Depth-graded multilayer coating

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A depth-graded multilayer coating is a multi-layer coating optimised for broadband response by varying the thickness of the layers used.

A multi-layer coating consisting of alternating layers with different optical properties and the same thickness will tend to have a narrow frequency response, getting narrower as more layers are added; for some applications such as precise focussing of a monochromatic laser light source this is exactly what's desired, but it is useless for astronomical optics where it is often required to detect a whole range of frequencies emitted by some source of interest.

The design of such coatings generally starts with an approximate analytical solution and then uses the simplex method of multi-variable optimisation to solve for optimal thicknesses of the layers.[1] Typically the thin layers (to reflect high-energy X-rays) are on the inside since low-energy X-rays are absorbed more readily. One model used is a power law distribution of thicknesses, with the thickness of the ith bilayer as a/(b+i)^c for some optimised a, b, c.

An optimum multilayer design depends on the graze angle, so ideally a different prescription would be used on each shell of a multi-shell X-ray Wolter mirror; in practice the same prescription is used for about ten shells.

Characterising such coatings requires a synchrotron as a variable-wavelength X-ray source.[2]

The Danish Space Research Institute in Copenhagen is (in 2012) the world centre of excellence for such coatings, though a good deal of the earlier research and development was done in Russia.


  1. ^ Wang, Zhanshan. "Fabrication and Characterization of Depth-Graded X-Ray Multilayers" (PDF). Proceedings of 8th International Conference in X-ray Microscopy.
  2. ^ Christensen, Finn. "Measured reflectance of graded multilayer mirrors designed for astronomical hard X-ray telescopes" (PDF). Cite journal requires |journal= (help)

Christensen, FE; Craig, WW; Windt, DL; Jimenez-Garate, MA; Hailey, CJ; Harrison, FA; Mao, PH; Chakan, JM; Ziegler, E; Honkimaki, V; "Measured reflectance of graded multilayer mirrors designed for astronomical hard X-ray telescopes," NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A-ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT Volume: 451 Issue: 3 Pages: 572-581 Published: SEP 11 2000