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 intensity distribution 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 equal
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| - Van Cittert–Zernike-theorema (nl)
- Van Cittert–Zernike theorem (en)
- 范西特-泽尼克定理 (zh)
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| - Het Van Cittert–Zernike-theorema is een stelling uit de fysische optica waarmee bewezen wordt dat de coherentie van straling uit een verre, monochromatische bron gelijk is aan de Fouriertransformatie van de intensiteitsverdeling van de bron. Pieter Hendrik van Cittert bewees het theorema in 1934.Frits Zernike vond in 1938 een eenvoudiger afleiding zodat de stelling als het Van Cittert–Zernike-theorema bekendstaat. Met dit theorema is de gedeeltelijke ruimtelijke coherentie van straling te berekenen. Het is van belang voor apertuursynthese in de radioastronomie, adaptieve optiek van telescopen, lasers en vrije-elektronenlasers als gedeeltelijk coherente stralingsbronnen. (nl)
- 范西特-泽尼克定理是相干性理论中的一个公式，它研究的是单色扩展光源光场的空间相干性。它表明了在一定条件下，一个远距离的非相干源共有相干方程的傅里叶变换等于它的复合能见度。这说明了一个不相干源的波前会在远距离相干地出现。如果我们在一个源前测量波前，我们的测量会被周围的源所主导。如果我们在远离该源的情况下做同样的测试，我们测量则不会被某一个源所主导，两个源几乎等量地对波前产生影响。 原因可以简单地被形象化，就像往一个平静的池塘内扔两块石头。在湖心附近，由两个石头带来的干扰非常复杂。当干扰传播至池塘边缘时，波会变得平滑并且看起来几乎是圆形的。 定理在1934年由范西特（P. H. van Cittert）得出，1938年泽尼克（Frits Zernike）做出了简略证明。 (zh)
- 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 intensity distribution 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 equal (en)
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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 intensity distribution 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. (en)
- Het Van Cittert–Zernike-theorema is een stelling uit de fysische optica waarmee bewezen wordt dat de coherentie van straling uit een verre, monochromatische bron gelijk is aan de Fouriertransformatie van de intensiteitsverdeling van de bron. Pieter Hendrik van Cittert bewees het theorema in 1934.Frits Zernike vond in 1938 een eenvoudiger afleiding zodat de stelling als het Van Cittert–Zernike-theorema bekendstaat. Met dit theorema is de gedeeltelijke ruimtelijke coherentie van straling te berekenen. Het is van belang voor apertuursynthese in de radioastronomie, adaptieve optiek van telescopen, lasers en vrije-elektronenlasers als gedeeltelijk coherente stralingsbronnen. (nl)
- 范西特-泽尼克定理是相干性理论中的一个公式，它研究的是单色扩展光源光场的空间相干性。它表明了在一定条件下，一个远距离的非相干源共有相干方程的傅里叶变换等于它的复合能见度。这说明了一个不相干源的波前会在远距离相干地出现。如果我们在一个源前测量波前，我们的测量会被周围的源所主导。如果我们在远离该源的情况下做同样的测试，我们测量则不会被某一个源所主导，两个源几乎等量地对波前产生影响。 原因可以简单地被形象化，就像往一个平静的池塘内扔两块石头。在湖心附近，由两个石头带来的干扰非常复杂。当干扰传播至池塘边缘时，波会变得平滑并且看起来几乎是圆形的。 定理在1934年由范西特（P. H. van Cittert）得出，1938年泽尼克（Frits Zernike）做出了简略证明。 (zh)
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