Boosting phase contrast with a grating Bonse-Hart interferometer of 200 nanometre grating period

Abstract

We report on a grating Bonse-Hart interferometer for phase-contrast imaging with hard X-rays. The method overcomes limitations in the level of sensitivity that can be achieved with the well-known Talbot grating interferometer, and without the stringent spectral filtering at any given incident angle imposed by the classic Bonse-Hart interferometer. The device operates in the far-field regime, where an incident beam is split by a diffraction grating into two widely separated beams, which are redirected by a second diffraction grating to merge at a third grating, where they coherently interfere. The wide separation of the interfering beams results in large phase contrast, and in some cases absolute phase images are obtained. Imaging experiments were performed using diffraction gratings of 200 nm period, at 22.5 keV and 1.5% spectral bandwidth on a bending-magnetic beamline. Novel design and fabrication process were used to achieve the small grating period. Using a slitted incident beam, we acquired absolute and differential phase images of lightly absorbing samples. An advantage of this method is that it uses only phase modulating gratings, which are easier to fabricate than absorption gratings of the same periods.

Keywords: X-ray; absolute phase; compact source; grating; interferometer; phase contrast.

Figure 1.

Two variants of the gBH interferometer. Both consist of a slit that limits the width of the incident beam, followed by three parallel gratings which are positioned in series and at equal spacing, then a gap and the X-ray camera. In variant (a) the first and third diffraction gratings have half the line density as that of the second grating. A pair of balanced diffraction pathways are represented by solid arrows. Other diffracted beams are represented by dotted arrows. Multiple diffraction pathways result in a number of separated diffraction bands on the camera. The pair of balanced paths interfere with each other to produce intensity fringes at the central band. When a sample intersects one or both of the interfering paths, it causes different phase shifts among them resulting in changes of the interference fringes. In variant (b) all three diffraction gratings have the same period. Two pairs of mutually balanced pathways are represented by solid arrows, which results in interference fringes in four diffraction bands on the camera. Variant (b) is realized in our experiment. (Online version in colour.)

Figure 2.

The intensity pattern on the camera in the gBH interferometer of variant (b) at X-ray photon energy of 22.5 keV. The lines of the gratings were oriented horizontally and the grating period was 200 nm. As illustrated in figure 1, the width of the incident beam was limited to 160 μm by a slit. Given the propagation distance of 65 cm between the last grating and the camera, multiple diffraction bands are separated in the image. Two pairs of balanced diffraction paths gave rise to the interference fringes in the +1, +2 and −1, −2 bands.

Figure 3.

Images acquired from a sample of two intersecting hairs. Image (a) is a direct projection. The edges are enhanced by Fresnel diffraction over the distance between the sample and the camera. Image (b,c) are acquired with the gBH interferometer. They are from one of the diffraction bands on the camera that contain interference fringes. Image (b) is the reference without the sample. Image (c) was taken with the sample in place. During a phase-stepping process, a series of such images were taken while stepping the position of one of the gratings. From these images the phase map (d) was retrieved. Image (d) represents the absolute phase shift of the X-ray wave after propagating through the sample. Referring to figure 1, the more vertical hair intersected both of the interfering X-ray beams, resulting in twin images of opposite phase values in (d). Phase wrapping are seen in both hairs owing to the fact that the phase shifts exceeded π.

Figure 4.

In this example, the sample consists of a distribution of polystyrene spheres. Image (a) is a direct projection. Edge enhancement is due to Fresnel diffraction over the distance between the sample and the camera. Image (b) is the phase image acquired by the gBH interferometer. The phase value of each bead can be positive or negative, depending on in which of the two interfering beams was it located. Also can be seen are overlapping phase images of two beads of opposite phases. These are from beads that were physically in separate beams.

Figure 5.

The projection (a) and phase (b) images of a spider. These were acquired in a number of steps. Each step covered a 150 μm wide band over the sample. The bands were tied together to give the full image. In the phase image (b), twin images of the spider of opposite phase values can be seen. They are vertically displaced from each other by 141 μm, which equals the separation of the two interfering X-ray beams at the location of the spider. The magnitude of the phase shifts exceeded π in many locations, resulting in frequent phase wrapping.