  Diffractive zone plate optics uses a thin micro-structure pattern to alter
the propagation direction of the incoming light wave. It has found important
applications in extreme-wavelength imaging where conventional refractive lenses
do not exist. The resolution limit of zone plate optics is determined by the
smallest width of the outermost zone. In order to improve the achievable
resolution, significant efforts have been devoted to the fabrication of very
small zone width with ultrahigh placement accuracy. Here, we report the use of
a diffractometer setup for bypassing the resolution limit of zone plate optics.
In our prototype, we mounted the sample on two rotation stages and used a
low-resolution binary zone plate to relay the sample plane to the detector. We
then performed both in-plane and out-of-plane sample rotations and captured the
corresponding raw images. The captured images were processed using a Fourier
ptychographic procedure for resolution improvement. The final achievable
resolution of the reported setup is not determined by the smallest width
structures of the employed binary zone plate; instead, it is determined by the
maximum angle of the out-of-plane rotation. In our experiment, we demonstrated
8-fold resolution improvement using both a resolution target and a titanium
dioxide sample. The reported approach may be able to bypass the fabrication
challenge of diffractive elements and open up new avenues for microscopy with
extreme wavelengths.
