Hard X-Ray Phase Tomography with Low-Brilliance Sources

We report on a method for tomographic phase contrast imaging of centimeter sized objects. As opposed to existing techniques, our approach can be used with low-brilliance, lab based x-ray sources and thus is of interest for a wide range of applications in medicine, biology, and nondestructive testing. The work is based on the recent development of a hard x-ray grating interferometer, which has been demonstrated to yield differential phase contrast projection images. Here we particularly focus on how this method can be used for tomographic reconstructions using filtered back projection algorithms to yield quantitative volumetric information of both the real and imaginary part of the samples’s refractive index.

Figure 1

Tomographic reconstruction. (a) Projection geometry. (b),(c) Back projection filter functions for (b) simple projection line integrals and (c) gradient projection integrals.

Figure 2

X-ray imaging interferometer. (a) Setup based on transmission gratings G0 through G2. (b) A phase object in the beam path causes a slight deflection of x rays changing the locally transmitted intensity through the arrangement formed by the gratings G1 and G2.

Figure 3

Results for a test sample containing empty and water-filled Teflon plastic tubes. (a) Conventional x-ray absorption projection; (b) differential phase contrast (DPC) projection; (c)–(e) tomograms obtained from (c) the logarithm of the absorption projections using the linear filter [Fig. 1b]; (d) the DPC projections using the linear filter [Fig. 1b]; and (e) the DPC projections using the imaginary sign filter [Fig. 1c]. The total exposure time for the 360 projections was 2 h.

Figure 4

Results for a biological object (a hornet). (a) Differential phase contrast projection; (b) tomographic slice through the reconstructed distribution of the real part of the refractive index $\delta (x,y,z)$; and (c) 3D rendering of $\delta (x,y,z)$ (see also 34). The volume data set of $400\times 400\times 800$ voxels was reconstructed from 360 projections recorded within a total exposure time 6 h [35].