-
Notifications
You must be signed in to change notification settings - Fork 0
/
HW11.jl
2233 lines (1811 loc) · 74.8 KB
/
HW11.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
### A Pluto.jl notebook ###
# v0.19.41
using Markdown
using InteractiveUtils
# ╔═╡ d1980bd2-babf-11ee-1dbb-dfefbdbdb36d
using PlutoUI, Plots, ImageShow, TestImages, FFTW, NDTools, IndexFunArrays, FileIO, FourierTools, SpecialFunctions, UrlDownload, ImageMagick
# ╔═╡ 637745b4-3d94-4407-997f-cddfd953271c
using RadonKA, DiffImageRotation
# ╔═╡ a7a9946e-0013-4cfe-aaf7-0c19da075abd
using Noise
# ╔═╡ 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
# ╔═╡ 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) .* ((λ^2 .* fx.^2 .+ λ^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
# ╔═╡ 2f85a4d9-8a83-492e-b85e-3fc39270ddb3
md"# 1. Radon Transform
In this part you are going to investigate different properties of the Radon transforms which is the backbone of computed tomography (CT).
For this you are going to use the functions `radon` and `backproject`.
Read the documentation how those functions work.
Investigate the following behaviours:
* Which interval of angles is necessary to reconstruct the object? E.g. [0, π / 4], [π / 2, 2 π], ...
* How many angles do you need to reconstruct the object fully? 10, 20, 100, 1000? Can you find an equation how many you need?
* Show the results of your investigations. Discuss them.
* Apply the filtered backprojection to obtain a better reconstruction. Use a Fourier transform along the first dimension of the sinogram only (see `ft`) and multiply with a ramp filter in Fourier space (see `rr` to create 1D ramp). Then simply use `backproject` of the filtered sinogram. Compare this to `backproject_filtered`.
* Explain qualitatively why the filtered backprojection works and what it does. How does the filtered sinogram look like?
"
# ╔═╡ 32ad3932-8da3-47d4-aee2-8979702a9107
md"## Answers
TODO
"
# ╔═╡ 2a507cc6-e5d5-41a8-be05-cb83d499a8eb
begin
object = select_region(select_region(Float32.(testimage("resolution_test_512")), new_size=(110, 110),
center=(250, 400)), new_size=(200, 200))
object ./= maximum(object)
object .*= 0.001
end;
# ╔═╡ 0f4f81ba-49a9-45d8-a18a-4760730264bb
simshow(object)
# ╔═╡ 2b3702e7-cc20-456d-96d4-b92f24292ca1
angles1 = TODO
# ╔═╡ 0afb8c90-2852-4193-a177-fc0cb6be4238
sinogram1 = TODO
# ╔═╡ c55e0129-24f9-4dfa-8e90-486e58544c4e
simshow(sinogram1)
# ╔═╡ f4f73c87-9029-4a02-9d1b-56c089c1c36b
angles2 = TODO
# ╔═╡ ad93799c-19ee-4b71-a13d-6005ccad2842
sinogram2 = TODO
# ╔═╡ 188bd5c9-ca50-4a98-9c3a-ffa7aca3ea68
simshow(sinogram2)
# ╔═╡ 11588081-29c5-4a81-a18c-22bc996bdf50
object_blurry1 = TODO
# ╔═╡ 2d736e9e-0845-4a0b-904c-1a50fc20e49b
object_blurry2 = TODO
# ╔═╡ db9169dc-a7ee-463d-9132-6050bd4032b4
simshow(object_blurry1)
# ╔═╡ 0e6013eb-2b35-4c67-97cd-898542810a22
simshow(object_blurry2)
# ╔═╡ a008e4cd-1045-4fb1-89c3-8fbe285985b5
ramp = TODO
# ╔═╡ 1154a3b9-14cc-44f9-b3df-cc87b5a33048
sinogram_filtered = real(TODO);
# ╔═╡ b3cea98e-0818-40a2-85ad-7f6e4ee26be8
object_filtered = TODO
# ╔═╡ 6905d702-62e2-4786-9e10-22283d28c520
[simshow(object) simshow(object_blurry2) simshow(object_filtered)]
# ╔═╡ c6e88cc7-0d42-4a91-80bc-28991a77021b
md"# 2. Diffraction Tomography
In this part we are doing the same but with a wave optical forward model.
The theory behind the Born approximation and the reconstruction is provided on Moodle.
In diffraction tomography we measure the scattered field with object and without.
We illuminate the object from different directions with a plane wave.
The obtained diffraction patterns we reconstruct to obtain the refractive index distribution of the object.
In this case the object is a refractive index distribution. It represents the difference between the surround refractive index, which is 1 here.
* Which angles are enough to recover the whole image? Try the full range of $[0, 2\pi]$, but also a partial range.
* What happens if the refractive index different gets too large? What is the reason for the failure? Change the values of `object` for that. Show images for that.
* Also, what happens if you scale `Ly` to smaller or bigger values? Show also an image for that.
Bonus:
* Find the mistake why our method is not quantitative. (We do not know ourselves...). The values are not quite correct.
"
# ╔═╡ 8cb18a83-20d6-4936-88f6-e42d63f43f32
md"## Answers
TODO
"
# ╔═╡ 9d4da6fb-c4af-4461-b584-264cdd6951b2
extrema(object)
# ╔═╡ 7081437e-4ec2-4959-a5ad-18d6483b3adb
N = size(object, 1)
# ╔═╡ 44d6bdaa-b889-4634-9fcc-94f390142d0a
λ = 633e-9
# ╔═╡ 298fff75-0691-452e-86c3-1f907c9377a0
Ly = 100e-6
# ╔═╡ 83f5f49c-1415-4737-abf3-2f0e86e7e0a5
Lx = Ly / N * 1
# ╔═╡ 468b6dae-fa2b-454f-ba97-7ea64c6ab510
z = range(0, Ly, N)
# ╔═╡ 106c4fdc-6fe7-4416-9fe3-a82a69824cab
"""
diffraction_tomography(object, λ, Lx, Ly, z, N, angles)
"""
function diffraction_tomography(object, λ, Lx, Ly, z, N, angles)
out_scattered = zeros(ComplexF64, (N, length(angles)))
out_diffraction = zeros(ComplexF64, (N, length(angles)))
dz = z[2] - z[1]
beam = gaussian((size(object, 1),1), sigma=40)
for (i, θ) in enumerate(angles)
object_r = imrotate(object, .-θ)
diffraction_with_field = bpm(beam, λ, Lx, Ly, z, 1, amplitude_array=cis.(2π / λ * dz .* reshape(object_r, (N, 1, N))), paraxial=false)
diffraction_without_field = bpm(beam, λ, Lx, Ly, z, 1, paraxial=false)
out_scattered[:, i] .= diffraction_with_field[:, 1, end]
out_diffraction[:, i] .= diffraction_without_field[:, 1, end]
end
return out_scattered, out_diffraction
end
# ╔═╡ c00e27d4-a637-41f9-90aa-e2126e94350a
"""
diffraction_tomography_reconstruction(out_scattered, out_diffraction, λ, Lx, Ly, z, N, angles)
"""
function diffraction_tomography_reconstruction(out_scattered, out_diffraction, λ, Lx, Ly, z, N, angles)
out_ft = zeros(ComplexF64, (N, N))
repetitions = zeros(Int, (N, N))
n = 1
k = 2π / λ
# wave vectors
k⃗y = 2π * fftshift(fftfreq(N, inv(Ly / N)))
k⃗z = sqrt.(max.(0, k.^2 .- k⃗y.^2))
k⃗y = 2π * fftshift(fftfreq(N, inv(Ly / N)))
k⃗z = sqrt.(max.(0, k.^2 .- k⃗y.^2))
# wave vector spacing
dky = abs.(k⃗y[2] - k⃗y[1])
k⃗0y = k * cos.(angles)
k⃗0z = k * sin.(angles)
z0 = 0.5 * z[end]
us = out_scattered .- out_diffraction
for (i, θ) in enumerate(angles)
s0y, s0z = k⃗0z[i], k⃗0y[i]
s⃗iy = k⃗y .* cos(θ) .+ k⃗z .* sin(θ)
s⃗iz = - k⃗y .* sin(θ) .+ k⃗z .* cos(θ)
us_tilde = -1im .* 2 .* k⃗z .* exp.(.- 1im .* k⃗z .* z0) .* ft(us[:, i]) ./ (Ly / N)
ix = clamp.(round.(Int, (s⃗iy .- s0y) ./ dky) .+ N ÷ 2 .+ 1, 1, N)
iz = clamp.(round.(Int, (s⃗iz .- s0z) ./ dky) .+ N ÷ 2 .+ 1, 1, N)
for iix in 1:length(ix)
out_ft[ix[iix], iz[iix]] += us_tilde[iix]
repetitions[ix[iix], iz[iix]] += 1
end
end
out_ft .= out_ft ./ max.(repetitions, 1)
out = ift(out_ft)
n_out = @. real(sqrt((4 * π * (out) / k^2) + n^2))
return n_out, out
end
# ╔═╡ 68623fa1-756d-40dd-9943-074dbf5c30ef
angles_D1 = TODO
# ╔═╡ cd58b548-11c9-4d58-94e1-fc8f73e83b0b
angles_D2 = TODO
# ╔═╡ 8261983b-1908-4d64-84bc-54708e3c85b8
simshow(object)
# ╔═╡ 7e98ddae-b3ff-44d7-b664-3043691a97bf
@time out_scattered, out_diffraction = diffraction_tomography(object, λ, Lx, Ly, z, N, angles_D1);
# ╔═╡ a0f7ee6c-67fe-4931-8920-b648c4688136
@time out_scattered2, out_diffraction2 = diffraction_tomography(object, λ, Lx, Ly, z, N, angles_D2);
# ╔═╡ e313c079-a81e-491e-92b8-cc9682789150
n_reconstructed, out = diffraction_tomography_reconstruction(out_scattered, out_diffraction, λ, Lx, Ly, z, N, angles_D1);
# ╔═╡ 688206b9-95d7-4e8a-b1a6-1075b7c64055
n_reconstructed2, out2 = diffraction_tomography_reconstruction(out_scattered2, out_diffraction2, λ, Lx, Ly, z, N, angles_D2);
# ╔═╡ d42dbfa5-574b-41a3-8f78-9f80cc971b8f
heatmap(n_reconstructed)
# ╔═╡ d98c86f6-9082-40f1-9a55-aebe797e0247
heatmap(n_reconstructed2)
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
DiffImageRotation = "cb1f95eb-7c3a-45bc-9e18-5c07f1beaacd"
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"
Noise = "81d43f40-5267-43b7-ae1c-8b967f377efa"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
RadonKA = "86de8297-835b-47df-b249-c04e8db91db5"
SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
TestImages = "5e47fb64-e119-507b-a336-dd2b206d9990"
UrlDownload = "856ac37a-3032-4c1c-9122-f86d88358c8b"
[compat]
DiffImageRotation = "~0.3.0"
FFTW = "~1.8.0"
FileIO = "~1.16.2"
FourierTools = "~0.4.2"
ImageMagick = "~1.3.1"
ImageShow = "~0.3.8"
IndexFunArrays = "~0.2.7"
NDTools = "~0.5.3"
Noise = "~0.3.3"
Plots = "~1.40.1"
PlutoUI = "~0.7.58"
RadonKA = "~0.6.1"
SpecialFunctions = "~2.3.1"
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 = "1.10.3"
manifest_format = "2.0"
project_hash = "1802333b5bd811e63043b423acd10aa5c90bd3f0"
[[deps.AbstractFFTs]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "d92ad398961a3ed262d8bf04a1a2b8340f915fef"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.5.0"
weakdeps = ["ChainRulesCore", "Test"]
[deps.AbstractFFTs.extensions]
AbstractFFTsChainRulesCoreExt = "ChainRulesCore"
AbstractFFTsTestExt = "Test"
[[deps.AbstractNFFTs]]
deps = ["LinearAlgebra", "Printf"]
git-tree-sha1 = "292e21e99dedb8621c15f185b8fdb4260bb3c429"
uuid = "7f219486-4aa7-41d6-80a7-e08ef20ceed7"
version = "0.8.2"
[[deps.AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "0f748c81756f2e5e6854298f11ad8b2dfae6911a"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.3.0"
[[deps.Adapt]]
deps = ["LinearAlgebra", "Requires"]
git-tree-sha1 = "0fb305e0253fd4e833d486914367a2ee2c2e78d0"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "4.0.1"
weakdeps = ["StaticArrays"]
[deps.Adapt.extensions]
AdaptStaticArraysExt = "StaticArrays"
[[deps.ArgCheck]]
git-tree-sha1 = "a3a402a35a2f7e0b87828ccabbd5ebfbebe356b4"
uuid = "dce04be8-c92d-5529-be00-80e4d2c0e197"
version = "2.3.0"
[[deps.ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
version = "1.1.1"
[[deps.Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
[[deps.Atomix]]
deps = ["UnsafeAtomics"]
git-tree-sha1 = "c06a868224ecba914baa6942988e2f2aade419be"
uuid = "a9b6321e-bd34-4604-b9c9-b65b8de01458"
version = "0.1.0"
[[deps.AxisArrays]]
deps = ["Dates", "IntervalSets", "IterTools", "RangeArrays"]
git-tree-sha1 = "16351be62963a67ac4083f748fdb3cca58bfd52f"
uuid = "39de3d68-74b9-583c-8d2d-e117c070f3a9"
version = "0.4.7"
[[deps.BangBang]]
deps = ["Compat", "ConstructionBase", "InitialValues", "LinearAlgebra", "Requires", "Setfield", "Tables"]
git-tree-sha1 = "7aa7ad1682f3d5754e3491bb59b8103cae28e3a3"
uuid = "198e06fe-97b7-11e9-32a5-e1d131e6ad66"
version = "0.3.40"
[deps.BangBang.extensions]
BangBangChainRulesCoreExt = "ChainRulesCore"
BangBangDataFramesExt = "DataFrames"
BangBangStaticArraysExt = "StaticArrays"
BangBangStructArraysExt = "StructArrays"
BangBangTypedTablesExt = "TypedTables"
[deps.BangBang.weakdeps]
ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
TypedTables = "9d95f2ec-7b3d-5a63-8d20-e2491e220bb9"
[[deps.Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
[[deps.Baselet]]
git-tree-sha1 = "aebf55e6d7795e02ca500a689d326ac979aaf89e"
uuid = "9718e550-a3fa-408a-8086-8db961cd8217"
version = "0.1.1"
[[deps.BasicInterpolators]]
deps = ["LinearAlgebra", "Memoize", "Random"]
git-tree-sha1 = "3f7be532673fc4a22825e7884e9e0e876236b12a"
uuid = "26cce99e-4866-4b6d-ab74-862489e035e0"
version = "0.7.1"
[[deps.BitFlags]]
git-tree-sha1 = "2dc09997850d68179b69dafb58ae806167a32b1b"
uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35"
version = "0.1.8"
[[deps.Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9e2a6b69137e6969bab0152632dcb3bc108c8bdd"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+1"
[[deps.CEnum]]
git-tree-sha1 = "389ad5c84de1ae7cf0e28e381131c98ea87d54fc"
uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
version = "0.5.0"
[[deps.Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.1+1"
[[deps.ChainRulesCore]]
deps = ["Compat", "LinearAlgebra"]
git-tree-sha1 = "575cd02e080939a33b6df6c5853d14924c08e35b"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.23.0"
weakdeps = ["SparseArrays"]
[deps.ChainRulesCore.extensions]
ChainRulesCoreSparseArraysExt = "SparseArrays"
[[deps.CodecZlib]]
deps = ["TranscodingStreams", "Zlib_jll"]
git-tree-sha1 = "59939d8a997469ee05c4b4944560a820f9ba0d73"
uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
version = "0.7.4"
[[deps.ColorSchemes]]
deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"]
git-tree-sha1 = "67c1f244b991cad9b0aa4b7540fb758c2488b129"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.24.0"
[[deps.ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "eb7f0f8307f71fac7c606984ea5fb2817275d6e4"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.4"
[[deps.ColorVectorSpace]]
deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statistics", "TensorCore"]
git-tree-sha1 = "a1f44953f2382ebb937d60dafbe2deea4bd23249"
uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
version = "0.10.0"
weakdeps = ["SpecialFunctions"]
[deps.ColorVectorSpace.extensions]
SpecialFunctionsExt = "SpecialFunctions"
[[deps.Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.10"
[[deps.Compat]]
deps = ["TOML", "UUIDs"]
git-tree-sha1 = "c955881e3c981181362ae4088b35995446298b80"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "4.14.0"
weakdeps = ["Dates", "LinearAlgebra"]
[deps.Compat.extensions]
CompatLinearAlgebraExt = "LinearAlgebra"
[[deps.CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
version = "1.1.1+0"
[[deps.CompositionsBase]]
git-tree-sha1 = "802bb88cd69dfd1509f6670416bd4434015693ad"
uuid = "a33af91c-f02d-484b-be07-31d278c5ca2b"
version = "0.1.2"
[deps.CompositionsBase.extensions]
CompositionsBaseInverseFunctionsExt = "InverseFunctions"
[deps.CompositionsBase.weakdeps]
InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"
[[deps.ConcurrentUtilities]]
deps = ["Serialization", "Sockets"]
git-tree-sha1 = "9c4708e3ed2b799e6124b5673a712dda0b596a9b"
uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb"
version = "2.3.1"
[[deps.ConstructionBase]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "c53fc348ca4d40d7b371e71fd52251839080cbc9"
uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
version = "1.5.4"
weakdeps = ["IntervalSets", "StaticArrays"]
[deps.ConstructionBase.extensions]
ConstructionBaseIntervalSetsExt = "IntervalSets"
ConstructionBaseStaticArraysExt = "StaticArrays"
[[deps.ContextVariablesX]]
deps = ["Compat", "Logging", "UUIDs"]
git-tree-sha1 = "25cc3803f1030ab855e383129dcd3dc294e322cc"
uuid = "6add18c4-b38d-439d-96f6-d6bc489c04c5"
version = "0.1.3"
[[deps.Contour]]
git-tree-sha1 = "d05d9e7b7aedff4e5b51a029dced05cfb6125781"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.6.2"
[[deps.DataAPI]]
git-tree-sha1 = "abe83f3a2f1b857aac70ef8b269080af17764bbe"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.16.0"
[[deps.DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "1fb174f0d48fe7d142e1109a10636bc1d14f5ac2"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.17"
[[deps.DataValueInterfaces]]
git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
version = "1.0.0"
[[deps.Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
[[deps.DefineSingletons]]
git-tree-sha1 = "0fba8b706d0178b4dc7fd44a96a92382c9065c2c"
uuid = "244e2a9f-e319-4986-a169-4d1fe445cd52"
version = "0.1.2"
[[deps.DelimitedFiles]]
deps = ["Mmap"]
git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae"
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
version = "1.9.1"
[[deps.DiffImageRotation]]
deps = ["Atomix", "ChainRulesCore", "KernelAbstractions"]
git-tree-sha1 = "bb3efab67a0e5fee71d06d94290deabf806cd93e"
uuid = "cb1f95eb-7c3a-45bc-9e18-5c07f1beaacd"
version = "0.3.0"
[[deps.Distances]]
deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
git-tree-sha1 = "66c4c81f259586e8f002eacebc177e1fb06363b0"
uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
version = "0.10.11"
weakdeps = ["ChainRulesCore", "SparseArrays"]
[deps.Distances.extensions]
DistancesChainRulesCoreExt = "ChainRulesCore"
DistancesSparseArraysExt = "SparseArrays"
[[deps.Distributed]]
deps = ["Random", "Serialization", "Sockets"]
uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
[[deps.DocStringExtensions]]
deps = ["LibGit2"]
git-tree-sha1 = "2fb1e02f2b635d0845df5d7c167fec4dd739b00d"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.9.3"
[[deps.Downloads]]
deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
version = "1.6.0"
[[deps.EpollShim_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8e9441ee83492030ace98f9789a654a6d0b1f643"
uuid = "2702e6a9-849d-5ed8-8c21-79e8b8f9ee43"
version = "0.0.20230411+0"
[[deps.ExceptionUnwrapping]]
deps = ["Test"]
git-tree-sha1 = "dcb08a0d93ec0b1cdc4af184b26b591e9695423a"
uuid = "460bff9d-24e4-43bc-9d9f-a8973cb893f4"
version = "0.1.10"
[[deps.Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "4558ab818dcceaab612d1bb8c19cee87eda2b83c"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.5.0+0"
[[deps.FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.1"
[[deps.FFMPEG_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Pkg", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "74faea50c1d007c85837327f6775bea60b5492dd"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.4.2+2"
[[deps.FFTW]]
deps = ["AbstractFFTs", "FFTW_jll", "LinearAlgebra", "MKL_jll", "Preferences", "Reexport"]
git-tree-sha1 = "4820348781ae578893311153d69049a93d05f39d"
uuid = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
version = "1.8.0"
[[deps.FFTW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c6033cc3892d0ef5bb9cd29b7f2f0331ea5184ea"
uuid = "f5851436-0d7a-5f13-b9de-f02708fd171a"
version = "3.3.10+0"
[[deps.FLoops]]
deps = ["BangBang", "Compat", "FLoopsBase", "InitialValues", "JuliaVariables", "MLStyle", "Serialization", "Setfield", "Transducers"]
git-tree-sha1 = "ffb97765602e3cbe59a0589d237bf07f245a8576"
uuid = "cc61a311-1640-44b5-9fba-1b764f453329"
version = "0.2.1"
[[deps.FLoopsBase]]
deps = ["ContextVariablesX"]
git-tree-sha1 = "656f7a6859be8673bf1f35da5670246b923964f7"
uuid = "b9860ae5-e623-471e-878b-f6a53c775ea6"
version = "0.1.1"
[[deps.FileIO]]
deps = ["Pkg", "Requires", "UUIDs"]
git-tree-sha1 = "c5c28c245101bd59154f649e19b038d15901b5dc"
uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
version = "1.16.2"
[[deps.FileWatching]]
uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
[[deps.FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"
[[deps.Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.93+0"
[[deps.Format]]
git-tree-sha1 = "f3cf88025f6d03c194d73f5d13fee9004a108329"
uuid = "1fa38f19-a742-5d3f-a2b9-30dd87b9d5f8"
version = "1.3.6"
[[deps.FourierTools]]
deps = ["ChainRulesCore", "FFTW", "IndexFunArrays", "LinearAlgebra", "NDTools", "NFFT", "PaddedViews", "Reexport", "ShiftedArrays"]
git-tree-sha1 = "8967a9d259ab1c50e3b3abc6b77d3e3d829d2e6d"
uuid = "b18b359b-aebc-45ac-a139-9c0ccbb2871e"
version = "0.4.2"
[[deps.FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "d8db6a5a2fe1381c1ea4ef2cab7c69c2de7f9ea0"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.13.1+0"
[[deps.FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.10+0"
[[deps.Future]]
deps = ["Random"]
uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"
[[deps.GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
git-tree-sha1 = "ff38ba61beff76b8f4acad8ab0c97ef73bb670cb"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.3.9+0"
[[deps.GR]]
deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Preferences", "Printf", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "UUIDs", "p7zip_jll"]
git-tree-sha1 = "8e2d86e06ceb4580110d9e716be26658effc5bfd"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.72.8"
[[deps.GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "da121cbdc95b065da07fbb93638367737969693f"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.72.8+0"
[[deps.Gettext_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
version = "0.21.0+0"
[[deps.Ghostscript_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "43ba3d3c82c18d88471cfd2924931658838c9d8f"
uuid = "61579ee1-b43e-5ca0-a5da-69d92c66a64b"
version = "9.55.0+4"
[[deps.Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Zlib_jll"]
git-tree-sha1 = "e94c92c7bf4819685eb80186d51c43e71d4afa17"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.76.5+0"
[[deps.Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
version = "1.3.14+0"
[[deps.Grisu]]
git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
version = "1.0.2"
[[deps.HTTP]]
deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "ExceptionUnwrapping", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
git-tree-sha1 = "ac7b73d562b8f4287c3b67b4c66a5395a19c1ae8"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "1.10.2"
[[deps.HarfBuzz_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
version = "2.8.1+1"
[[deps.Hyperscript]]
deps = ["Test"]
git-tree-sha1 = "179267cfa5e712760cd43dcae385d7ea90cc25a4"
uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91"
version = "0.0.5"
[[deps.HypertextLiteral]]
deps = ["Tricks"]
git-tree-sha1 = "7134810b1afce04bbc1045ca1985fbe81ce17653"
uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
version = "0.9.5"
[[deps.IOCapture]]
deps = ["Logging", "Random"]
git-tree-sha1 = "8b72179abc660bfab5e28472e019392b97d0985c"
uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
version = "0.2.4"
[[deps.ImageAxes]]
deps = ["AxisArrays", "ImageBase", "ImageCore", "Reexport", "SimpleTraits"]
git-tree-sha1 = "2e4520d67b0cef90865b3ef727594d2a58e0e1f8"
uuid = "2803e5a7-5153-5ecf-9a86-9b4c37f5f5ac"
version = "0.6.11"
[[deps.ImageBase]]
deps = ["ImageCore", "Reexport"]
git-tree-sha1 = "eb49b82c172811fd2c86759fa0553a2221feb909"
uuid = "c817782e-172a-44cc-b673-b171935fbb9e"
version = "0.1.7"
[[deps.ImageCore]]
deps = ["ColorVectorSpace", "Colors", "FixedPointNumbers", "MappedArrays", "MosaicViews", "OffsetArrays", "PaddedViews", "PrecompileTools", "Reexport"]
git-tree-sha1 = "b2a7eaa169c13f5bcae8131a83bc30eff8f71be0"
uuid = "a09fc81d-aa75-5fe9-8630-4744c3626534"
version = "0.10.2"
[[deps.ImageIO]]
deps = ["FileIO", "IndirectArrays", "JpegTurbo", "LazyModules", "Netpbm", "OpenEXR", "PNGFiles", "QOI", "Sixel", "TiffImages", "UUIDs"]
git-tree-sha1 = "bca20b2f5d00c4fbc192c3212da8fa79f4688009"
uuid = "82e4d734-157c-48bb-816b-45c225c6df19"
version = "0.6.7"
[[deps.ImageMagick]]
deps = ["FileIO", "ImageCore", "ImageMagick_jll", "InteractiveUtils"]
git-tree-sha1 = "8e2eae13d144d545ef829324f1f0a5a4fe4340f3"
uuid = "6218d12a-5da1-5696-b52f-db25d2ecc6d1"
version = "1.3.1"
[[deps.ImageMagick_jll]]
deps = ["Artifacts", "Ghostscript_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "OpenJpeg_jll", "Pkg", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "8d2e786fd090199a91ecbf4a66d03aedd0fb24d4"
uuid = "c73af94c-d91f-53ed-93a7-00f77d67a9d7"
version = "6.9.11+4"