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HW02.jl
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HW02.jl
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### 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 = TODO
# ╔═╡ 528dd60e-939f-441f-bf09-99ddb7d2ff71
Ny = TODO
# ╔═╡ ad861f4e-23d0-40c6-bd5e-111c73328cc1
Ly = TODO
# ╔═╡ 3bc86215-a65e-43b2-b5af-8c58f3c5fa66
Lx = TODO
# ╔═╡ 015a340e-ebb2-444f-b528-d8047083872d
grating_period = TODO
# ╔═╡ 6fa588e6-85d6-4c34-b878-e3aa3c88d061
x = TODO
# ╔═╡ 610680c4-b44b-4ad9-82b7-57323c2626a9
y = range(-Lx /2, Lx / 2, Nx)
# ╔═╡ 9d26b78f-8348-421d-8642-776db3d245ff
amplitude_grating = TODO
# ╔═╡ 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 = TODO
# ╔═╡ 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 = TODO
# ╔═╡ 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])
# ╔═╡ 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 = TODO
# ╔═╡ 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])
# ╔═╡ 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"""
Edit this LaTeX code to show some equations
$$\tilde f(k) = \int f(x) \exp(-2\pi i k x) dx$$
"""
# ╔═╡ 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.
"
# ╔═╡ 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 = 0
# ╔═╡ 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
md"Can you explain what just happened? Why are the monkeys not exactly reproduced?"
# ╔═╡ 311311b8-d8d4-4513-9a15-551049c9c0e1
md"""## 2.1 Answer
Give some reasoning here.
"""
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
FourierTools = "b18b359b-aebc-45ac-a139-9c0ccbb2871e"
ImageMagick = "6218d12a-5da1-5696-b52f-db25d2ecc6d1"
ImageShow = "4e3cecfd-b093-5904-9786-8bbb286a6a31"
IndexFunArrays = "613c443e-d742-454e-bfc6-1d7f8dd76566"
NDTools = "98581153-e998-4eef-8d0d-5ec2c052313d"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoTest = "cb4044da-4d16-4ffa-a6a3-8cad7f73ebdc"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
TestImages = "5e47fb64-e119-507b-a336-dd2b206d9990"
UrlDownload = "856ac37a-3032-4c1c-9122-f86d88358c8b"
[compat]
FFTW = "~1.8.0"
FileIO = "~1.16.2"
FourierTools = "~0.4.2"
ImageMagick = "~1.3.0"
ImageShow = "~0.3.8"
IndexFunArrays = "~0.2.7"
NDTools = "~0.5.3"
Plots = "~1.40.0"
PlutoTest = "~0.2.2"
PlutoUI = "~0.7.55"
TestImages = "~1.8.0"
UrlDownload = "~1.0.1"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised
julia_version = "1.10.1"
manifest_format = "2.0"
project_hash = "13ab4e5aa3255750e5bc269360db43635dc248f7"
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