Shaped and apodized apertures for direct imaging of extra solar planets

In this communication, we analyze the possibility of detecting exoplanets using shaped and apodized apertures alone (without coronagraphy) for the case of a perfect telescope operated in space. In a first section, after a brief introduction to the theory of diffraction and the determination of several useful parameters, we show that the effects of shaped and apodized aperture can be presented in an unified manner, making use of the Radon transform of the aperture of the telescope. This permits a simple comparison of the techniques of apodization and aperture shaping between them. An illustration of this approach is made for a few apertures. In a second section, we introduce the semi-classical theory of photodetection. Using simplificative assumptions, we derive signal-to-noise ratio (SNR) expressions and draw the corresponding curves for an experiment using a circular telescope apodized by a prolate spheroidal function. We found that for given condition there is an apodization that can optimize the SNR. This apodization is generally a very strong one.