Optimized shaped pupil masks for pupil with obscuration

The main components of the SPICA coronagraphic instrument have initially been bar-code apodizing masks, i.e. shaped pupils optimized in one dimension. Their free-standing designs make them manufacturable without a glass substrate, which implies an absolute achromaticity and no additional wavefront errors. However, shaped pupils can now be optimized in two dimensions and can thus take full advantage of the geometry of any arbitrary aperture, in particular obstructed apertures such as SPICA's. Hence, 2D shaped pupils often have higher throughputs while offering the same angular resolutions and contrast. Alternatively, better resolutions or contrast can be obtained for the same throughput. Although some of these new masks are free-standing, this property cannot be constrained if the optimization problem has to remain convex linear. We propose to address this issue in different ways, and we present here examples of freestanding masks for a variety of contrasts, and inner working angles. Moreover, in all other coronagraphic instruments, contrast smaller than 10-5 can only be obtained if a dedicated adaptive optics system uses one or several deformable mirrors to compensate for wavefront aberrations. The finite number of actuators sets the size of the angular area in which quasi-static speckles can be corrected. This puts a natural limit on the outer working angle for which the shaped pupils are designed. The limited number of actuators is also responsible for an additional diffracted energy, or quilting orders, that can prevent faint companions to be detected. This effect can and must be taken into account in the optimization process. Finally, shaped pupils can be computed for a given nominal phase aberration pattern in the pupil plane, although the solutions depend in this case on the observation wavelength. We illustrate this possibility by optimizing an apodizer for the James Webb space telescope, and by testing its chromaticity and its robustness to phase changes.

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