Rectangular-Mask Coronagraphs for High-Contrast Imaging
  We present yet another new family of masks for high-contrast imaging as required for the to-be-built terrestrial planet finder space telescope. The ``best'' design involves a square entrance pupil having a 4-vane spider, a square image-plane mask containing a plus-sign shaped occulter to block the starlight inside 0.6 lambda/D, and a Lyot-plane mask consisting of a rectangular array of rectangular opennings. Using Fraunhofer analysis, we show that the optical system can image a planet 10^{-10} times as bright as an on-axis star in four rectangular regions given by {(xi,zeta): 1.4 < | xi | < 20, 1.4 < | zeta | < 20}.   Since the design involves an image plane mask, pointing error is an issue. We show that the design can tolerate pointing errors of about 0.05 lambda/D.   The inclusion of a 4-vane spider in the entrance pupil provides the possibility to build a mirror-only on-axis system thereby greatly reducing the negative effects of polarization.   Each of the masks can be realized as two masks consisting of stripes of opaque material with the stripes oriented at right angles to each other. We call these striped masks barcode masks. We show that it is sufficient for the barcode masks by themselves to provide 10^{-5} contrast. This then guarantees that the full system will provide the required 10^{-10} contrast. 
Robert J. Vanderbei, N. Jeremy Kasdin, David N. Spergel