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Abstract
We show how to improve microfocus X-ray radiography by using the SOPHIAS silicon-on-insulator pixel detector in conjunction with an amplitude grating. Single-exposure multi-energy absorption and differential phase contrast imaging was performed using the single amplitude grating method. The sensitivity in differential phase contrast imaging in a two-pixel-pitch setup was enhanced by 39% in comparison with the previously reported method [F. Krejci, Rev. Sci. Instrum. 81, 113702 (2010).] by analyzing charge-sharing effects. Small-angle-scattering imaging was also possible in the two-pixel-pitch setup by counting the number of X-ray photons passing the pixel boundaries.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
X-ray absorption radiography with a microfocus x-ray source plays an important role in a variety of industrial and medical applications and in materials science, because it enables nondestructive observation of the inside of materials with high spatial resolution. Recently, to enhance soft-tissue contrast and to obtain nanometer-scale structural information, x-ray differential phase-contrast (DPC) and small-angle-scattering (SAS) (dark-field) imaging have been additionally combined with absorption imaging by using techniques such as the propagation-based method [1] and x-ray Talbot interferometer [2].
In an x-ray Talbot interferometer, phase and analyzer gratings are used to quantitatively obtain absorption, DPC, and SAS images [3]. The images are extracted from the measured data by numerically analyzing several moiré images between the interference pattern (self-image) of the phase grating and analyzer grating. However, optical parameters such as the source size, the pitches of the gratings, and the distances of the gratings are fixed in relation to the x-ray energy of the interferometer, whose operation relies on interference between x-rays. Thus, it is difficult to obtain x-ray images for several different x-ray energies.
As a result, methods that do not use x-ray interference have been proposed, wherein a shadowgraph of an amplitude grating is employed instead of the self-image of the phase grating. Olivo et al. demonstrated an edge illumination (EI) method using a conventional x-ray source and two amplitude gratings [4]. In this method, the x-ray beam is divided up into an array of x-ray beams by an amplitude grating (sample mask) placed in front of the sample. A second amplitude grating (detector mask) is set in front of the detector, of which the pattern is arranged to partially block each x-ray beam. Thus, any slight shift of the x-ray beams caused by refraction in the sample is detectable with high sensitivity. This method is applicable to polychromatic x-ray source, since it does not use x-ray interference. Endrizzi et al. confirmed that x-rays at all energies typically used in x-ray imaging are available for use in the EI method [5].
Despite of these advantages of the EI method, there still remain issues such as manufacturability and production cost of the second grating. Several groups have proposed methods that do not require the second grating [6–10]. Wen et al. demonstrated DPC imaging, in which the shadowgraph of the amplitude grating is directly detected by the detector and DPC images are acquired by Fourier analysis of the shadowgraphs [6]. Krejci et al. set the amplitude grating for the pitch of the shadowgraph to be two-pixel lengths on the detector [7]. In this method, x-ray refraction angles are estimated from the intensity ratio between the two pixels. However, while DPC images were successfully extracted, SAS images were not obtained. Vittoria et al. proposed an approach to obtain DPC and SAS images by fitting the intensity distribution of the four-pixel-pitch shadowgraph with Gaussian functions [8].
In this study, we demonstrate a state-of-art implementation of a novel pixel detector SOPHIAS (silicon-on-insulator photon imaging array sensor) [11] for DPC and SAS imaging in conjunction with a polychromatic microfocus x-ray source and single amplitude grating method. The SOPHIAS detector is an integration-type pixel detector with 1.9 Mpixels with a pixel size of 30 μm square. It operates up to 60 frames/s and has thick silicon photodiode with a thickness of 500 μm. This detector is originally developed for x-ray free-electron laser experiments. Target performance includes single x-ray photon sensitivity and high peak signal detection of 7 M electrons/pixel. In order to realize this performance, multiple sensor nodes has been implemented in a pixel, where a small fraction of the signal charge is transferred to the lower gain amplifier, while the large fraction is delivered to high gain amplifier. Then, the SOPHIAS detector is operated with a true correlated-double-sampling operation mode, where the kTC noise was removed. In the measurements described in this manuscript, the frame rate is 40 fps, that is, 25 msec for one frame. The integration time is 8.3 msec and the rest of 16.7 msec is read out time. We can perform photon counting with energy resolution when the number of photons for 9 pixels during the integration time of 8.3 msec is less than one. Therefore, the maximum photon rate is 1/0.0083/9 = 13.4 photons/pixel/sec in this condition. This gives us opportunity to utilize it as a spectro-imaging device with sub-pixel spatial resolution [12]. In the first part of this paper, we describe single-exposure multi-energy DPC imaging, which is very useful for observing unknown samples in practical applications. In the second part, we demonstrate improvements to DPC and SAS imaging in the two-pixel-pitch-shadowgraph setup by analyzing electric charge shared by neighboring pixels.
2. Single-exposure multi-energy DPC imaging
A schematic diagram of the optical system used in this study is shown in Fig. 1. The x-rays generated from the microfocus x-ray source are divided up into an array of x-ray beams by the amplitude grating. The source size is approximately 2 μm in diameter on the W target in this study. The amplitude grating is made with Au lines of 10 μm thickness. The size of the grating is 10 mm × 10 mm. The pitch of the grating (d1) is 8 μm. The pixel size of the detector is 30 μm × 30 μm. The distances between the source and grating, R, and source and detector, L, are 5.3 and 100 cm. The shadowgraph on the detector has a pitch of 150 μm (d2), equivalent to a length of 5 pixels in the detector. The magnification of the grating image (MG) is 18.9. The x-ray energy used for DPC imaging is more than 8 keV, so that the grating image on the detector can be regarded as a shadowgraph without taking interference effects into account; this was confirmed by performing a numerical simulation based on Fresnel diffraction theory [13].
To derive the absorption, DPC, and SAS images from a single observed image, we carried out a least squares fitting of 5 pixels of data around each pixel, aligned perpendicular to the shadowgraph, using a sinusoidal function, and obtained results for the amplitude, phase-shift, and baseline of the fitted sinusoidal function. We derived the three images by comparing these parameters with those obtained without a sample present [14].
The SOPHIAS detector [10] was operated at 40 fps in this study. The sensitive silicon layer with a thickness of 500 μm was fully depleted at the bias voltage of 124 V. In this report, the sensor was over-depleted by biasing 200 V during all the measurements. The sensor was cooled down to −20 °C during operation in dry air. The detector sensitive area is 2159 pixels × 891 pixels (64.77 mm × 26.73 mm).
In order to estimate the x-ray photon energy, we performed an event selection procedure as described by Tsunemi and Nakashima et al. [15, 16]. Briefly, the events were detected if the signal exceed the event threshold of 3.3 keV. After detecting the events, neighboring 8 pixels were searched, and if the signal is larger than the split threshold of 1.3-1.6 keV, the events were categorized as split events as shown in Fig. 2. These thresholds were empirically decided by verifying x-ray energy spectrum obtained by SOPHIAS. X-ray photon energy were obtained by summing the charges of central pixel and neighboring pixel with signal exceeding the split threshold. We categorized the event type of charge sharing by the number of charged pixels. The origin of the cross-talk in SOPHIAS are identified to the charge spread before the charge-voltage conversion, and electric cross-talk after the charge-voltage conversion. The former was measured to be 18.6 μm FWHM by using a knife-edge method with Cu target X-ray source at the voltage of 40 keV. The latter electric noise was measured to well below than 5%. Therefore the electric cross talk is small enough that we can neglect this in this study.
Figure 3 shows the x-ray spectra from the W target obtained by SOPHIAS together with the spectrum obtained by a commercially available CdZnTe (CZT) detector. The tube voltage and current were 40 kV and 10 μA, respectively, and 1000 frames were analyzed. The exposure time is 25 s. The SOPHIAS detector system used in this study shows system noise of 180 e-rms, where system noise includes readout and dark-signal-induced noises. Taking into account of the energy required for single electron-hole pair generation of 3.6 eV, the system noise is equivalent to 0.7 keV in standard deviation, which is consistent with the energy resolution of the single event spectrum (s) in Fig. 3. The energy spectrum with all the events (a) in Fig. 3 shows structure originating from the three peaks of the W Lα (8.40 keV), W Lβ (9.67 keV), and W Lγ (11.28 keV) lines. These were well separated in the CZT detector spectra. The SOPHIAS spectra with all events included (a) matched well to the convoluted spectra of Gaussian distribution with standard deviation of 1 keV and the CZT detector spectrum after weighting the difference of the quantum efficiency of SOPHIAS and CZT detectors (not shown here). We thus conclude that the current SOPHIAS detector has an effective energy resolution of 1 keV in standard deviation. The spectra obtained by SOPHIAS are also shown for each event type of charge sharing. The peak position is shifted to higher energy side for multiple events. Electric charge generated by higher energy photons increases and the spatial distribution of the charge spreads in the sensor layer, resulting in higher rate of multiple events. The generation rates of single, double, and triple events were 14.0, 43.9, and 23.1%, respectively, in the 5-15 keV energy range. 86% of the x-ray photons generate multi-pixel events, of which allows us to utilize charge sharing phenomena for sub-pixel resolution, as described in the second part of this study.
Fig. 3 X-ray spectra from W target obtained by SOPHIAS and CdZnTe detector. The spectra obtained by SOPHIAS are shown for each event type of charge sharing.
Figure 4(a) shows shadowgraphs obtained for all energies (0-40 keV) and for 10 ± 5, 20 ± 5, and 30 ± 5 keV ranges. A 0.2-mm-thick aluminum filter was inserted between the source and grating to reduce W characteristic x-rays. The grating images are clear for all energy ranges except for the 30 keV image, which is relatively noisy owing to the small number of incident photons. Figure 4(b) shows cross-sectional profiles of these images normalized by the average value; high visibilities of 51, 59, 52, and 40% were obtained for the all energies, 10, 20, and 30 keV ranges. Figure 4(c) shows similar cross-sectional profiles, but normalized to the maximum intensity. We can see that the minimum intensity increases with x-ray energy. This is due to an increase in x-ray transmitted through the 10-μm-thick gold grating. This is consistent with the visibility of the 10 keV energy range being higher than that of the all-energies range.
Fig. 4 (a) Grating images obtained for all energies (0-40 keV) and for 10 ± 5, 20 ± 5, and 30 ± 5 keV ranges. 2000 frames were employed for the analysis. The exposure time is 50 s. (b), (c) Intensity profiles along the lines perpendicular to the gratings in the grating images. Each profile is normalized by the average in (b) and maximum values in (c).
Figures 5 and 6 show x-ray absorption and DPC images of polymethyl methacrylate (PMMA) (ϕ3 mm) and Si (ϕ1 mm) spheres extracted from the single-exposure data. The samples were placed at a distance of 16 cm and 6 cm from the x-ray source, and 30000 frames were used in the analysis. The exposure time is 750 s. X-ray images for the 8 ± 2 keV and 15 ± 2 keV energy ranges are shown, of which the separation is much larger than the energy resolution of SOPHIAS.
Fig. 5 X-ray absorption (a, b), differential phase contrast (d, e) images, and section profiles (c, f) of PMMA sphere (ϕ3 mm) obtained for 8-keV (a, d) and 15-keV (b, e) x-rays. In the section profiles, observations and theoretical estimations are shown as solid and dashed lines, respectively. The scale in (a) gives the length at the sample position.
Fig. 6 X-ray absorption (a, b), differential phase contrast (d, e) images, and section profiles (c, f) of Si sphere (ϕ1 mm) obtained for 8-keV (a, d) and 15-keV (b, e) x-rays. In the section profiles, observations and theoretical estimations are shown as solid and dashed lines, respectively. The scale in (a) gives the length at the sample position.
We can see that the cross-sectional profiles of the absorption and DPC images of the PMMA sphere shown in Figs. 5(c) and 5(f) demonstrate very good agreement with the theoretically expected values for the density of PMMA (1.19 g/cm3), thereby indicating the validity of our method. Conventional measurements using polychromatic x-rays and a detector without an energy resolution are difficult to compare with estimates, even absorption images, because of beam hardening in which the high-energy component of the x-rays penetrating the samples increases depending on the thickness distribution of the samples. These results indicate that use of energy-resolved pixel detectors is very effective for dual-energy x-ray imaging characterizing materials [17], which reduces the uncertainty arising from beam hardening.
Regarding the absorption and DPC images of the Si sphere with relatively high density (2.33 g/cm3), 8 keV is too low an energy; the x-rays passing through the sample center are very weak, so that we cannot obtain enough information from either image (see Fig. 6). In contrast, the line profiles in the images obtained with 15 keV x-rays are similar to the theoretical expectations. It should be noted that these 8 and 15 keV x-ray images were both obtained from one single-exposure measurement. This is very important in actual applications such as characterization and inspection of unknown samples and samples consisting of materials with a variety of thicknesses, because we can select the most suitable x-ray energy for imaging after the measurement.
3. Improvements of DPC and SAS images using charge sharing analysis
One of the advantages of x-ray absorption radiography using a microfocus x-ray source is high spatial resolution, determined by the source size and the detector spatial resolution. In the case of DPC and SAS imaging using the setup shown in Fig. 1, the pitch of the shadowgraph on the detector limits the spatial resolution. Here, in order to prevent degradation of spatial resolution, Krejci et al. investigated imaging using a shadowgraph with a two-pixel pitch setup of the detector [7]. The advantage of the two-pixel pitch setup is high spatial resolution comparing with long pitch setups. However, two problems arose in their study. One is the degradation of phase sensitivity in DPC images due to charge sharing. The other is inability to obtain SAS images. In this part of our study, we show how phase sensitivity in DPC imaging can be enhanced and how to obtain SAS images by analysing charge sharing.
Figure 7 schematically illustrates the arrangement of the x-ray beam and detector pixels in the two-pixel-pitch setup. Each x-ray beam from the amplitude grating is initially aligned to illuminate the boundary of the two pixels. The beam shifts because of refraction and broadens because of SAS in the samples. The refraction angle can be estimated by the ratio of the numbers of x-ray photons entering the two pixels. The previous study reported in [7] used the electric charge integrated during the exposure instead of the photon numbers, but the resultant charge sharing between the pixel boundaries indicated by (r) and (s) in Fig. 7 degraded the sensitivity of the x-ray beam shift, because the charge sharing reduces the ratio. Furthermore, the previous study did not estimate the broadening of the beam.
Fig. 7 Schematic arrangement of x-ray beam and detector pixels in the two-pixel-pitch setup. X-ray beam is initially aligned to illuminate the boundary (r) of the two pixels. The x-ray beam shifts and broadens due to refraction and SAS in samples, respectively.
We estimated the refraction angle of the beam by using the photon number. Charge sharing analysis, wherein charges in neighboring pixels are compared for each photon, allows us to distinguish the pixel that the x-ray photon fell on. Figure 8 plots calibration curves showing the relation between the x-ray beam position and the count ratio between the two pixels when the amplitude grating was placed at R = 13.3 cm (MG is 7.5.) and the beam was shifted by moving the amplitude grating by a piezo driver. We can clearly see that the curve obtained from the x-ray photon numbers has a higher gradient than the one obtained from the electric charge, indicating the x-ray photon number method has higher sensitivity in x-ray refraction. A count ratio of 0.525 was obtained for a 1 μm beam shift, which is 39% higher than that of the electric charge method.
Fig. 8 Calibration curves showing the relationship between x-ray beam position and the count ratio between two pixels in the two-pixel-pitch setup. Solid and open circles show the ratios computed using the photon number and the electric charge, respectively. The right figure is an enlargement where the curves cross around the origin.
We extracted SAS images in the two-pixel-pitch setup by counting the number of x-ray photons causing charge sharing at the pixel boundary denoted by (s) in Fig. 7. Beam broadening increases the number of photons passing close to the pixel boundary. We distinguished the photons by utilizing charge sharing analysis.
Figure 9(a) shows the absorption, DPC, and SAS images of a PTFE wire (ϕ1 mm) and a mechanical pencil lead (ϕ0.5 mm) obtained with the two-pixel-pitch setup in the energy range of 5-15 keV. The samples were placed 25 cm from the x-ray source and 8000 frames were analyzed. The exposure time is 200 s. We obtained two images with and without samples. Absorption image expresses the ratio of the total count of the two pixels between the two images. DPC signals show the refraction angle of x-ray beam caused by the samples calibrated from the count ratio between the two pixels. SAS signals indicate the increments of the number of x-ray photons causing charge sharing at the pixel boundary (s) after the sample insertion. For comparison, we show the results of the five-pixel-pitch setup described in the first part of this paper, where the amplitude grating was set at R = 5.3 cm (MG is 18.9).
Fig. 9 (a) Absorption, DPC, and SAS images of a PTFE wire (ϕ1 mm) and a mechanical pencil lead (ϕ0.5 mm) obtained with 5-15 keV x-rays in the two- and five-pixel-pitch setups. (b), (c) Cross-sectional profiles of DPC and SAS images. The dashed line in (b) is the theoretical estimate.
We can see the artifacts at the edges of the samples in the DPC and SAS images obtained with the five-pixel-pitch setup, which seem to be bright dashed lines. These artifacts occurred during the least squares fitting of 5 pixels of data including sample edges. In contrast, the artifacts are not visible in the images obtained in the two-pixel-pitch setup, because only two pixels are influenced by the sample edges.
Figures 9(b) and 9(c) show cross-sectional profiles of the DPC and SAS images, respectively. We can see good agreement between the observations and theoretical estimation in the DPC profiles, indicating the validity of the two-pixel-pitch measurement. In the SAS images, we cannot see the SAS signals inside of the PTFE sample, but can see them in the pencil lead for both profiles. The pencil lead has a fine structure causing SAS signals [18], so these results indicate that our method can obtain SAS images, although they are not quantitative differently from the conventional Talbot interferometer results.
Figure 10 shows the results for a small fish having a relatively complicated structure, placed at a distance of 12 cm from the x-ray source. The energy range is 5-15 keV. Periodic artifacts appear in the magnified five-pixel-pitch images image, and they are due to the fine structure of the sample having a length scale similar to the shadowgraph pitch at the detector position, causing periodical artifacts. On the other hand, the clear high spatial resolution images without artifacts are obtained with the two-pixel-pitch setup.
Fig. 10 Absorption and DPC, SAS images of small fish obtained with 5-15 keV x-rays. The exposure time is 200 s.
4. Summary
We demonstrated the effective use of the SOPHIAS detector for microfocus x-ray radiography in conjunction with the single amplitude grating method. First, we described single-exposure multi-energy absorption and DPC imaging, which is very useful for observing unknown samples or samples with different thicknesses in practical applications. Then, we demonstrated how DPC imaging can be improved in the two-pixel-pitch-shadowgraph setup by analyzing charge sharing; the sensitivity of DPC images was enhanced by 39% compared with that of the conventional method. We also showed SAS imaging in the two-pixel-pitch setup by counting photon numbers passing the pixel boundaries. These results extend the range of application of x-ray radiography using microfocus x-ray source. In this study we limited the demonstrations using relatively low x-ray energy. However, we consider that the measurements using higher energy x-rays around 30 keV will be available by modifying the incident x-ray energy spectrum. For higher energy imaging, we have to improve the detector efficiency and to increase the grating thickness. In order to improve the spatial resolution, we have to decrease the pitch of the grating, although the grating pitch has the tradeoff relation with the thickness of the grating.
We demonstrated single-exposure multi-energy imaging in the section 2. To our knowledge, we do not know the measurement results of the level equivalent to us. For most photon-counting pixel-detectors, including Timepix and Medipix, there are one or two thresholds that you can set to determine X-ray energy [19]. Therefore, it is impossible to measure the spectrum of incident X-rays with one measurement. Usually, we measure the spectrum by performing multiple measurements while changing the threshold values. Even with the latest Medipix 3, there are eight thresholds that can be set, and it is impossible to obtain the spectrum as shown in Fig. 3 by one measurement. We showed that it is possible to obtain images of almost arbitrary energy range after one measurement, which is very meaningful for microfocus X-ray radiography. In addition, since the pixel size of Timepix and Medipix is as large as 55 μm, even if using the same two-pixel-pitch setup, its spatial resolution is inferior to our result.
Funding
Japan Society for the Promotion of Science (JSPS) KAKENHI (Grant Number 16H00948, 16H00949, 16K13787), and partly by MEXT KAKENHI Grant number 25109007, and partly by X-ray Free-Electron Laser Priority Strategy Program (Ministry of Education, Culture, Sports, Science and Technology of Japan).
Acknowledgments
The authors thank Shimadzu Co. for use of the microfocus x-ray source.
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