  Interferometry provides one of the possible routes to ultra-high angular
resolution for X-ray and gamma-ray astronomy. Sub-micro-arc-second angular
resolution, necessary to achieve objectives such as imaging the regions around
the event horizon of a super-massive black hole at the center of an active
galaxy, can be achieved if beams from parts of the incoming wavefront separated
by 100s of meters can be stably and accurately brought together at small
angles. One way of achieving this is by using grazing incidence mirrors. We
here investigate an alternative approach in which the beams are recombined by
optical elements working in transmission. It is shown that the use of
diffractive elements is a particularly attractive option. We report
experimental results from a simple 2-beam interferometer using a low-cost
commercially available profiled film as the diffractive elements. A
rotationally symmetric filled (or mostly filled) aperture variant of such an
interferometer, equivalent to an X-ray axicon, is shown to offer a much wider
bandpass than either a Phase Fresnel Lens (PFL) or a PFL with a refractive lens
in an achromatic pair. Simulations of an example system are presented.
