Van Cittert–Zernike theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-31

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Van_Cittert%E2%80%93Zernike_theorem


00:01:53 1 Statement of the theorem
00:04:07 2 The mutual coherence function
00:07:05 3 Proof of the theorem
00:35:58 4 Assumptions of the theorem
00:36:24 4.1 Incoherence of the source
00:42:00 4.2 Distance to the source
00:43:59 4.3 Angular size of the source
00:46:15 4.4 Quasi-monochromatic waves
00:48:18 4.5 Two-dimensional source
00:49:00 4.6 Homogeneity of the medium
00:50:16 5 Hopkins' formula
00:54:08 6 Applications of the theorem
00:54:17 6.1 Aperture synthesis
00:56:04 6.2 Adaptive optics
00:57:38 6.3 Free-electron laser
00:57:56 7 See also



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SUMMARY
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The Van Cittert–Zernike theorem, named after physicists Pieter Hendrik van Cittert and Frits Zernike, is a formula in coherence theory that states that under certain conditions the Fourier transform of the mutual coherence function of a distant, incoherent source is equal to its complex visibility.  This implies that the wavefront from an incoherent source will appear mostly coherent at large distances.  Intuitively, this can be understood by considering the wavefronts created by two incoherent sources.  If we measure the wavefront immediately in front of one of the sources, our measurement will be dominated by the nearby source.  If we make the same measurement far from the sources, our measurement will no longer be dominated by a single source; both sources will contribute almost equally to the wavefront at large distances.
This reasoning can be easily visualized by dropping two stones in the center of a calm pond.  Near the center of the pond, the disturbance created by the two stones will be very complicated.  As the disturbance propagates towards the edge of the pond, however, the waves will smooth out and will appear to be nearly circular.
The van Cittert–Zernike theorem has important implications for radio astronomy.  With the exception of pulsars and masers, all astronomical sources are spatially incoherent.  Nevertheless, because they are observed at distances large enough to satisfy the van Cittert–Zernike theorem, these objects exhibit a non-zero degree of coherence at different points in the imaging plane.  By measuring the degree of coherence at different points in the imaging plane (the so-called "visibility function") of an astronomical object, a radio astronomer can thereby reconstruct the source's brightness distribution and make a two-dimensional map of the source's appearance.