On the uniqueness of image reconstruction from the amplitude of radiointerferometric response

Details On the uniqueness of image reconstruction from the amplitude of radiointerferometric response On the uniqueness of image reconstruction from the amplitude of radiointerferometric response

May 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983ap%26ss..92...31f&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 92, no. 1, May 1983, p. 31-36.

Mathematics

2

Image Reconstruction, Radio Interferometers, Uniqueness Theorem, Very Long Base Interferometry, Amplitudes, Existence Theorems, Fourier Transformation, Functions (Mathematics), Point Sources, Visibility

Scientific paper

A theorem providing the basis for the reconstruction of the radio image of a source from the modulus of the visibility function is proved. The result explains the efficiency of various numerical methods of image reconstruction that use only amplitude data. The theorem is a pure existence theorem; it does not make it possible to produce an algorithm for reconstructing the brightness distribution from the modulus of the visibility function. It proves only the possibility in principle of such a procedure for sources whose brightness distribution is physically reasonable. It is noted that, from a purely theoretical viewpoint, amplitude measurements give exhaustive information about the structure of the source; this is because, in astrophysics, nonuniqueness owing to translations and reflections in nonessential. Phase information, however, is necessary if a high-quality 'true' radio map of the source is required.

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