X-ray and Gamma-ray focusing and interferometry

X-ray Phase Fresnel lenses (PFLs) can be considered as diffraction gratings with rotational (axial) symmetry and radially-varying pitch. The achromatic combinations of refractive and diffractive lenses that have been proposed for applications in X-ray and gamma-ray astronomy may then be regarded as grisms, again with variable pitch and axial symmetry. This way of looking at optics for very high angular resolution high-energy astronomy leads to the consideration of systems that bridge the gap between focusing and interferometry. X-ray diffractive Axicons and PFLs are shown to be limiting cases of a family of designs that are the X-ray equivalents of "Axilenses", offering different combinations of effective area and bandpass. It is shown that linear gratings can be used as diffractive alternatives to the grazing incidence mirror "periscopes" that have been investigated as beam combiners in an interferometer. The gratings form achromatic fringes in a process related to the Talbot effect. The results of simulations and of a laboratory demonstration-of-principle experiment are presented.