On the Simulation of Complex Visibilities in Imaging Radiometry by Aperture Synthesis

The basic observables of an imaging interferometer by aperture synthesis are the complex visibilities. Under some conditions, they can be simulated with the aid of the van Cittert- Zernike theorem. However, owing to underlying assumptions, some important effects that may alter them cannot be taken into account. This paper is devoted to the numerical simulation of complex visibilities without any reference to the van Cittert-Zernike theorem, in such a way that these effects can be taken into account. The emission from an extended source is modeled using a linear superposition of random waves emitted by a collection of point sources, which are all assumed to behave like black bodies at thermal equilibrium. These random waves are numerically generated with the aid of white noises filtered in such a way that their power spectral densities follow the shape of Planck distributions at the temperature of the point sources over a wide range of frequencies. The radio signal is then transported to the antennas, where the voltage patterns are taken into account as well as the filters response of the bandpass receivers. It is, therefore, sent to the correlator unit for being cross-correlated. From emission to correlation, perturbing effects can be introduced at any time. To illustrate this modeling method, numerical simulations are carried out in the L-band around 1413.5 MHz in reference to the SMOS-next project led by the French Space Agency. The results are discussed and compared with the estimates provided by the van Cittert-Zernike theorem. Owing to the amount of calculations to be performed, massive parallel architectures like that found in GPU have been required.