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I've been trying to understand the various concepts behind x-ray optics compared to standard visible/IR optics like mirrors and such. However, the x-ray mirrors I've been finding typically have optimal angles of reflectance on the order of a few milliradians, particularly for hard x-rays. I think I mostly understand the reasons for this (having something to do with Bragg diffraction?), but, say, for absorption experiments with low sample density, it may be necessary to use something analogous to a multipass absorption cell. Since x-rays can't be reflected at anywhere near 90° with high efficiency, can a multipass absorption cell be constructed for x-rays (say, with fiber optics or something else)? Has anyone done so?

Multiple Google searches for such a thing have turned up nothing, but maybe I'm just searching for the wrong thing.

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I guess the idea here would be to make something like a ring cavity for ordinary light, where the light is bounced around a closed loop. Which is something you see done in dye lasers, and has probably been used to do laser spectroscopy at some point.

The problem with this is that if your deflection angle is a few milliradians, then you would require thousands of bounces to come all the way back around to where you started. Since the reflection efficiency isn't perfect, you would lose most of your x-rays by the time you managed to get them back in line for a second pass. Even if the reflectivity was 99.9% (which it isn't in the x-ray band), you'd only have about 37% of the light left after 1000 bounces.

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  • $\begingroup$ Refractive index of most (all?) materials is less then 1 for X-rays and at very small angles (since n=0.9999) you would have total internal reflection. $\endgroup$
    – gigacyan
    Commented Dec 17, 2010 at 8:23
  • $\begingroup$ @gigacyan -- Yes, the reflection is due to total internal reflection (sometimes called total external reflection in this case!) No, that doesn't mean the reflectivity has to be 100%! There's scattering and there's absorption. $\endgroup$
    – Steve Byrnes
    Commented Jun 5, 2011 at 7:13
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Maybe you don't need a multipass cell after all. Check out this recent paper in Nature Physics which reports experimental results on very high (above 90%) reflection off diamond even at the normal incidence(!) for hard X-rays (energies up to 20-30 keV).

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I am quite certain that no multipass absorption cell exists for X-rays. In the X-ray absorption spectroscopy community, people strive to make their samples about one attenuation length thick, as this maximizes the signal to noise ratio. To find out the attenuation length of your material, I would recommend the excellent online calculators of the Center for X-ray Optics: http://henke.lbl.gov/optical_constants/ . The "attenuation length of a solid" calculator is probably what you want (it works equally well for gases and liquids as long as you provide the correct mass density). The attenuation length will vary over several orders of magnitude depending on the X-ray photon energy.

If you are in a situation where you have very little sample material and need to do an X-ray absorption spectroscopy experiment, a total fluorescence yield type experiment may be an option.

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