Designing asymmetric and branched petals for planet-finding occulters

One of the proposed methods for finding small extrasolar planets is through use of an occulter, a spacecraft which flies in formation with a space-based telescope to block the light from a star, while leaving nearby planets unaffected. This is accomplished by placing the occulter far enough from the telescope to give it a small angular size, and by carefully choosing the shape to strongly suppress the starlight at the telescope aperture. For most designs, this shape takes the form of a number of bilaterally-symmetric structures called petals, arrayed about a circular central disk. In this paper, we show that the necessary number of petals may be reduced by the introduction of an asymmetry in the petal shape, and describe a a general procedure for producing such a shape by optimization for any occulter with petals. In addition, we show that permitting openings within each petal allows a number of additional modifications to be made without affecting the suppression.