ds. Unified Survey of Fourier Synthesis Methodologies.pdfVIP

Astronomical Data Analysis Software and Systems VI ASP Conference Series, Vol. 125, 1997 Gareth Hunt and H. E. Payne, eds. Unified Survey of Fourier Synthesis Methodologies P. Mar´echal, E. Anterrieu, and A. Lannes Laboratoire d’Astrophysique and CERFACS, Observatoire ´ Midi-Pyr´en´ees, 14, Avenue Edouard Belin F-31400 Toulouse (France) Abstract. This paper deals with theoretical and practical results on aperture synthesis. Full attention is devoted to the Fourier synthesis oper- ation, which proves to be the central issue with regard to the global prob- lem. Different regularization techniques are shown to derive from a unique principle: the Principle of Maximum Entropy on the Mean (PMEM). This is the case for WIPE, as well as for the traditional Maximum Entropy Method (and for some others). In order to compare the performances of different regularizers, some numerical simulations are presented. 1. Introduction to Aperture Synthesis Let u ≡ u(j,k) denote the spatial frequency corresponding to the baseline (j,k) of the interferometric device, and let (j ) be the aberration phase term of pupil element j . The central problem is to reconstruct both the brightness distri- bution φ (of some object) and the pupil phase function , by using as data complex-visibility measurements of the form V (u(j,k)). The latter are related to φ and by the equation V (u(j,k)) = exp iβ (u(j,k)) φ(u(j,k)), in which β (u(j,k)) := (j ) − (k) and φ is the Fourier transform of φ. Solving for φ (assuming that β is known) is a Fourier synthesis operation, while solving for β corresponds to a phase calibration operation. T