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Applied Radiation and Isotopes 65 (2007) 1337–1344 www.elsevier.com/locate/apradiso
Benchtop phase-contrast X-ray imaging O. Gundogdu, E. Nirgianaki, E. Che Ismail, P.M. Jenneson, D.A. Bradley Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK Received 2 April 2007; received in revised form 9 July 2007; accepted 9 July 2007
Abstract Clinical radiography has traditionally been based on contrast obtained from absorption when X-rays pass through the body. The contrast obtained from traditional radiography can be rather poor, particularly when it comes to soft tissue. A wide range of media of interest in materials science, biology and medicine exhibit very weak absorption contrast, but they nevertheless produce significant phase shifts with X-rays. The use of phase information for imaging purposes is therefore an attractive prospect. Some of the X-ray phasecontrast imaging methods require highly monochromatic plane wave radiation and sophisticated X-ray optics. However, the propagation-based phase-contrast imaging method adapted in this paper is a relatively simple method to implement, essentially requiring only a microfocal X-ray tube and electronic detection. In this paper, we present imaging results obtained from two different benchtop X-ray sources employing the free space propagation method. X-ray phase-contrast imaging provides higher contrast in many samples, including biological tissues that have negligible absorption contrast. r 2007 Elsevier Ltd. All rights reserved. Keywords: X-ray; Phase contrast; Biological tissue imaging; In-line; Free propagation
1. Introduction To date, in clinical practice, X-ray imaging has been based on detection of differences in absorption of X-rays passing through the tissues being imaged. However, absorption imaging only provides low contrast for low Z elements. During the last decade, a number of novel methods have been developed, taking into account the phase shift the X-rays experience as a result of coherent X-ray scattering. This allows an increase in image contrast, especially in imaging weakly absorbing samples. Some of the existing X-ray phase-contrast imaging methods require highly monochromatic plane wave radiation and sophisticated X-ray optics (Wilkins et al., 1996). However, the method adapted herein, known as propagation-based phase-contrast imaging but also as refractionenhanced imaging, is a relatively simple method to implement, essentially requiring only a small focus X-ray tube and electronic detection. The three main methods used as phase-contrast techniques are illustrated in Fig. 1 (Wilkins et al., 1996; Lewis et al., 2005). Corresponding author. Tel.: +44 1483 682699; fax: +44 1483 686781.
E-mail address:
[email protected] (O. Gundogdu). 0969-8043/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2007.07.009
In biomedical research, attempts are being made to apply phase-contrast imaging techniques to a number of challenging clinical situations, including mammography, radiographic investigation of degenerative joint disease (bone is clearly visualised in conventional radiography, while cartilage is not) and lung imaging (Lewis, 2004). In the latter case, because of the difference in X-ray phase shift caused by blood and soft tissue, blood vessels can be revealed with phase-contrast image without the use of any contrast agent. In addition, and in regard to tumour imaging, because of the fact that more blood vessels are created near the cancerous cells for nutrition, phase contrast might also contribute to diagnosis of cancer. Even functional imaging might be possible if a material that modulates X-ray phase tends to concentrate to a particular location or condition (Momose et al., 2000).
2. Theory Three different methods of phase imaging can be identified: the interferometric method, diffraction-enhanced imaging and in-line propagation. In the latter case, the simplicity of the experimental set-up encourages
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Analyzer Sample X-rays
Sample
Sample
X-rays Crystal
Crystal
Crystal
Collimator Crystal
Fig. 1. (a) X-ray interferometry, (b) diffraction-enhanced imaging (DEI) and (c) propagation-based imaging.
investigation of its possible implementation in clinical practice. 2.1. X-ray phase modulation When a wave interacts with matter, both its amplitude and phase are modified. This change can be described by a complex form of the refractive index n of the medium, the value of n deviating only very slightly from unity n ¼ 1 d þ ib,
(1)
where d is the refractive index decrement due to phase shift and b describes X-ray absorption (Baruchel et al., 2000). b and the mass attenuation coefficient, written here as m, are related as follows: m¼
4pb , lr
(2)
where l is the wavelength and r is the mass density. The related phase change and attenuation on propagating a distance x are given by Z Z 2p I 4p F¼ dðxÞ dx and log bðxÞ dx, ¼ l I0 l (3) where I0 is the incident intensity and I the final intensity. Therefore, the absorption and the phase shift of an X-ray beam propagating through an object are dependent upon both d and b of the material being traversed (Lewis, 2004). An important aspect of phase-contrast imaging is that the d of tissues is generally much greater than b within the diagnostic X-ray energy range, as an example, in the mammography energy range, 15–30 keV, the phase shift term d can be 1000 times greater than the absorption term b. Additionally, b diminishes more rapidly than d as the incident photon energy increases, the functional dependencies being d / E 2 and b / E 4 . As such, low-dose imaging is possible since, when using absorption, soft tissue differences are only apparent at low energies (Lewis, 2004). The techniques used for phase-sensitive imaging methods in X-ray radiography can be classified according to whether they are interferometric methods, methods using an analyser (diffraction enhanced imaging, DEI) or propagation methods. Each has its advantages or disadvantages (Pfeiffer et al., 2006).
The X-ray interferometric technique is complex to realise and to implement experimentally, requiring a crystal interferometer. This method is restricted to synchrotron radiation sources because of the intensity, monochromaticity and the spatial coherence demands of the method. The incident beam is diffracted from the first silicon blade of the interferometer and splits into two coherent X-ray beams. These beams fall into the second silicon blade that works as a mirror causing them to converge towards one another. A sample placed in the optical path of one of the beams between the analyser and mirror will create phase shifts in that beam and distort its wavefront. As a result, the recombined beams will produce interference fringes on the X-ray detector positioned behind the analyser (Lewis, 2004; Fitzgerald, 2000). Because of its sensitivity, an X-ray interferometer needs almost perfect alignment and stability of the crystals. The best results are acquired from a monolithic device in which all crystals are made from a single large ingot of crystalline silicon. Although this technique provides good stability and inherent alignment, ingot sizes limit the field of view to about 3 cm. Synchrotron radiation is used for DEI, the method requiring an intense beam of X-rays, with spatial and temporal coherence. DEI takes advantage of the narrow angular acceptance of Bragg reflections from perfect crystals such as silicon. A monochromatic X-ray beam from the synchrotron passes through the object and falls upon an analyser silicon crystal. X-rays are diffracted only if they satisfy Bragg’s condition, eventually impinging onto the detector surface. The graph of diffracted X-ray intensity versus angle of the crystal is known as the ‘rocking curve’ and it has an approximately Gaussian shape. The diffracted X-rays from the analyser are received by the detector and form an image. If the analyser angle is set at 01 (the peak of the rocking curve), then absorption images are retrieved that are free of scattered X-ray photons providing that the scatter angle is larger than the width of the rocking curve. If the angle of the analyser is set to one that yields an intensity corresponding to half of that at the peak of the rocking curve, then the reflectivity for X-rays that pass through the object undeviated is 50%. Deviated X-rays will be reflected with lower or higher efficiency depending on the angle they have when they fall upon the crystal relative to the rocking
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curve. This technique is quite sensitive to refraction effects of X-rays (Lewis, 2004; Lewis et al., 2003). It has been demonstrated that DEI can produce images in which the contrast is entirely due to absorption or entirely due to changes of the refractive indices in tissue. It is also possible to construct an image containing both refraction and absorption information. In propagation-based phase contrast (refractionenhanced imaging, REI), the X-rays transmitted through the object at various angles will propagate over the distance between the object and the detector. For the situation of the detector being located directly behind the sample, a conventional absorption image is obtained, while at greater distances from the object, a phase-contrast image will be formed. The radiation sources that can be used must have spatial coherence (not necessarily temporal or chromatic coherence). Thus, while synchrotron radiation can certainly be used, combining spatial and temporal coherence, conventional polychromatic microfocus X-ray tubes can also be used, having sufficiently spatial coherence (Snigireva and Snigirev, 2006). X-ray photons travel through the object, interacting with it by the photoelectric effect, Compton scattering and coherent (Rayleigh) scattering. Coherently scattered photons deflect from their initial path at small angles. This kind of refraction of radiation occurs at the boundaries separating various media in an object of different X-ray refractive indices. At sufficient distances between the object and the detector, the propagated deflected X-ray photons can be practically observed to form an intensity superimposition that are due to photoelectric and scatter mechanisms, producing intensity variations (Kotre and Birch, 1999). In order to achieve phase-contrast imaging, the X-ray tube must provide a sufficient degree of spatial or lateral coherence which is given by d¼
lr1 , f
(4)
where l is the wavelength, r1 is the distance between the source and the object and f is the focal spot size of the tube. Therefore, phase information retrieval is easier with lowenergy X-ray photons, a large source-to-object distance and a small source size (Lewis, 2004). Temporal coherence or monochromaticity is not essential and as such phasecontrast imaging can also be performed with polychromatic radiation (Wilkins et al., 1996). The magnification that occurs at a distance r2 is given by the relation M ¼1þ
r2 . r1
(5)
With the benefit of magnification, the spatial resolution of the phase-contrast images is also improved, due to the rescaling to the original object size.
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The image contrast obtained from the X-ray intensity profiles of an object is provided by the relation Contrast ¼
I max I min , I max þ I min
(6)
where Imax and Imin are the maximum and minimum intensities recorded across some imaged boundary. Another parameter that can be calculated in the image is the penumbra arising from the finite size of the focal spot in the magnification images. From simple geometry, the geometrical unsharpness is r2 Ug ¼ f , (7) r1 where r1 is the distance between the source and the object, r2 is the distance between the object and the detector and f is the focal spot size. Because of this unsharpness, it has been reported that beyond a certain magnification depending on the X-ray microfocal tube, photon energies used and detector system, there is no further improvement in image quality. However, phase shifting is still observed when the edge enhancement is significantly greater than the blurring (Kotre and Birch, 1999; Matsuo et al., 2005). In conventional radiography, the primary-to-scatter X-ray photon ratio detected is improved by employing an anti-scatter grid, being achieved at the cost of requiring the exposure to be increased. In phase-contrast geometry, an appropriate air gap r2 is required and therefore this can provide scatter rejection without the need for a grid, one possibility being that lower doses might be achieved. An air gap of 25 cm is considered an adequate distance in terms of scatter elimination (Kotre and Birch, 1999). 3. Review of some studies Experiments employing synchrotron radiation have demonstrated propagation-enhanced contrast to be a valuable analytical tool in X-ray imaging. As an example, phase-contrast images of in vitro breast tissue specimens have been reported to provide superior quality to conventional mammographic images (Arfelli et al., 2000). Momose and Fukuda (1995) utilised an X-ray interferometer to image rat cerebellar slices that were not stained with contrast agent. While in the absorption-contrast image no clear structure of the cerebellum was observed, in the phase-contrast image the layer structure could be seen. The contrast change caused by a lipid removal procedure was investigated, it being found that a high percentage of lipid in myelin was related with improved image contrast. This result suggests that phase-contrast imaging might be useful for diagnosing of demyelinating disease. In Momose et al. (2000), the ability to depict blood vessels in mouse livers without using any contrast medium was investigated, use being made of an X-ray interferometer and synchrotron radiation. Because of the difference in X-ray phase shift
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caused by blood and soft tissue, trees of blood vessels were revealed in the phase-contrast image. Because of the ability of phase-contrast X-ray imaging to discriminate blood vessels in the liver without contrast agents, it may be attractive from a diagnostic point of view for further development for both in vitro and in vivo investigations. In regard to DEI, Yagi et al. (1999) used a thirdgeneration synchrotron radiation source to allow observation of refraction of X-rays in the microradian range. The refraction produced a high-contrast image of mouse lung when recorded at a distance of 6.5 m from the specimen. The images obtained were shown to be sensitive to the relative presence of air in the lung and therefore to lesions in the lung. Lewis et al. (2003) captured DEI images of mouse legs, heart, liver and lungs using DEI technique. The changes of the refractive indices were greater at the boundaries of the different kinds of tissue, resulting in greater edge enhancement effect and a three-dimensional appearance to the images. In Arfelli et al. (1998), the applicability of phase-contrast technique to mammography was demonstrated, the group producing images of mammographic phantoms of a few centimetres thick while delivering radiation doses that were either lower or comparable to that needed in conventional mammography. Details, including thin calcium deposits and 50 mm diameter nylon wires not observed in conventional images were revealed through the phase technique. In Matsuo et al. (2005) phase-contrast images of plant seeds and a plastic fiber were retrieved with a microfocus X-ray tube of 0.1 mm focal spot size. Tube voltage was set to 26 or 28 keV depending upon the object to be imaged, the image contrast of the plastic fibre being increased by edge enhancement. Moreover, as the spatial frequency of the X-ray images increased, the sharpness gained through phase shifting increased. Donnelly and Price (2002) evaluated polychromatic phase-contrast radiography, using a 0.1 mm focal spot tungsten anode X-ray tube operating in the few tens of kV range. The object imaged was a poorly attenuating, sharp edge consisting of a lucite sheet of 3 mm thickness. Phasecontrast images were acquired using the free propagation space technique while altering the tube voltage. The image receptor was a single emulsion X-ray mammography cassette. Optical density profiles were obtained across the edge of the object using a film digitiser and X-ray refractive indices were calculated. Increased keV caused a gradual decrease of the X-ray refractive index. The decrease was relatively small over the range of accelerating potentials studied and even at the highest potentials, strong edge enhancement effects were present. Indeed, the small reduction in edge enhancement was almost certainly accompanied by a decreased radiation dose at the higher potentials. Wu and Liu (2003) have examined design and theoretical foundations in clinical implementation of X-ray phasecontrast imaging. Phase-contrast mammography was considered a possible application, conventional X-ray
mammography being appreciated to be limited by sensitivity. The study indicated the need for small and bright focal spot X-ray tubes, allowing sufficient spatial coherence while also providing for a distance between tube and object of no greater than 1 m, sufficient for the phase enhancement in the images to become apparent. The focal spot would also need to be bright enough to allow image acquisition to be completed in a short exposure time by providing a sufficiently high exposure rate. The design incorporated the use of a film-based system, offering good detector resolution although limited dynamic range. By computer simulation, the design evaluated source to object distance, object-to-detector distance, magnification, X-ray tube focal spot size (kV) the tube target material and filtering, the entrance skin exposure, absorbed dose and exposure time. Experiments performed to validate the simulated design showed agreement with the theoretical analysis. In particular, the magnification at which maximum phase information was retrieved was at 1.54 . Beyond this magnification, the edges became blurred and contrast enhancement was lost, dose also increasing. The computer simulations and experiments indicated it to be feasible to construct a phase-contrast mammography system. Recently, Konica Minolta have developed the first digital mammography system utilising phase-contrast technology. The magnification factor used in this REGIUS PureView mammography system is 1.75 , the system combining phase-contrast mammography (PCM) and computed radiography (CR) technology. A molybdenum X-ray tube with a 100 mm focal spot is employed. 4. Present studies At Surrey, use has been made of the experimental set-up illustrated in Fig. 2, comprising an X-ray tube, a 12 bit position-sensitive charged couple device (CCD) detector and an external fan. The system is mounted on an optical rail that enables separations of up to 1.5 m. As previously noted, it is necessary for the radiation to enjoy high spatial or lateral coherence; for this reason, a small focal size tube is optimal. The Mo anode X-ray tube used was an Oxford Instruments Series 5000 Model XTF5011, of focal spot size 110 mm, supplying anode currents from 0 to 1.0 mA and anode voltages from 4 to 50 kV. The cone angle of the generated beam was 251. No internal filtration and no additional external filtration was used. The detector used in this experiment is a model XDI, Photonics Science CCD camera. The light-sensitive side of the semiconductor is coupled to a gadolinium oxysulphide scintillator which converts X-rays into visible light. This coupling is achieved by a direct microfibre optic coupling method. The XDI is a high-speed, high-resolution digital X-ray camera incorporating a 1330 1030 active pixel matrix CCD, each pixel being 6.7 mm square. The camera offers a 10 or 20 MHz readout. A micro-fibre optic coupler
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unsharpness (mm)
0.20 0.16 0.12 0.08 0.04 0.00 0
Fig. 2. Several images were obtained by altering the distances r1 and r2. The distance between the tube and the detector was constant at 1.5 m.
transfers the light from an optimised scintillator input to the CCD sensor to achieve the greatest possible efficiency. Using this device, an image can be integrated for exposure times from several seconds up to several minutes for the weakest signals. The software used for retrieval of the images was Image-Pro Plus version 4.1.0.0 and the software used for the profile processing was IDL version 6.0.
0.2
0.4 0.6 0.8 object - detector distance (m)
1
Fig. 3. Plot of geometrical unsharpness as a function of distance between object and detector.
5. Results and discussion
Fig. 4. (a) Picture of a plastic cylinder of 0.8 mm wall thickness, (b) conventional absorption image and (c) phase-contrast edge enhanced image.
130 Conventional r1=1m r2=0.5m
120 110 grey scale
As previously mentioned, blurring in the image increases with increase in the distance between the object and detector. The geometrical unsharpness for the particular X-ray tube is shown in the plot of Fig. 3. Beyond 0.7 m, blurring in the image is significant to cause loss of edge enhancement. The first object imaged was a plastic cylinder of 0.8 mm wall thickness as shown in Fig. 4a. The images were obtained at 28 keV and 1 mA for 1 min using the Oxford tube with a focal spot size of 110 mm. The distance between the tube and the detector was 1.5 m with the object in contact with the detector (absorption image) as shown in Fig. 4b. Fig. 4c shows the phase-contrast-enhanced image obtained. The distance between the tube and the object was 1 m and between the object and the detector 0.5 m giving a magnification of 1.5 . A conventional (absorption) image was first obtained, the object being located as close as possible to the window of the detector. The distance between the X-ray tube and the detector was kept at 1.5 m. Several images were subsequently retrieved, in each case altering the position of the object between the tube and the detector. Fig. 5 shows profile comparison between a conventional radiograph and the one obtained to provide phase-contrast imaging with object to detector distance of 1 m and source to object of 0.5 m. Because of the presence of quantum noise in the image, the mean of 250 profiles was calculated. This procedure was carried out using the program IDL (Interactive Data Language). In order to see how contrast is modulated, the position of the object was adjusted and several profiles were calculated altering the distances r1 and r2 by 0.1 m each time. For each image retrieved at a different position, the
100 90 80 70 0
10
20
30 40 50 number of pixels
60
70
80
Fig. 5. Profiles of the plastic cylinder obtained at 28 keV and 60 mA. The dotted line is the profile of the absorption image and the solid line is the phase-contrast image profile with 1.5 magnification.
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contrast was calculated by Eq. (6). Fig. 6 shows different profiles of the plastic cylinder. Fig. 7 shows the contrast of the images against magnification. It shows that having large magnifications does not contribute to contrast improvement and ultimately the phase imaging properties. The second object that was imaged was a drinking straw with a wall thickness of 0.14 mm. This object is also a plastic cylinder and was chosen because of the smaller thickness in comparison with the former test object, thus, less attenuation is expected. That way, it can be checked whether for a less substantial object the refraction results are as evident as in the previous sample. The profiles measured in this case are shown in Fig. 8. Fig. 8a shows the conventional absorption image and while Fig. 8b shows the phase-contrast enhanced image of the drinking straw. The position of this object was adjusted and several profiles were calculated by altering the distances r1 and r2 by 0.2 m each time. For each image retrieved at a different position, the contrast was calculated (Figs. 9 and 10).
Fig. 8. Images of the drinking straw obtained at 28 keV and 1 mA for 1 min. (a) The distance between the tube and the detector is 1.5 m and the object is in contact with the detector (absorption image), (b) the distance between the tube and the object is 0.9 m and between the object and the detector is 0.6 m (phase-contrast image with 1.67 magnification).
120 conventional r =1.3m r =0.2m r =1.1m r =0.4m r =0.9m r =0.6m
115
grey scale
110 130 Conventional r =1.4m r =0.1m r =1.3m r =0.2m r =1.2m r =0.3m r =1.1m r =0.4m r =1m r =0.5m r =0.9m r =0.6m
120
grey scale
110
105 100 95
100
90 1
5
9
13
90
17 21 25 number of pixels
29
33
37
Fig. 9. Four different profiles of the drinking straw obtained at 28 keV and 60 mA. The distances r1 and r2 were altered by 0.2 m each time. As the magnification increases, the forms of the profiles change with more obvious alterations between grey scales at the edges of the object.
80 70 10
20
30 40 50 number of pixels
60
70
80
0.25
Fig. 6. Seven different profiles of the plastic cylinder obtained at 28 keV and 60 mA. The distances r1 and r2 were altered by 0.1 m for each measurement.
0.44
0.20 contrast
0
0.15 0.10
0.42 contrast
0.40
0.05
0.38
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
magnification
0.36 0.34 0.32 0.30 1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Fig. 10. Contrast of images of the drinking straw, retrieved with different geometries and hence magnifications. By increasing the magnification, the contrast increases significantly until 1.5 magnification and over this magnification, the contrast increases only very slightly.
magnification Fig. 7. Contrast of images retrieved with different geometries—magnifications. By increasing the magnification, the contrast increases rapidly at the beginning and is kept almost stable for magnification over 1.4 .
In addition to the above objects, a biological sample was also used to observe the results of phase-contrast imaging. In particular, a dead wasp as shown in Fig. 11a was imaged
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Fig. 12. X-ray images obtained with Hamamatsu L8321 X-ray tube at 40 kVp and 100 mA with 1 min exposure time. (a) Absorption image and (b) phase-contrast image obtained at r1 ¼ 20 cm and r2 ¼ 65 cm. Fig. 11. Comparison between (a) conventional absorption imaging and (b) phase-contrast imaging of a wasp at 25 keV and 120 mA with 1.5 magnification.
in a conventional geometry (absorption image) and in phase-contrast geometry as shown in Fig. 11b (r1 ¼ 1 m and r2 ¼ 0.5 m). For these images, no profiles were retrieved but only the difference in image quality was observed. Fig. 11a shows the conventional absorption image and Fig. 11b shows the phase-enhanced image of the same wasp. The phase-contrast image has been rescaled to its original size in order to be compared with the conventional image. Some of the features that are not visible in the conventional absorption image can now clearly be seen in the phase-contrast images, such as wings and chambers in the antennae as pointed out by arrows. The benchtop X-ray phase imaging is being continually developed at Surrey, using and developing different X-ray sources and imaging systems. Fig. 12 shows the latest X-ray images of the same wasp using a Hamamatsu L8321, Hamamatsu Photonics microfocus X-ray tube with much smaller focal spot (3 mm) using a tungsten target. Two kinds of anode material, W filament or LaB6 single crystal,
are interchangeable. The cathode is the transmissive W layer (5 mm thickness), which is deposited onto a 5 mm Be window. Two stage electromagnets are designed to focus the electrons onto a spot size of 1 mm. While the W filament provides a longer life with a spot size of approximately 1 mm, the LaB6 filament has a shorter life but provides a focal spot sizes smaller than 1 mm. Fig. 12a shows the X-ray absorption image obtained with 1 min acquisition time at 40 kVp and 100 mA. Unlike the Oxford tube with its 110 mm focal spot size, the best resolution is not obtained in contact, as the focal spot of the Hamamatsu tube is smaller than the detector pixel pitch. It is obvious from Fig. 12b that we have obtained a much improved contrast and resolution. This is due to the fact that the geometric blurring or penumbra effect has changed, allowing us a better magnification with much better contrast function than the tube previously reported. 6. Conclusions Most of the experiments conducted for phase-contrast exploration employ synchrotron radiation because of its
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intensity and its spatial and temporal coherence. These experiments have shown that refraction-induced contrast is a very valuable analytical tool in X-ray imaging. Although it is possible to use such a source for clinical research, it would not be possible to use it for routine clinical applications because of the size, cost and availability of synchrotron facilities. Probably, in the future, compact X-ray sources with high intensity and monochromaticity will be developed in order to overcome this limitation and be used as a medical imaging tools. Even now, with currently existing X-ray tubes, phase-shifting effects can be visualised as has been shown in the experimental part of this study. The phase-imaging capabilities of our new X-ray system will be investigated further. References Arfelli, F., Assant, M., Bonvicini, V., Bravin, A., Cantatore, G., Castelli, E., Dalla Palma, L., Di Michiel, M., Longo, R., Olivo, A., Pani, S., Pontoni, D., Poropat, P., Prest, M., Rashevsky, A., Tromba, G., Vacchi, A., Vallazza, E., Zanconati, F., 1998. Low-dose phase contrast X-ray medical imaging. Phys. Med. Biol. 43, 2845–2852. Arfelli, F., Bonvicini, V., Bravin, A., Cantatore, G., Castelli, E., Dalla Palma, L., Di Michiel, M., Fabrizioli, M., Longo, R., Menk, R., Olivo, A., Pani, S., Pontoni, D., Poropat, P., Prest, M., Rashevsky, A., Ratti, M., Rigon, L., Tromba, G., Vacchi, A., Vallazza, E., Zanconati, F., 2000. Mammography with synchrotron radiation: phase-detection techniques. Radiology 215, 286–293. Baruchel, J., Buffiere, J., Maire, E., Merle, P., Peix, G., 2000. X-ray Tomography in Material Science. Hermes Science Publications, Paris, pp. 29–42. Donnelly, E., Price, R., 2002. Quantification of the effect of kVp on edgeenhancement index in phase-contrast radiography. Med. Phys. 29, 999–1002.
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