Focusing X-Rays

July 20, 2015

There are quite a few television shows and movies featuring "ghosts."[1] Among the supposed abilities of these incorporeal beings are the ability to walk through objects and have objects pass through them. There are some major inconsistencies in the nature of such ghosts, since they can handle objects, and they don't fall though floors. There are second-order inconsistencies, like their ability to speak, which requires manipulation of air.

X-Rays have a commonality with ghosts, since they can pass through objects. Their passage is not entirely unimpeded, since there's aways some attenuation. The transmittance of X-rays through a material follows the law,

in which I/I0 is the ratio of intensity to initial intensity, μ/ρ is the mass attenuation coefficient of the specific material at the specific X-ray energy, and ℓ is the distance through the material. There are tables of μ/ρ for many materials at various X-ray energies.[2]

Hand mit Ringen
(Hand with Rings)

X-ray radiograph by Wilhelm Röntgen of the left hand of his wife, Anna Bertha Ludwig, December 22, 1895.

In this first medical X-ray radiograph, it can be seen that the mass attenuation coefficient of bone is much greater than that of flesh.

(Via Wikimedia Commons.)

Although X-rays will zoom through materials, there are special cases when reflection of X-rays will occur. X-rays will reflect from perfect crystals when the wavelength of the X-rays and the spacing of crystal planes meet the Bragg condition:

in which λ is the X-ray wavelength, d is the spacing between crystal planes, θ is the incident angle of the X-rays, and n is the order of the reflection. The condition, n = 1, is the equivalent of a mirror reflection (see figure).

Bragg reflection from a crystal plane. (Illustration by the author using Inkscape.)

While crystal reflection is a way to produce an X-ray mirror, the mirror reflection occurs only at the specific combination of wavelength and atomic spacing. You can't use Bragg reflection from a planar crystal to make X-ray optics, such as the equivalent of a telescope mirror, even at a specific wavelength, since the incident angle changes. One exotic method to get around this limitation is by bending a crystal; but, as you can imagine, most crystals would rather shatter than bend.

One method of forming an X-ray telescope is a coded-aperture mask. The mask, as its name implies, doesn't focus X-rays, it blocks them in a way that the direction of an X-ray can be calculated from the resulting pattern on an imaging detector. The BeppoSAX X-ray telescope uses a coded aperture mask with a 256 x 256 pattern etched into stainless steel (see figure).

Each of the 65,536 grid elements is a square millimeter.

(European Southern Observatory image, used with permission of Astronomy and Astrophysics.)

Zone plates will focus X-rays, just as they are able to focus visible light. A zone plate uses the interference of waves to focus X-rays, but there's a way to actually focus X-rays by reflection. If X-rays impinge on a metal surface, they will obey Snell's law, so there's an angle for which total internal reflection is obtained.

For X-rays, this grazing angle is very small, from a few arc-minutes to about a degree, depending on wavelength. This principle is used to focus X-rays in a Wolter telescope. A microstructured optical array is an X-ray analog of an optical fiber bundle. Such an array is prepared by cutting channels into silicon wafers using MEMS processing techniques. X-rays are guided by reflection from the gently-curved sidewalls of the channels.

In a recent advance in X-ray optics, scientists from Argonne National Laboratory (Argonne, Illinois) have demonstrated how rapidly oscillating micromechanical mirrors can be used to switch highly intense X-rays by setting the incidence angle just under, or just over, the critical angle for total internal reflection. Nanosecond switching of an X-ray beam was attained at more than a 100-kHz repetition rate.[3-4] A schematic of their device is shown in the figure.

Argonne National Laboratory micromechanical X-ray mirror. The beam is switched at the critical angle for total internal reflection.

(Argonne National Laboratory image courtesy of Daniel Lopez.)

The MEMS reflectors were atomically smooth and flat, a necessary condition for reflecting X-ray photons of tenth nanometer wavelength at grazing angles. The reflecting device was fabricated on a (100)-face silicon wafer, and the mirror was 10 μm thick and 500 μm by 500 μm in dimension. The support was a a pair of torsional flexures anchored to the wafer (see photo).[3]

Scanning electron micrograph of the Argonne micromechanical X-ray mirror.

The speed of the device came from its oscillation, which is synchronized with the X-ray pulses emanating from the test source. It would be possible to fabricate mirrors with MHz oscillation rate. Says Argonne emeritus scientist, Gopal Shenoy, "It will herald a new era of dramatically new and improved kinds of X-ray experiments."[4] Stephen Streiffer, Associate Laboratory Director for Photon Sciences and Director of the Advanced Photon Source, remarks that
"Extremely compact devices such as this promise a revolution in our ability to manipulate photons coming from synchrotron light sources, not only providing an on-off switch enabling ultrahigh time-resolution studies, but ultimately promising new ways to steer, filter, and shape X-ray pulses as well... This is a premier example of the innovation that results from collaboration between nanoscientists and X-ray scientists."[4]

The new technology, developed by scientists from Argonne's Center for Nanoscale Materials and the Advanced Photon Source, was funded by the Office of Science of the United States Department of Energy.[4]

An example of pulse selection by the Argonne X-ray mirror.

One narrow pulse is selected from a pulse train of X-rays.

(Figs. 3b and 3c of ref. 3, reformatted, licensed under a Creative Commons license.)[3)]

References:

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