Imaging characteristics of a cosinusoidal complex-amplitude object illuminated with acoustically phase-modulated laser light are investigated in association with periodicity, one of the most noticeable features of the acoustically modified mutual intensity of laser light. Because of this periodicity, the image contrast is much more enhanced with an increase in the acoustic power. This effect is explained by the fact that many higher-order components of the object spectrum are transmitted by a limiting pupil of the imaging system in the presence of the acoustic wave. Theoretical predictions are shown to be in good agreement with experimental results.