Zone plates in general

The spatial resolution of X-ray microscopes is, in common with all focusing X-ray optical systems, limited primary by the quality of the optical elements. For the ID21 X-ray microscopes the critical components are X-ray lenses which are used. Although refractive lenses are available and used at the ESRF, at lower energies they become inefficient due to absorption effects and the spatial resolutions they offer remain moderate. Currently the highest resolution and most efficient X-ray lenses are available based upon diffractive focusing processes. These lenses, known as zone plates, offer spatial resolutions which are as low as 40nm [10] and focusing efficiencies which can exceed 50% [11].

What are zone plates and how do they work ?

The basic properties of a zone plate were already described in 1875 by 
J.L. Soret [2]

By modification of the wave front in a way which has a focusing effect on the X-rays. They form a concentric circular diffraction grating where the position of adjacent zones reproduce that of Fresnel half period zones. 
Zone plates behave in many respects like a circular lens with focusing behaviour which approximates that described by the thin lens formula 1/p +1/q = 1/f. The main difference is that a zone plate has different diffraction orders and therefore several focal spots.
For zone plate based systems the minimum resolvable structure size is limited by the width of the outermost zone of the lens.

References:

1. A. Fresnel: Calcul de l'intensite de la lumiere au centre de l'ombre d'un ecran, Oeuvres completes d' Augustin Fresnel, Vol.1, Note 1, 365 (1866)
2. J.L. Soret: Ueber die von Kreisgittern erzeugten Diffraktionsphaenomene, 
Ann.Phys.Chem 156, 99 (1875)
3. R.W. Wood: Phase-reversal zone-plates, and diffraction-telescopes, Philosophical Magazine, Series 5,  45, 511 (1898)
4. K. Miyamoto: The phase Fresnel lens, JOSA 51, 17 (1961)
5. A.V. Baez: Fresnel zone plate for optical image formation using extreme ultraviolet and soft X-ray radiation, JOSA 51, 405 (1961)
6. D.J. Stigliani et.al: Resolving power of a zone plate, JOSA 57, 610 (1967)
7. G. Schmahl et.al: Lichtstarke Zonenplatten als abbildende Systeme fuer weiche Roentgenstrahlen, Optik 29, 577 (1969)
8. M.Young: Zone plates and their aberrations, JOSA 62, 972 (1972)
9. J. Kirz: Phase zone plates for x rays and the extreme uv, JOSA 64, 301 (1974)
10. C.David et.al, Low distortion e-beam lithography for fabriction of high resolution germanium and tantalum zone plates, J.Vac.Sci.Technol. B 13 (6), 2762 (1995)
10. D. Weiss et.al, Appl.Phys.Lett. 72, 1805 (1998)
11. E. Di Fabrizio et.al, Nature 401, 895 (1999)