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A long x-ray pathway based on an x-ray back-diffraction cavity for coherent x-ray beam experiments is presented. In the present work, such a setup was tested and used for propagation-based x-ray phase contrast imaging (PBI). This setup showed to be useful for PBI purposes, with the advantage of being compact (3 m long) when compared with long x-ray synchrotron beamlines with dimensions from tens to hundreds of meters.
©2008 Optical Society of America
1. Introduction
High quality x-ray beam (high coherent x-ray beam) is achieved by setting the experimental hutch as far as possible from the source. It can be assembled by using asymmetrically-cut crystals [1-2]. However, in this case, the longitudinal beam coherence is lost [3] and, such a setup works only for a specific energy. Another way to do that is to build long x-ray pathways [4-5] to achieve such condition. One can have high transverse x-ray coherence length (lateral coherence - lt) with a small source and a long x-ray pathway. The lateral coherence (lt) is given by:
where λ is the wavelength of the incoming x-ray beam, d is the source to sample distance and σx is the source size.
Among others, coherent x-ray beam can be used for phase contrast x-ray imaging. Such imaging technique has been used for several applications in archeology [6-7], biology [8-9], medicine [10-11] and materials science [12-13] to reveal structures that are invisible by attenuation contrast x-ray imaging. Variant techniques are reported in the literature [14-18]. Propagation-based x-ray phase contrast imaging (PBI) is well known by its simplicity: it does not require any sophisticated optics. The unique requirement is a high quality small source with high brilliance provided by conventional micro focus x-ray sources [16,19-20] or, by high brilliance and low emittance third generation synchrotron sources [12,21].
In x-ray back-diffraction geometry (diffraction at Bragg angles around π/2) [22-23] the diffracted h-beam overlap the incident beam. In such geometry, the widths of single crystal rocking curves are much larger (~10-3 rad) than those for conventional x-ray diffraction angles (~10-6 rad). Back-diffraction is also characterized by high angular acceptance with high energy resolution and high sensitivity to the angular position of the rocking curve with respect to variations in the lattice parameter. This geometry has been used in several kinds of experiments [24-31]. The experimental difficulty of this type of measurement lies on the detection of the diffracted h-beam which involves the need of semi-transparent detectors [30] or very long distances between the crystal and the detector [31].
In the present work a new synchrotron setup based on a “virtual” long x-ray pathway is presented. The idea is to have a far away source by using an x-ray back-diffraction cavity: two Si crystals diffracting several times at Bragg angles around π/2. Such a setup show to be compact compared with long x-ray beam pathways presented elsewhere [4-5].
This paper shows a description of the experimental setup followed by its characterization for PBI purposes. Images of a polypropylene tube and a three leaf acquired at different sample to detector distances will be shown. The paper finishes with the conclusions
2. Experiment
The setup was assembled in the XRD2 beamline at Laboratorio Nacional de Luz Sincrotron (LNLS- Brazilian synchrotron) (Fig. 1). The energy of the incoming x-ray white beam was selected by the beamline monochromator (Si 111, placed at 8.7 m from the source) at 9.684 keV. Downstream of the monochromator was mounted the x-ray back-diffraction cavity: a non-dispersive double crystal Si 660 setup in back-diffraction geometry. The first Si 660 crystal was set at 19 m from the source. The second Si 660 was placed 3.3 m further downstream. A vacuum path was set between them to reduce the attenuation/scattering of the beam in the air. The crystals were 130 mm long and 40 mm wide. These crystals were oriented, cut and chemically polished (etching) with a precision better than 0.1°. They were designed to work with a beam of 2 mm in height ×40 mm wide and, with a total of 10 bounces in the cavity (5 in each crystal). However, in the present work, the x-ray cavity was used with only 4 bounces (2 in each crystal) with a diffraction angle of 89.56°. The sample was placed after the cavity. Therefore, the beam pathway was increased by 13.2 m, i.e., the source to sample distance was increased to 32.2 m. The vertical source size (σx) at XRD2 beamline at LNLS is about 170 µm. By using the Eq. (1) one can have the transverse coherence length of 12 µm. With such lateral coherence, the XRD2 beamline becomes competitive with, for example, the SYRMEP beamline at ELETTRA [32] (lt~15 µm at 9.7 keV) for PBI purposes (radiography and tomography) in edge detection geometry.
In the present setup, the sample to detector distance (D, Fig. 1) can vary from 0 mm (sample in contact with the CCD detector) to 1 m. This means that one can acquire conventional synchrotron radiography (CSR) and PBI in the same setup. The images were acquired with a direct conversion CCD detector, which has 1242×1152 pixels of 22.5×22.5 µm2 each. Coupled translators, for sample and detector, with a range of 100 mm each, were also employed.
Fig. 1. Propagation-based x-ray phase contrast imaging setup (PBI) based on an x-ray back-diffraction cavity.
3. Results
To characterize the PBI setup proposed here, images of a polypropylene tube at different sample to detector distances were acquired. The images are shown in Fig. 2. It is easy to see that phase effects at the tube edges are much more emphasized when the detector is placed at longer distances with respect to the sample. This can be quantified by looking at the cross sections of the images (Fig. 3). The contrast at the edges (phase effects) increase with the sample to detector distance. These phase effects are attributed to the strong phase jumps at the external and internal borders of the tube.
An image of a tree leaf was also acquired (Fig. 4). Details in the leaf, such as the vessels and cork warts are much more defined at longer sample to detector distances. This happens because phase effects are more emphasized at longer sample to detector distances, which can be checked also by the edge enhancement at the top border of the leaf (Fig. 4(b)).
The results show that the idea to create a compact long x-ray pathway based on an x-ray back-diffraction cavity works, i.e., phase effects due to the improved lateral coherence were detected.
Fig. 2. Images of the polypropylene tube: (a) Conventional synchrotron radiography at D=0 mm; (b) Propagation-based x-ray phase contrast image (PBI) at D=160 mm and (c) PBI at D=700 mm. Exposure time: 10 min.
Fig. 3. Cross section profiles of the images shown in Fig. 2. (a) Conventional synchrotron radiography at D=0 mm; (b) PBI at D=160 mm and (c) PBI at D=700 mm. The phase effects (dashed circles) are more pronounced at larger sample to detector distances (D).
Fig. 4. Propagation-based x-ray phase contrast images (PBIs) of a tree leaf at two different sample to detector distances: a) 160 mm and b) 700mm. The vessels and cork warts (indicated by dashed circles) are more defined in the image acquired at longer distance (b). Phase effects at the sample border are also more emphasized in the image b): see, for instance, an edge enhancement effect in the top of the image. Exposure time: 10 min.
4. Conclusion
An effective long x-ray path was demonstrated for phase contrast contrast x-ray imaging purposes over a short distance by using x-ray back-scattering diffraction geometry with the Bragg angle around π/2 to fold the beam multiple times. Such a setup is shown to be useful for propagation-based x-ray phase contrast imaging (PBI).
It is worth noticing that with a good vacuum path, one could achieve 20 diffractions in the back-diffraction cavity, so that the lateral coherence could be improved in such a way that inline beam holography could be realized. Also, this compact setup can be implemented in any x-ray beamline to improve the beam coherence for imaging and experiments requiring an xray coherent beam. However, it is good to emphasize that the crystals have to operate at specific energies, for the different allowed diffraction planes. For the employed x-ray energy, about 2% is lost in each diffraction (photoelectric absorption); this means that 40% of intensity can be lost after 20 diffractions. Also, the bandwidth (Δλ/λ) of the back-diffraction cavity is about 10-6. This means that the intensity loss (photon flux) is about two orders magnitude after the cavity, once that the bandwidth of the upstream Si 111 is about 10-4. Even with this intensity loss, such a setup seems to be reasonable for working with third generation synchrotron machines.
Speaking about the use of this setup at LNLS, we note that it can be used as alternative to the standard analyzer-based x-ray phase contrast imaging setup [33], with the advantage of being an easier phase contrast imaging technique, especially for tomography purposes (post image processing). Also, other experiments requiring coherent x-ray beams are envisaged.
Acknowledgments
The authors are grateful to LNLS/MCT (proposal D10A-6588/2007) for the beamtime and FUNPAR/UFPR for the financial support. M.G. Hönnicke is grateful to CNPq/PDJ for his funding.
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