Radon approach to shaped and apodized apertures for imaging exoplanets

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.