In the first paper in this series, we described the principle of a coronagr
aph utilizing a four-quadrant phase mask and the results of numerical simul
ations obtained in the perfect case. In this second paper, we performed add
itional numerical simulations to assess in more detail the performances and
limitations of this coronagraph under real conditions. The effect of geome
trical parameters such as shape and size of both the phase mask and the Lyo
t stop is studied. We also analyze the effect of low- and high-order aberra
tions generated, for instance, by the atmospheric turbulence. An important
issue is the wavelength dependence of the phase mask. We show that the perf
ormance decreases rapidly as the spectral bandwidth is increased, and as a
consequence, we discuss the manufacturing of achromatized masks using multi
ple thin films. An optical concept is proposed.