An efficient technique to achieve isotropic edge enhancement in optics involves applying
a radial Hilbert transform on the object spectrum. Here we demonstrate a simple setup
for isotropic edge-enhancement in soft-x-ray microscopy, using a single diffractive
Laguerre-Gaussian zone plate (LGZP) for radial Hilbert transform. Since the LGZP acts
as a beam-splitter, diffraction efficiency problems usually associated with x-ray
microscopy optics are not present in this system. As numerically demonstrated, the
setup can detect optical path differences as small as lambda/50 with high contrast.
(C) 2009 Optical Society of America
