File:Van Cittert-Zernike.webm

This is a file from the Wikimedia Commons
From English Wikipedia @ Freddythechick
The media handler extension for this file format is missing. Advanced media features may not work unless the file is viewed at Wikimedia Commons.

Van_Cittert-Zernike.webm ‎(file size: 1.28 MB, MIME type: video/webm)

Summary

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

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

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero 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.

Captions

van Cittert–Zernike theorem: an incoherent source seen from far away appears (spatially) coherent.

Items portrayed in this file

depicts

field

coherence

inception

30 June 2023

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current11:49, 3 July 2023Thumbnail for version as of 11:49, 3 July 2023 (1.28 MB)wikimediacommons>BertoUploaded own work with UploadWizard

The following page uses this file:

Retrieved from "https://enwiki.freddythechick.net/wiki/File:Van_Cittert-Zernike.webm"