  In the context of high dynamic range imaging, this study presents a
breakthrough for the understanding of Apodized Pupil Lyot Coronagraphs, making
them available for arbitrary aperture shapes. These new solutions find
immediate application in current, ground-based coronagraphic studies (Gemini,
VLT) and in existing instruments (AEOS Lyot Project). They also offer the
possiblity of a search for an on-axis design for TPF. The unobstructed aperture
case has already been solved by Aime et al. (2002) and Soummer et al. (2003).
Analytical solutions with identical properties exist in the general case and,
in particular, for centrally obscured apertures. Chromatic effects can be
mitigated with a numerical optimization. The combination of analytical and
numerical solutions enables the study of the complete parameter space (central
obstruction, apodization throughput, mask size, bandwidth, and Lyot stop size).
