Relaxing the sensitivity of nuller coronagraphs to finite stellar diameters using apodization

Nuller coronagraphs such as the Achromatic-Interfero-Coronagraph (AIC) can perfectly cancel the starlight by destructively interfering it with itself, if the star is unresolved and exactly on-axis. Small pointing errors as well as the finite stellar diameter of the targeted star may however greatly degrade the performance of this type of coronagraph. Observed at 600nm with an AIC behind a 10 m telescope, the Sun at 10 pc would present an apparent angular diameter of 0.001" that would induce a star-leakage of 10(-6) times the maximum intensity of the star at 0.1". The expected flux ratio between a Sun-like star and an Earth-like planet is however much lower (10(-10) in the visible). We show through an analytical formalism that an apodized nuller coronagraph (ANC) can achieve planet detections with much higher contrasts. Expressions of the local contrast ratio and of the signal-to-noise ratio are derived. We first use for demonstrative purposes Sonine profiles and spheroidal prolate profiles. Concentric ring profiles, obtained through a numerical optimization, are also presented. The efficiency of these 3 types of apodizations is discussed.