File:Van Cittert-Zernike.webm
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Van_Cittert-Zernike.webm (WebM audio/video file, VP8, length 9.2 s, 480 × 480 pixels, 1.17 Mbps overall, file size: 1.28 MB)
Captions
Captions
van Cittert–Zernike theorem: an incoherent source seen from far away appears (spatially) coherent.
Summary
[edit]| Description |
English: The van Cittert–Zernike theorem is usually phrased in terms of fringe visibility, but a simpler way to look at it is that a incoherent source seen from far away enough will look like a point source (i.e. spatially coherent). |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1674801693228417031?s=20 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 13.1 code
[edit]c = 10^8;
w[x0_, y0_, t_, \[Omega]0_, \[Sigma]_, \[Phi]0_] :=
E^(-(t^2/(2 \[Sigma]^2)))*E^(-I \[Omega]0 t)*E^(I \[Phi]0)*E^(
I \[Omega]0/c Sqrt[(x - x0)^2 + (y - y0)^2])/
Sqrt[(x - x0)^2 + (y -
y0)^2](*HankelH1[1,\[Omega]0/cSqrt[(x-x0)^2+(y-y0)^2]]*)
\[Omega]0 = 10^10;
p1 = {-0.2, 0};
p2 = {0.2, -0.05};
p3 = {0.1, 0.15};
\[Alpha]1 = 1; \[Alpha]2 = Sqrt[2.]; \[Alpha]3 = Sqrt[3.];
k0 = \[Omega]0/c; \[Lambda]0 = (2 \[Pi])/k0;
plot0[\[Tau]_, range_, shift_] := ContourPlot[{
Re[w[p1[[1]], p1[[2]], \[Tau], \[Alpha]1*\[Omega]0, 10^3, 0]] == 0
,
Re[w[p2[[1]], p2[[2]], \[Tau], \[Alpha]2*\[Omega]0, 10^3, 0]] == 0
,
Re[w[p3[[1]], p3[[2]], \[Tau], \[Alpha]3*\[Omega]0, 10^3, 0]] == 0
}, {x, -range, range}, {y, -range, range},
ContourStyle -> {LightGray, LightGray, LightGray, Black},
Epilog -> {Black, Disk[p1, 0.01], Disk[p2, 0.01], Disk[p3, 0.01]},
PlotPoints -> 50, Frame -> False]
frame0 = plot0[0, 0.5, 0];
sinstep[t_] := Sin[\[Pi]/2 t]^2
plot1[\[Tau]_, range_, shift_, t_] := ContourPlot[{
Re[w[p1[[1]], p1[[2]], \[Tau], \[Alpha]1*\[Omega]0, 10^3, 0]] == 0
,
Re[w[p2[[1]], p2[[2]], \[Tau], \[Alpha]2*\[Omega]0, 10^3, 0]] == 0
,
Re[w[p3[[1]], p3[[2]], \[Tau], \[Alpha]3*\[Omega]0, 10^3, 0]] == 0
,
Re[w[p1[[1]], p1[[2]], \[Tau], \[Alpha]1*\[Omega]0, 10^3, 0] +
w[p2[[1]], p2[[2]], \[Tau], \[Alpha]2*\[Omega]0, 10^3, 0] +
w[p3[[1]], p3[[2]], \[Tau], \[Alpha]3*\[Omega]0, 10^3, 0]] == 0
}, {x, -range, range}, {y, -range, range},
ContourStyle -> {LightGray, LightGray, LightGray,
Directive[Opacity[sinstep[t]], Black]},
Epilog -> {Black, Disk[p1, 0.01], Disk[p2, 0.01], Disk[p3, 0.01]},
PlotPoints -> 50, Frame -> False]
frames1 = Table[plot1[0, 0.5, 0, t], {t, 0, 1, 1/20.}];
plot2[\[Tau]_, range_, shift_] := ContourPlot[{
Re[w[p1[[1]], p1[[2]], \[Tau], \[Alpha]1*\[Omega]0, 10^3, 0]] == 0
,
Re[w[p2[[1]], p2[[2]], \[Tau], \[Alpha]2*\[Omega]0, 10^3, 0]] == 0
,
Re[w[p3[[1]], p3[[2]], \[Tau], \[Alpha]3*\[Omega]0, 10^3, 0]] == 0
,
Re[w[p1[[1]], p1[[2]], \[Tau], \[Alpha]1*\[Omega]0, 10^3, 0] +
w[p2[[1]], p2[[2]], \[Tau], \[Alpha]2*\[Omega]0, 10^3, 0] +
w[p3[[1]], p3[[2]], \[Tau], \[Alpha]3*\[Omega]0, 10^3, 0]] == 0
}, {x, -range, range}, {y, -range + shift, range + shift},
ContourStyle -> {LightGray, LightGray, LightGray, Black},
Epilog -> {Black, Disk[p1, 0.01], Disk[p2, 0.01], Disk[p3, 0.01]},
PlotPoints -> 50, Frame -> False]
frames2 = Table[plot2[0, 0.5, 5*sinstep[t]], {t, 0, 1, 1/50}];
ListAnimate[Join[Table[frame0, {5}], frames1, Table[frames1[[-1]], {5}], frames2,
Table[frames2[[-1]], {10}]]]
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following license:
 
|
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
|
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 10:49, 3 July 2023 | 9.2 s, 480 × 480 (1.28 MB) | Berto (talk | contribs) | Uploaded own work with UploadWizard |
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