Imaging with hypertelescopes: a simple modal approach
Université de Nice Sophia Antipolis, Centre National de la Recherche Scientifique, UMR 6525 H. Fizeau, Observatoire de la Côte d'Azur, Campus Valrose, 06108 Nice Cedex 2, France e-mail: Claude.Aime@unice.fr
Received:
12
September
2007
Accepted:
18
February
2008
Aims. We give a simple analysis of imaging with hypertelescopes, a technique proposed by Labeyrie to produce snapshot images using arrays of telescopes. The approach is modal: we describe the transformations induced by the densification onto a sinusoidal decomposition of the focal image instead of the usual point spread function approach.
Methods. We first express the image formed at the focus of a diluted array of apertures as the product
of the diffraction pattern of the
elementary apertures 
by the object-dependent
interference term 
between all apertures. The
interference term, which can be written in the form of a Fourier
Series for an extremely diluted array, produces replications of the object, which makes observing the image difficult. We express the focal image after the densification using the approach
of Tallon and Tallon-Bosc.
Results. The result is very simple for an extremely diluted array. We show that the focal
image in a periscopic densification of the array can be written as
, where γ is the factor of
densification. There is a dilatation of the interference term
while the diffraction term is unchanged. After de-zooming, the
image can be written as 
, an expression which clearly indicates that the final image corresponds to the center of the Fizeau
image intensified by 
. The imaging limitations of hypertelescopes are
therefore those of the original configuration. The effect of the
suppression of image replications is illustrated in a numerical
simulation for a fully redundant configuration and a non-redundant one.
Key words: instrumentation: interferometers / instrumentation: high angular resolution / telescopes
© ESO, 2008