On the mapping of extended sources with nonlinear correlation antennas

Drane, Charles J.; Parrent, George B.

doi:10.1109/tap.1962.1137838

Cited by 9 publications

(3 citation statements)

References 6 publications

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“….l 1 ; l 2 ; / is similar to the coherence function of a source or object discussed by Drane and Parrent (1962) and Beran and Parrent (1964 It can be shown by using the Schwarz inequality that 0 Ä j N .l 1 ; l 2 ; /j Ä 1. The extreme values of 0 and 1 correspond to the cases of complete incoherence and complete coherence, respectively.…”

Section: Source Coherencementioning

confidence: 79%

“…Fully coherent sources are not amenable to synthesis imaging using the van CittertZernike principle and thus do not fall within the area of principal concern of this book. Further material on coherence and partial coherence can be found, for example, in Beran and Parrent (1964), Born and Wolf (1999), Drane and Parrent (1962), Wolf (1965, 1995), MacPhie (1964), andGoodman (1985).…”

Section: Scattering and The Propagation Of Coherencementioning

confidence: 99%

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Van Cittert–Zernike Theorem, Spatial Coherence, and Scattering

Thompson

Moran

Swenson

2017

Astronomy and Astrophysics Library

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This chapter is concerned with the van Cittert-Zernike theorem, including an examination of the assumptions involved in its derivation, the requirement of spatial incoherence of a source, and the interferometer response to a coherent source. Some optical terminology is used, for example, mutual coherence, which includes complex visibility. There is also a brief discussion of some aspects of scattering by irregularities in the propagation medium. Much of the development of the theory of coherence and similar concepts of electromagnetic radiation is to be found in the literature of optics. The terminology is sometimes different from that which has evolved in radio interferometry, but many of the physical situations are similar or identical. However, in spite of the similarity, the literature shows that in the early development of radio astronomy, the optical experience was hardly ever mentioned, an exception being the reference by Bracewell (1958) to Zernike (1938) for the concept of the complex degree of coherence. The van Cittert-Zernike theorem contains a simple formalism that includes the basic principles of correlation in electromagnetic fields. Van Cittert-Zernike TheoremWe showed in Chaps. 2 and 3 that the cross-correlation of the signals received in spaced antennas can be used to form an image of the intensity distribution of a distant cosmic source through a Fourier transform relationship. This result is a form of the van Cittert-Zernike theorem, which originated in optics. The basis for the theorem is a study published by van Cittert in 1934 and followed a few years later by a simpler derivation by Zernike. A description of the result established by van Cittert and Zernike is given by Born and Wolf (1999, Chap. 10). The original form of the result does not specifically refer to the Fourier transform relationship between intensity and mutual coherence but is essentially as follows.

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Section: Source Coherencementioning

confidence: 79%

Section: Scattering and The Propagation Of Coherencementioning

confidence: 99%

Van Cittert–Zernike Theorem, Spatial Coherence, and Scattering

Thompson

Moran

Swenson

2017

Astronomy and Astrophysics Library

View full text Add to dashboard Cite

show abstract

“…In Equation (28) in Chapter 3 it was indicated that a coherent quasi-monochromatic source distribution has the following mutual coherence function,…”

Section: Cross-correlation System Outputs For Coherent and Incoherentmentioning

confidence: 99%