Fresnel zone plate (rus. зонная пластинка Френеля otherwise зонная пластинка) — a system of alternating transparent and opaque rings (zones) having specific width and diameter and used to focus radiation in accordance with the laws of wave optics.


Many tasks of X-ray diffraction and spectroscopy (for example, XAFS, see X-ray absorption fine structure) require high local sensitivity. This is particularly important when information about the spatial distribution of chemical elements and their oxidation state can not be obtained by standard methods of electron microscopy.

However, it is almost impossible to focus X-rays using conventional lenses, since their refractive index in various media that are transparent for them is practically constant, and is very close to 1. The X-ray beam can be focused to a diameter of 10 nm using the wave properties of light and the wave front propagation laws of Huygens-Fresnel.

The Fresnel zone plate, like an ordinary lens, focuses a parallel beam of radiation into one point, the focus. The zone plate has a primary focus, and an infinite number of secondary focuses. The path difference of waves from adjacent transparent areas to the main focus is equal to the radiation wavelength. The waves from the transparent zones arrive to the focal point in phases, giving rise to constructive interference. To satisfy this condition, the radii of the transparent rings should be equal to,

where is the sequence number of the ring, is the wavelength, and is the focal length. The distance to the main focus depends on the wavelength of the incident radiation and is determined using the formula,

where is the diameter of the lens, is the width of the last opaque ring,

where are integer numbers. The resolution of the zone plate is determined by the Rayleigh criterion and is approximately equal to (more precisely 1.22 ).


Circuit diagram of an X-ray microscope built with Fresnel zone plates [4].
Circuit diagram of an X-ray microscope built with Fresnel zone plates [4].


  • Guda Alexander A.
  • Soldatov Alexander V.


  1. Fetisov, G.V. Synchrotron radiation. Methods for studying the structure of substances (in Russian) / G.V. Fetisov - Moscow: "Fizmatlit" Publisher, 2007. - 672 p.
  2. Sivukhin D.V. The course of general physics (in Russian), . V. 4. 3 ed. — Moscow.: Fizmatlit, 2006. — 792 pp.
  3. Günther S., Kaulich B., Gregoratti L., Kiskinova M. // Prog. Surf. Sci. 2002. V. 70. P. 187–260.
  4. Chao Weilun, Harteneck B.D. et al. // Proc. 8th Int. Conf. X-ray Microscopy IPAP Conf., 2006. Series 7. P. 4–6.
  5. Attwood D. Soft X-rays and Extreme Ultraviolet Radiation: Principles and Applications. — Cambridge University Press, 1999. — 540 p.

Contact us