size(X)

# ╔═╡ 5e8702b6-f4bb-43e9-ad57-6df9a09599bf
M = Y * pinv(X);

# ╔═╡ f7ce5e1d-fcae-4375-b6a7-8196cdda2900
@bind k2 Slider(1:K)

# ╔═╡ 9da248b2-cfcb-4cf4-ab3c-51c49dd46e98
simshow(reshape(X[:, k2], N, N))

# ╔═╡ 28673109-5cdd-4a6c-959d-bbeafe2dd8be
simshow(reshape(M * X[:,k2], N, N))

# ╔═╡ d19cc836-1b70-4ca9-9463-f395caccc42d
simshow(fwd(reshape(X[:, k2], N, N)))

# ╔═╡ 4d0e7787-be34-4fcb-a55c-3d83678a59e1
md"# 3. Propagate object with matrix
Output seems to match well.
"

# ╔═╡ 5bc0ade2-7e89-41e4-9daa-926fb2975de2
simshow(img)

# ╔═╡ d65764cb-fdf4-4e98-8daa-b617d9f0e86f
simshow(reshape(M * reshape(img, :), N, N))

# ╔═╡ ff517230-dccd-4ece-bc67-3370a36eb068
simshow(fwd(img))

# ╔═╡ 81f7c46f-773f-4c0c-ac75-df02fdd2ecc7
# inverting M does not work because it's not a full rank matrix, hence we use a pseudoinverse
inv2M = inv(M' * M + 0.1 * I) * M';

# ╔═╡ 1d1c09e2-0a3b-4ebf-94db-227d4a89ae63
simshow(reshape(inv2M * reshape(fwd(img), :), N, N))

# ╔═╡ f1d204d7-c4be-4365-9013-afce2137c8d9
simshow(img)

# ╔═╡ 00000000-0000-0000-0000-000000000001
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version = "0.2.1"

[[deps.UnsafeAtomicsLLVM]]
deps = ["LLVM", "UnsafeAtomics"]
git-tree-sha1 = "323e3d0acf5e78a56dfae7bd8928c989b4f3083e"
uuid = "d80eeb9a-aca5-4d75-85e5-170c8b632249"
version = "0.1.3"

[[deps.Unzip]]
git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.2.0"

[[deps.UrlDownload]]
deps = ["HTTP", "ProgressMeter"]
git-tree-sha1 = "758aeefcf0bfdd04cd88e6e3bc9feb9e8c7d6d70"
uuid = "856ac37a-3032-4c1c-9122-f86d88358c8b"
version = "1.0.1"

[[deps.Wayland_jll]]
deps = ["Artifacts", "EpollShim_jll", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "7558e29847e99bc3f04d6569e82d0f5c54460703"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.21.0+1"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "93f43ab61b16ddfb2fd3bb13b3ce241cafb0e6c9"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.31.0+0"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"]
git-tree-sha1 = "07e470dabc5a6a4254ffebc29a1b3fc01464e105"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.12.5+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "afead5aba5aa507ad5a3bf01f58f82c8d1403495"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.8.6+0"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "6035850dcc70518ca32f012e46015b9beeda49d8"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.11+0"

[[deps.Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "34d526d318358a859d7de23da945578e8e8727b7"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.4+0"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[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 = "1ea2ebe8ffa31f9c324e8c1d6e86b4165b84a024"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.43+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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