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Most (but not all) coronagraphs are derived from the Lyot coronronagraph design originally developped for observing the solar corona. In this type of coronagraph, starlight rejection is achieved by the combination of an occulting focal plane mask and a pupil plane stop, the Lyot stop.
In a Lyot coronagraph, the telescope pupil and the focal plane mask are not perfectly fitted one for another, resulting in stellar leaks which are often unacceptably high. Lyot's original design has been improved in many recent coronagraph designs. As shown in the figure, this has been achieved by either finding a good "fit" between the pupil and focal plane masks with amplitude apodization (light green area in the lower right of the figure), or introducing phase in the focal plane mask (light blue area in the lower left of the figure).
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