Given the reflective nature of extreme ultraviolet lithography and its extremely short operational wavelength, roughness of the optical surfaces is of significant concern. In particular, roughness in the mask multilayer leads to image plane speckle and ultimately patterned line-edge or line-width variability in the imaging process. Here we consider the implications of this effect for future high numerical aperture (NA) systems that are assumed to require anamorphic magnification projection optics. The results show significant anisotropic behavior at high NA as well as a substantial increase in relative patterned line variability in the shadowed direction when comparing 0.55 NA to 0.33 NA, despite the assumption of an anamorphic magnification system. The shadowed-direction patterned line variability is 2× larger than for unshadowed lines, and the majority of the increase in variability occurs in the low frequency regime.