Noninterferometric phase-contrast images obtained with incoherent x-ray sources

Transcription

1 Noninterferometric phase-contrast images obtained with incoherent x-ray sources Alessandro Olivo,* Konstantin Ignatyev, Peter R. T. Munro, and Robert D. Speller Department of Medical Physics and Bioengineering, University College London, Malet Place, Gower Street, London WC1E 6BT, UK *Corresponding author: Received 4 January 2011; revised 9 February 2011; accepted 11 February 2011; posted 15 February 2011 (Doc. ID ); published 18 April 2011 We report on what are believed to be the first full-scale images obtained with the coded aperture concept, which uses conventional x-ray sources without the need to collimate/aperture their output. We discuss the differences in the underpinning physical principles with respect to other methods, and explain why these might lead to a more efficient use of the source. In particular, we discuss how the evaluation of the first imaging system provided promising indications on the method s potential to detect details invisible to conventional absorption methods, use an increased average x-ray energy, and reduce exposure times all important aspects with regards to real-world implementations Optical Society of America OCIS codes: , , In x-ray phase-contrast imaging (XPCi), contrast arises from the phase changes that x rays undergo when crossing an object, which enhances detail visibility [1,2]. XPCi methods developed so far [3] require spatial coherence, i.e., synchrotron radiation (SR) or microfocal sources, which prevented realworld implementations. Extended sources have been used [4] by collimating/aperturing the source in order to make it sufficiently coherent. This, however, may result in increasing the exposure time, as very narrow apertures are obtained in structures with a much larger thickness, resulting in nonnegligible angular filtration of the emitted beam. Here we present what are believed to be the first full-scale images obtained with a different approach, which exploits x-ray refraction by means of pixel edge illumination obtained through coded aperture systems [5 7]. The realization and evaluation of the first full-scale imaging system allowed us to demonstrate that the method enables the visualization of details invisible with conventional absorption-based techniques, that it allows increasing the average x-ray energy while maintaining a detectable signal, and /11/ $15.00/ Optical Society of America that it could provide a way to reduce the overall exposure time compared to other methods. A simplified way to describe the behavior of photons in matter is provided by the refractive index [8] n ¼ 1 δ þ iβ. Variations in δ translate into different x-ray velocities, which distort the wavefront and can be used to generate image contrast. These distortions are often detected by means of interferometers, either based on perfect crystals [9] (Bonse/Hart) or gratings [4,10,11] (Talbot or Talbot/Lau interferometers). These are used to generate interferograms, which are perturbed by the introduction of a sample. Recording these perturbations allows the generation of an image of the sample that caused them. For the interferometer to create a detectable interferogram, the source must either be spatially coherent, or be made spatially coherent by means of a third, source grating (which corresponds to switching from the Talbot to the Talbot Lau configuration). The approach discussed here does not require the generation of interferograms, as it is based purely on x-ray refraction. Wavefront distortions translate into local deviations in the photon direction, and the deviation angle α is proportional to the gradient of δ: 20 April 2011 / Vol. 50, No. 12 / APPLIED OPTICS 1765

2 α ¼ λ 2π j~ x;y Φj¼ Z ~ x;y object δðx; y; zþdz ; ð1þ where λ is the x-ray wavelength and z is the x-ray propagation direction. The total phase shift Φ is given by the integral of δ along the z direction multiplied by 2π=λ. ~ x;y is the gradient operator where derivatives are performed along the transverse directions only. Although the wave optics description based on Fresnel/Kirchoff integrals is more rigorous [2,8,12], it has been demonstrated that, under relaxed coherence conditions like the ones described here, the two approaches yield equivalent results [13]. Refraction-based XPCi converts phase effects into image contrast by means of a system sensitive to deviations in the photon direction. At SR facilities, this is often done by means of silicon crystals placed between sample and detector: the crystal s reflectivity curve is used to analyze photon directions [1,14,15]. If used with polychromatic sources [1,16], crystals select the appropriate components of the beam and discard the others. In coded aperture XPCi, a similar discrimination of the photon direction is obtained by illuminating only the edges of the detector pixels [17]. Consider a single detector pixel illuminated by a collimated x-ray beam [Fig. 1(a)]. Instead of centring the beam in the middle of the pixel, the beam is aligned with one pixel edge. If an object is scanned through the beam, when the object (or a detail inside it) touches the upper side of the beam, some photons that in absence of the object would miss the pixel are deviated to fall inside it [dashed arrow in Fig. 1(a)], increasing the number of counts. Likewise, when the object grazes the lower part of the beam, photons that would normally hit the detector are deviated outside it [dashed arrow in Fig. 1(b)]. In this way, a differential XPCi profile resembling that obtained using an analyzer crystal is acquired [17], while allowing the full use of a polychromatic and divergent beam. This is obtained by means of coded aperture setups, which simply allow repeating the process outlined above for every detector row (or column) of an area detector illuminated by a divergent, polychromatic beam [5,7]. In this case, the use of an area detector makes sample scanning unnecessary. A schematic of the setup is shown in Fig. 2, while Fig. 3 shows a scanning electron microscope of a portion of one of the coded aperture masks. A detailed description of the working principles of coded aperture XPCi was given previously, both based on the simplified ray-tracing approach [18] and on the more rigorous diffraction theory [19], and will, therefore, not be repeated here for brevity s sake. It should be noted that, although there might be similarities between the appearance of the coded aperture XPCi system and a Talbot interferometer, they are based on different principles. The gratings in a Talbot interferometer have a much smaller pitch, to allow sufficient sensitivity to small angular deviations. The two gratings must be separated by one of the wavelength and pitch-dependent Talbot distances, and multiple images at different positions of one of the gratings ( phase stepping ) are acquired, allowing the extraction of differential XPCi, absorption, and dark-field images. In coded aperture XPCi, the aperture pitch matches that of the pixels in the detector, i.e., is between 1 and 2 orders of magnitude greater than in Talbot gratings, which is what allows the use of larger sources without additional collimation. It would be impossible to use such a large pitch with a grating interferometer, as this would result in insufficient angular sensitivity. In our case, the sensitivity is obtained by exploiting the edge illumination principle: Fig. 1. Schematic of the edge illumination working principle. (a) and (b) show the image formation principle for a single pixel and a single collimated beam, aligned with the edge of the pixel. Photons deviated due to refraction in the sample can change their status from undetected to detected (a) or vice versa (b), creating the positive and negative peaks of differential XPCi. Fig. 2. Schematic of the coded aperture setup: two sets of coded apertures (SA, sample apertures, and DA, detector apertures) allow repeating the situation depicted in Fig. 1 for all rows (or columns) of an area detector. The sample is placed immediately downstream of the sample apertures, almost in contact with them. P is the detector pixel size and ΔP the fraction of the pixel directly illuminated by radiation: this can be changed simply by displacing SA with respect to DA. A smaller ΔP results in increased sensitivity but also in increased exposure time APPLIED OPTICS / Vol. 50, No. 12 / 20 April 2011

3 Fig. 3. Scanning electron microscope image of a small area on the top of the detector mask (apertures in dark gray). The pitch has been slightly reduced with respect to the desired one (100 mm) to allow for a small distance between mask and detector, hence facilitating mask positioning and alignment. each thin individual beam straddling the edge between sensitive and insensitive regions on the detector yields high sensitivity to small angular deviations. The remaining part of each pixel is not illuminated, meaning that the refraction signal is not washed out by unwanted background. To further clarify this point, let us stress that if we aligned the coded apertures masks such that the apertures overlapped, thus fully illuminating the sensitive part of the pixel, most of the method sensitivity would be lost: it is the misalignment between the masks that creates the sensitivity. This comes at a cost of an increased exposure time, but overall the balance could be advantageous, as discussed below. Generally speaking, the exposure time required to maintain the same x-ray statistics scales linearly with the fraction of the pixel surface exposed to radiation, and the way in which the system sensitivity increases with a reduced exposed fraction is discussed in detail in [7]. The large aperture pitch also results in simplified alignment requirements and increased robustness against environmental vibrations and temperature variations, and makes scaling the system by tiling multiple masks easier. As an application example, we show a difficult case in security inspections. In conventional x-ray imaging, the detection of plastic explosives is made problematic by materials having similar attenuation characteristics, such as cheeses, liquids, and other plastics. Therefore, the ability to contextualize such objects with respect to wires and other components that could indicate the presence of a threat becomes important. Such a capability is not ideally handled by absorption contrast imaging due to a lack of information in the signal, which motivates the need for an XPCi technique. We have designed a system capable of operating at hard x-ray energies [20], and used it to image a custom-made phantom containing a 2 mm thick simulated plastic explosive and 70 μm thick aluminum wires. Coded aperture masks with 100 μm gold thickness and an overall area of 36 cm 2 were fabricated to the authors design by Creatv Microtech (Potomac, Maryland). In the detector mask, apertures are 30 μm wide, 6 cm long and the pitch is just below 100 μm, to allow matching the apertures to every second pixel column on the detector (see Fig. 3). The presample mask is identical, apart form a scaling factor (50%, see below) accounting for the beam divergence. A W target x-ray source, used in hospital work since the mid-1980s [21], was employed, jointly with the Hamamatsu C9732DK flat panel detector, a passive-pixel complementary metal oxide semiconductor sensor with a pixel size of 50 μm (rebinned to match the above aperture pitch). Figure 4(a) shows an image taken at a tube potential of 40 kvp. All details are visible: the thin Al conductors, the 2 mm plastic cylinder simulating the explosive and, behind it, a 300 μm thick polyethylene binding fibre. The source-to-detector distance was 2 m with the sample placed in the middle. Figure 4(b) shows the absorption image at the same photon statistics, obtained by placing the sample in contact with the detector, in which the only discernible feature is the plastic cylinder. Optimum image acquisition depends upon the available x-ray flux and the way in which the sample is presented (e.g., scanned versus static acquisitions). The above images were obtained by acquiring images at five subpixel positions and combining them to obtain an image with increased resolution ( dithering ). In a scanned acquisition mode like that of most security systems, acquiring multiple images of this kind would be just an issue of how frequently the detector is read out. However, to demonstrate that this is not essential to the method, we also show the undithered image (Fig. 5). Its resolution is coarser and the pixelization is apparent, but all features are still detected. In this case, as the pitch of the detector apertures typically matches that of the detector pixels, the image resolution is determined by the Fig. 4. Coded aperture XPCi versus conventional absorption imaging. (a) and (b) show the coded aperture XPCi and the conventional absorption image, respectively, of the same sample, obtained at the same photon statistics, i.e., at the same level of background noise. 20 April 2011 / Vol. 50, No. 12 / APPLIED OPTICS 1767

4 Fig. 5. Undithered coded aperture XPCi image. Images presented in Fig. 2 were dithered, i.e., combinations of a series of images taken at various subpixel displacements. Here an image taken without the dithering procedure shows, despite a coarser overall resolution, that all details are still detected. This allows further reducing the exposure time. pixel size; if a subpixel dithering step is applied, then the resolution is driven by the dithering step itself, provided this is larger than or equal to the size of the apertures in the detector mask (which effectively reshape the detector point spread function). This demonstrates the flexibility of the method with regard to accommodating whatever photon flux is available. Finally, to demonstrate the robustness of the method against increasing x-ray energy, an image of the same sample taken at 100 kvp is shown in Fig. 6. A reduction in the contrast, in agreement with the behavior of δ versus average photon energy, is encountered, but all details are still detected. To avoid damaging the target, all images were acquired with a tube current of 1 ma, resulting in exposure times between 40 and 60 s (for the nondithered images). These seem to be at least 1 order of magnitude below any other XPCi acquisition with non-sr sources to date, as, to the best of our knowledge, comparable exposure times were only achieved by exploiting tube currents as high as ma [22,23] (at the same tube voltage, i.e., 40 kv). The use of a source with a similar power, but with a focal spot size comparable to that used in this study (e.g., FR-E+ SuperBright, Rigaku, Japan), could, therefore, be expected to allow acquisition times of the order of a few seconds. This is clearly a preliminary result, as a rigorous comparison would require imaging the same sample with the various techniques, and reach an x-ray statistics resulting in exactly the same signal-to-noise ratio. However, it provides Fig. 6. High-energy coded aperture XPCi image. This was taken at 100 instead of 40 kvp: the increased average beam energy causes the expected reduction in the contrast, but despite this all details are still detected. an encouraging indication, and further investigations will ensue as: 1. in applications requiring softer x rays (e.g., mammography), we would use thinner masks, therefore increasing their angular acceptance even further, and 2. we have preliminary indications, albeit only at the simulated level, that the overall system length could be reduced from 2 mto1:5 1:6 m[7], which would allow a further increase in the flux reaching the detector. We are currently in the phase of commissioning a Rigaku MM-07 source, which will be used to investigate these important aspects in the near future. We used a focal spot of 50 μm, about 1 order of magnitude larger than those used in previous XPCi experiments with microfocal sources; however, we have previously demonstrated that focal spots up to 100 μm can be used without affecting image quality [7]. It should be noted that, according to the definition recently given by Wu and Liu [24], the method is a phase-contrast imaging rather than a phase imaging one, in that it does not yet allow the extraction of quantitative information. However, a formalism describing image formation was previously derived [18,19], and we are currently developing it further to allow phase retrieval approaches. Finally, the technique can be made sensitive to phase effects in two directions simultaneously through individual L-shaped apertures matching each pixel [25], even though in its present state this method does not allow analytically separating x and y information unless additional mask/sample motion is employed. This project is funded under the Innovative Research Call in Explosives and Weapons Detection (2007), a cross-government programme sponsored by Home Office Scientific Development Branch (HOSDB), Department for Transport (DfT), Center for the Protection of National Infrastructure (CPNI) and Metropolitan Police Service (MPS). A. Olivo is supported by a Career Acceleration Fellowship awarded by the UK Engineering and Physical Sciences Research Council (EP/G004250/1). References 1. T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, Phase-contrast imaging of weakly absorbing materials using hard x-rays, Nature 373, (1995). 2. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation, Rev. Sci. Instrum. 66, (1995). 3. R. Lewis, Medical phase-contrast x-ray imaging: current status and future prospects, Phys. Med. Biol. 49, (2004). 4. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, Phase retrieval and differential phase-contrast imaging with lowbrilliance x-ray sources, Nature Phys. 2, (2006) APPLIED OPTICS / Vol. 50, No. 12 / 20 April 2011

5 5. A. Olivo and R. Speller, A coded-aperture approach allowing x-ray phase contrast imaging with conventional sources, Appl. Phys. Lett. 91, (2007). 6. A. Olivo, D. Chana, and R. Speller, A preliminary investigation of the potential of phase contrast x-ray imaging in the field of homeland security, J. Phys. D 41, (2008). 7. A. Olivo and R. Speller, Modelling of a novel x-ray phase contrast imaging technique based on coded apertures, Phys. Med. Biol. 52, (2007). 8. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980). 9. A. Momose, T. Takeda, Y. Itai, and K. Hirano, Phase-contrast x-ray computed tomography for observing biological soft tissues, Nat. Med. 2, (1996). 10. J. F. Clauser, Ultrahigh resolution interferometric x-ray imaging, U.S. patent (22 September 1998). 11. A. Momose, A. W. Yashiro, T. Takeda, Y. Suzuki, and T. Hattori, Phase tomography by x-ray Talbot interferometry for biological imaging, Jpn. J. Appl. Phys. 45, (2006). 12. A. Olivo and R. Speller, Experimental validation of a simple model capable of predicting the phase contrast imaging capabilities of an x-ray imaging system, Phys. Med. Biol. 51, (2006). 13. A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, The effects of the imaging system on the validity limits of the rayoptical approach to phase contrast imaging, Med. Phys. 32, (2005). 14. V. N. Ingal and E. A. Beliaevskaya, X-ray plane-wave topography observation of the phase contrast from a noncrystalline object, J. Phys. D 28, (1995). 15. D. Chapman, W. Thomlinson, R. E. Johnson, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, Diffraction enhanced x-ray imaging, Phys. Med. Biol. 42, (1997). 16. D. J. Vine, D. M. Paganin, K. M. Pavlov, J. Kräusslich, O. Wehrhan, I. Uschmann, and E. Förster, Analyzer-based phase contrast imaging and phase retrieval using a rotating anode x-ray source, Appl. Phys. Lett. 91, (2007). 17. A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field, Med. Phys. 28, (2001). 18. A. Olivo and R. Speller, Image formation principles in codedaperture based x-ray phase contrast imaging, Phys. Med. Biol. 53, (2008). 19. P. R. T. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, The relationship between wave and geometrical optics models of coded aperture type x-ray phase contrast imaging systems, Opt. Express 18, (2010). 20. A. Olivo, K. Ignatyev, P. R. T. Munro, and R. D. Speller, Design and realization of a coded-aperture based x-ray phase contrast imaging for homeland security applications, Nucl. Instrum. Methods Phys. Res. A 610, (2009). 21. J. C. Buckland-Wright, A new high-definition microfocal x- ray unit, Br. J. Radiol. 62, (1989). 22. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, Hard-x-ray dark-field imaging using a grating interferometer, Nat. Mater. 7, (2008). 23. A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, Grating-based x-ray phase imaging using multiline x-ray source, Jpn. J. Appl. Phys. 48, (2009). 24. X. Wu and H. Liu, Clarification of aspects in in-line phasesensitive x-ray imaging, Med. Phys. 34, (2007). 25. A. Olivo, S. E. Bohndiek, J. A. Griffiths, A. Konstantinidis, and R. D. Speller, A non-free-space propagation x-ray phase contrast imaging method sensitive to phase effects in two directions simultaneously, Appl. Phys. Lett. 94, (2009). 20 April 2011 / Vol. 50, No. 12 / APPLIED OPTICS 1769