Degradation of an image by Gaussian longitudinal motion

The effect of random longitudinal motion of an image is discussed. Numerical results are given for systems with circular and annular pupils. It is shown that, for a given value of the image motion, the time-averaged Strehl ratio is larger for a larger value of the obscuration ratio of an annular pupil. We also show that the time-averaged image irradiance distribution near its center and the corresponding encircled power can be obtained from their aberration-free values by multiplying them by the Strehl ratio.