We present configurations of shaped pupil coronagraphs optimized for a realistic telescope to directly detect extrasolar giant planets in the mid-IR wavelengths. This study is linked to the development of the coronagraphic instrument aboard SPICA (SPace Infrared telescope for Cosmology and Astrophysics). We made a systematic assessment of the performance of the “checkerboard” and “concentric ring” masks, introducing a large central obstruction (C.O.) due to a secondary mirror and its related support spiders. With a small secondary mirror, we also propose a modification to the original symmetrical checkerboard apodization, which enables us to achieve a $10^{-7}$ contrast level at $4.0\ \lambda/D$. The transmission through the optimal binary masks exhibits abrupt increases and plateaus as the inner working angle (IWA) is increased. We attribute these properties of binary apodization function to the existence of threshold IWAs that allow large openings in the pupil.