Fig. 1. Strehl ratio (solid curve) as a function of the core size. The approximations given by Eq. (6) (dotted curve) and Eq. (7) (short dashed-dotted curve) are also shown. Note that the latter is indistinguishable from the exact one. The Strehl ratio limit by Sales and Morris (dash-dotted curve) and by the parabolic approximation (dash-dot-dotted curve) are also shown for comparison. Finally, the peak-to-sidelobe ratio (dashed curve) for 0-π filters is shown in the secondary axis.

Fig. 2. Amplitude PSF for a clear pupil of radius 1, i.e., the first term of Eq. (9) (dashed curve), which acts as a reference. The second term of Eq. (9) is shown for t=−1 (solid curve) and t=0.5 (dotted curve). For any t value, the first zero of the PSF is the point where its corresponding second term equals the reference.

Fig. 3. Amplitude PSF for a clear pupil of radius 1, i.e., the first term of Eq. (10) (dashed curve). The second term of Eq. (10) is shown for two-zone filters of radius ρ2 (dash-dotted curve) and ρ1b (solid curve), and for a three-zone filter of radii ρ1 and ρ2 (dotted curve).

Fig. 4. Strehl ratio as a function of the core size for two-zone phase filters with a different phase difference: π/2 (circles), 3π/4 filters (triangles), 7π/8 filters (crosses), 15π/16 (squares) and π (solid curve).