Reducing star leakage with a nuller coronagraph

Abstract

Aims. Our objective is to test the improvement of the detection capabilities of a nuller coronagraph when it is coupled to an apodizer. We call this instrument an apodized nuller coronagraph (ANC). Methods. With the usual Fourier optics formalism we first derive the analytical expression of the intensity distribution for an off-axis point-like source in the aperture and the focal plane of an ANC. Then the star leakage is obtained by integration of this response over the angular extension of the star. In this process are included the star’s angular diameter, the apodization strength and the diameter of the telescope. Eventually we consider an application to the specific case of Sonine apodization. Results. From this analytical approach we obtain expressions of the contrast and signal-to-noise ratio for the direct detection of an exoplanet. These expressions involving instrumental parameters allow one to optimize the required minimum telescope’s diameter and apodization strength with respect to the detection of a given target in spite of star leakage. We show that the direct detection of an exoplanet in a solar-like system can be obtained with a nuller coronagraph as soon as the aperture is sufficiently apodized, although the energy throughput of the system is reduced. For a system at 10 pc, an 8-m class telescope appears necessary to detect an exo-Earth, while no larger than a 2-m class telescope is required for an exo-Jupiter.