Traditional coronagraph design is reviewed and extended to the case of arbitrary pupil geometries with adaptive optics (AO). By selecting a desired focal plane occulting mask and specifying the expected Strehl ratio achieved by the AO system, the design for a matched Lyot stop is given. The outline of the optimum Lyot stop is derived using general considerations of the residual halo from an on-axis source, as well as by maximizing the signal-to-noise ratio. A continuous transmission variant of the optimum Lyot stop is also found by means of a heuristic argument. It is suggested that essentially the same result may be found using a matched-filter analog from signal processing theory. The resulting Lyot stops for multi-segment telescope apertures can be quite unexpected, and a case with six circular segments is considered as an example.
Johanan L. Codona, Johanan L. Codona,
"Stellar coronagraphs for telescopes with arbitrary pupils", Proc. SPIE 5169, Astronomical Adaptive Optics Systems and Applications, (24 December 2003); doi: 10.1117/12.530013; https://doi.org/10.1117/12.530013