A&A 434, 785-794 (2005)
DOI: 10.1051/0004-6361:20042311

Radon approach to shaped and apodized apertures for imaging exoplanets

C. Aime

UMR 6525 Laboratoire Universitaire d'Astrophysique de Nice, Université de Nice Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 2, France
    e-mail: Claude.Aime@unice.fr

(Received 3 November 2004 / Accepted 10 December 2004)

Abstract
In this paper, we present a new approach to the study of shaped and apodized apertures for the detection of exoplanets. It is based on a Radon transform of the telescope aperture and makes it possible to present the effects of shaped and apodized apertures in a unified manner for an objective comparison between them. An illustration of this approach is made for a few apertures. Our conclusion favors the apodized apertures. The approach also permits us to obtain new results. In a second part of the paper, we derive expressions for the signal-to-noise ratio (SNR) of an experiment using an apodized aperture and draw the corresponding curves for the example of a circular telescope apodized by a prolate spheroidal function. We found that a very marked improvement of the SNR can be obtained using apodization techniques. There is an apodization that optimizes the SNR for a given observation; this apodization is generally very strong. The analysis is made for the case of a perfect telescope operated in space.

Key words: techniques: high angular resolution -- instrumentation: high angular resolution -- telescopes

© ESO 2005