Dark-field imaging is demonstrated with a conventional hard-x-ray source

In optical microscopy , dark-field imaging is a well-established means of enhancing contrast. By diverting most of the illuminating light before it reaches the focal plane and imaging only with light that scattered within the sample, one can highlight small scattering inhomogeneities that are hard to discern in the glare of the illumination source.

One would like to do the same with x-ray imaging. Bone and some pathological tissues incorporate microscopic x-ray scattering sites that would provide much better contrast than one gets with conventional medical radiographs, which rely entirely on x-ray absorption. Dark-field x-ray imaging would also help security screening by distinguishing between microscopically homogeneous soft materials and similarly absorbing explosives like Semtex that incorporate telltale micro-granule scatterers. And for safety inspection of materials, microfractured regions would reveal themselves as x-ray scatterers in a dark-field image.

The problem with x rays, and especially with the hard, multi-keV x rays needed to penetrate samples of reasonable thickness, is the lack of efficient optical elements that could function like lenses. In recent years crystal surfaces have begun to serve as efficient Bragg reflectors for dark-field imaging with hard x rays. ¹ But producing crystal-based dark-field images with practical exposure times requires extremely well-collimated monochromatic beams of a kind that are available only at very brilliant synchrotron light sources—hardly a practical way of doing routine medical or surveillance imaging.

But now, Franz Pfeiffer and coworkers at the Paul Scherrer Institute (PSI) in Switzerland have demonstrated a way of doing dark-field imaging with hard x rays from an ordinary laboratory source much like the x-ray tubes used in most hospitals. ² The technique employs a pair of interferometer gratings fabricated by Christian David of the PSI group. Interferometry usually requires the coherence provided by a pointlike monochromatic source. But an x-ray tube like the one used at PSI yields a beam with a broad energy spectrum centered around 30 keV that cannot be focused down to a point much smaller than a square millimeter.

Therefore Pfeiffer and company covered the focus of the x-ray beam with a much coarser third grating (G₀ in figure 1(a)) that imposed a vertically striated modulation with a periodicity of 73 µm on the beam. That modulation just after the x-ray source suffices to provide the effective coherence in the transverse x direction required for the much finer phase-modulation and analyzer-absorption gratings (G₁ and G₂ in the figure) downstream of the sample to imprint interferometric information about its distribution of scatterers on the imaging detector.

Revealing microscatterers

The PSI detector is limited by its pixel structure to a resolution on the order of 0.1 mm, far too coarse to resolve the micron-sized scatterers of interest. But their effect on the interferometric pattern produced at the detector by the gratings G₁ and G₂ shows up quite clearly in the group’s dark-field images.

Placed just downstream of the sample, G₁ is a phase mask that imparts to the transmitted x-ray wavefront a phase modulation with a period p₁ of 4 µm. By an interference phenomenon known in optics as the fractional Talbot effect, that phase modulation produces an intensity modulation with precisely half the period of G₁ at a distance D = 4 cm farther downstream (see figure 1(b)). So that’s where Pfeiffer and company placed their analyzer-absorption grating G₂, with a period p ₂ of 2 µm, followed immediately by the pixelated detector.

In the absence of the intervening sample, the intensity modulation just before G₂ would be neatly sinusoidal, with a period of 2 µm. But the interference pattern tends to be washed out locally by small-angle x-ray scattering in the sample. The trick, then, is to deduce the distribution of microscatterers in the sample from their reduction of spatial oscillation amplitude at different points on the detector.

To that end, the group scans G₂, with its opaque striations, across the face of the detector for a few oscillation periods. The data recorded during the scan are the set of x-ray intensities I(m,n,x ₂), where m and n index the detector’s rectangular array of some 10⁵ pixels and x ₂ marks the progress of G₂ as it steps in the x direction in increments of p ₂/4.

After the G₂ scan, the x ₂ dependence of the x-ray intensity recorded by each pixel is Fourier analyzed. If one ignores the small contributions of higher harmonics of the fundamental oscillation period p ₂, each Fourier analysis yields the three-parameter fit $$I\left(m,n,x_2\right)\approx a\left(m,n\right)+b\left(m,n\right)\text{sin}\left[2\pi x_2/p_2-\phi \left(m,n\right)\right]$$ (see figure 1(c)). When the fitted parameters are normalized to measurements made with the sample absent, the mean intensities a(m,n) correspond to what’s recorded in a conventional x-ray radiograph, which exploits only absorption. The phases φ(m,n) are what one exploits in phase-sensitive x-ray imaging, a complementary alternative to dark-field imaging (see reference and the article by Richard Fitzgerald in Physics Today, July 2000, page 23 ). The dark-field imaging information is carried by the visibility function $$V\left(m,n\right)\equiv b\left(m,n\right)/a\left(m,n\right),$$ which measures the fractional depth of the interferometric oscillation.

The visibility function for a given pixel is an inverse measure of the local small-angle scattering power integrated over the projection of the pixel through the sample. The visibility of the oscillation at a point on the detector plane is most effectively reduced by x-ray scattering through an angle of p ₂/2D in the sample. Because the 0.2-mm pixel width is a hundred times bigger than p ₂, one needn’t worry about scattering events recorded in the wrong pixel.

Comparison

Figure 2(a), the PSI group’s dark-field image of a chicken wing, demonstrates the technique’s potential for improved contrast in medical imaging. The image is a map of V(m,n) created from the fitted Fourier parameters. It effectively subtracts off the mean glare of unabsorbed, unscattered x rays from the source. In the blackest regions of the image, the visibility function is the same as it is with no sample, and the whitest regions are where V is most diminished by scattering in the sample. In the sense that figure 2(a) is an analytically processed construct based on several interferometric exposures, it is a less direct dark-field image than one gets with crystal manipulation of an x-ray beam at an accelerator light source.

For comparison, figure 2(b) shows what amounts to a conventional x-ray transmission image of the same sample, derived from the fitted a parameters for the same exposures that yielded the dark-field image. The much better bone contrast in the dark-field image is attributed by Pfeiffer and company to the strongly scattering microstructure of the porous bones. Scattering at soft-tissue boundaries and interfaces also provides good contour contrast. But the apparent absence of significant scattering in the bulk of the soft tissue renders it largely invisible in the dark-field image, even though its x-ray absorption is clearly manifested in the conventional radiograph. That suggests a useful complementarity between the two imaging modalities.

The two images were produced with five-second x-ray exposures at each of eight different positions of the analyzer-absorption grating. Keeping a living sample adequately still for almost a minute is problematic. But, says Pfeiffer, this proof-of-principle demonstration was carried out with an antiquated second-hand x-ray tube. With a more up-to-date source—albeit still describable as “ordinary”—and a thicker detector of higher quantum efficiency, he expects that exposure time can be cut a hundredfold. In any case, the wide band-pass acceptance of the new grating-based method allows much shorter exposure times than crystal-based dark-field imaging would require with a spectrally broad x-ray source of comparable brightness.

Absorption of x rays decreases with increasing energy, and soft tissue is less absorbing than bone. Therefore conventional clinical imaging of soft tissue—mammography, for example—is done with relatively low-energy hard x rays of about 30 keV to insure adequate absorption. But absorption and its attendant ionization are precisely what subjects the patient to radiation risk. Because dark-field imaging does not depend on absorption, it could be done with less hazardous 100-keV x rays. “That shouldn’t be difficult,” says Pfeiffer. “But it will require the fabrication of diffraction gratings thick enough to absorb the more penetrating high-energy x rays.”