X-ray multimodal imaging using a random-phase object

We demonstrate an extension of the x-ray grating interferometer three modal imaging method to a generalized stepping scheme using a phase object with small, random features. The method allows the recovery of the absorption, scattering, and two-dimensional phase image of the sample from a raster scan of the phase object. An additional extension of the method to recover the effective wave-front curvature is also described. The technique provides fine sensitivity and high spatial resolution and has only low requirements on spatial and longitudinal coherence of the x-ray beam. Imaging modes and processing methods are explained, and an experimental demonstration of the technique is provided by imaging a feather and the quantitative characterization of a compound refractive lens.

Figure 1

Schematic of a two-dimensional x-ray grating interferometer. Gratings are placed in an x-ray beam downstream from a sample to create an interference pattern. The distortion of this pattern from the one obtained when no sample is inserted into the beam permits the recovery of the phase shift induced by the sample.

Figure 2

Processing representation.

Figure 3

Schematic of a generalized stepping imaging setup. A phase object with small features is mounted on a 2D piezo motor beyond the sample, and a highly resolving detector is placed at a distance $d$. The 2D raster scan of the scattering object allows one to calculate the scattering vector $v$ for each pixel when the sample is introduced into the beam.

Figure 4

(a) The blue (dark gray) and the red (light gray) area on the phase object represent the pattern seen by two different pixels when scanning this object in a collimated x-ray beam: in this case the pixels are adjacent and $(r,s)=(1,0)$. (b) A similar sketch for the case of a noncollimated beam. The distance $\chi$ is defined as the offset between the similar part of the recorded pattern.

Figure 5

Differential characterization of a 2D CRL. (a), (b) First image of the scan, respectively, with and without the sample inserted in the beam. The bounded squares show the patterns recorded in each of the scans in the pixel marked $T$. (c) Horizontal and (d) vertical differential wave-front slopes.

Figure 6

(a) First image acquired during the scan of the membrane. (b) Effective second derivative of the x-ray beam wave-front after propagation through the CRL. (c) Effective wave-front slope obtained by integrating the measured beam's second derivative. The inset shows the effect of the multilayer monochromator phase errors on the amplitude of the fringes. The dashed and plain lines show, respectively, a horizontal and a vertical cut across the CRL.

Figure 7

(a) Vertical and (b) horizontal differential wave-front gradients. (c) Scattering image. (d) Absorption image. One can see in the absorption and scattering images vertical stripes due to the multilayer monochromator instabilities.