We discuss from the viewpoint of the Strehl ratio versus defocus, or t
he normalized axial-irradiance distribution, the influence of decenter
ing the dark mask of an annular pupil. Our treatment, which is valid f
or pupil apertures with any Fresnel number, permits us to infer that t
he axial behavior of a noncentrally obscured pupil is equivalent to th
at of an apodizer with continuous amplitude variations. Hence the Stre
hl ratio versus defocus of an optical system can be shaped by use of n
oncentered dark masks that act as continuous gray apodizers. Several n
umerically evaluated examples are presented.