1. Introduction

X-ray phase contrast and dark-field imaging has experienced a tremendous boost in the last two decades, as subtle details with substantially improved sensitivity can be revealed by these advanced X-ray imaging techniques over the conventional absorption contrast imaging. Diverse X-ray phase contrast imaging and dark-field imaging techniques have been developed, and remarkable achievement has been made in biomedical diagnostics, material science and palaeontology [1–5]. Combined with the absorption and phase contrast imaging, X-ray dark-field imaging provides complementary scattering information from the samples by reveal fine features due to sub-pixel inhomogeneity [6]. The most common phase contrast methods include crystal interferometry [7], analyzer-based imaging (ABI) [8], propagation-based imaging (PBI) [9] and grating-based imaging (GBI) [10]. Although these methods use different experimental setups, the signals provided in the raw images are all related to variations in the X-ray refractive index within the sample under study. A comprehensive comparison among PBI, ABI and GBI techniques has recently been made to help choose the most suitable technique for a given application [11,12]. Among all these X-ray phase contrast techniques, GBI has been extensively investigated and shows great potential for practical application since it can be implemented using low-coherence and polychromatic X-ray sources [13]. Recently, the X-ray speckle based imaging (SBI) technique has been demonstrated to retrieve multimodal images by analyzing the changes in the speckle patterns [14–16]. Instead of high precision X-ray gratings as required for the GBI technique, only a piece of filter membrane or abrasive paper with random structure is needed in the SBI technique. Although the two techniques appear to work on quite different principles, it was shown that the GBI technique can be treated as a special case of SBI technique [17]. However, no comparative study between GBI and SBI has been reported so far. In this work, we focus on the systematic experimental comparison between the grating- and speckle-based techniques for synchrotron-based X-ray imaging. Advantages, drawbacks and limitations of the two techniques for both X-ray phase and dark-field imaging are discussed.

2. Method

For grating-based imaging technique, a standard grating interferometer consists of a phase grating and an analyzer grating. A one-dimensional (1D) phase grating is commonly used as a beam splitter to form the interference pattern, and a single 1D analyzer grating placed at an odd order of the Talbot distance from the phase grating acts as a transmission mask [18]. The Moiré fringes are created by a superposition of the self-image of the phase grating and the analyzer grating with a small inclination angle between them. An X-ray area detector is then placed immediately behind the analyzer grating to record these fringes. Grating interferometry can work in either moiré fringe analysis mode or phase stepping mode. Although only a single image is required for moiré fringe analysis mode [19], it suffers from low spatial resolution, which is limited by the period of the moiré fringe. To improve the spatial resolution, the phase stepping mode is often used by scanning either the phase or the analyzer grating perpendicular to the grating line direction. Alternatively, combination of a high resolution X-ray detector and grating can also be used to obtain single shot X-ray phase contrast images using spatial harmonic analysis approach. This scheme is particularly useful when 2D gratings are employed to obtain two-direction phase contrast images without the use of analyzer grating [20,21]. In this case, the spatial resolution and angular sensitivity is limited by the grating period.

Figure 1 shows the comparison of the scanning approaches for GBI and SBI for retrieving the multiple contrast images from the collected detector signal. As demonstrated in Fig. 1(a), the intensity for each detector pixel will oscillate periodically as the grating is scanned. The Fast Fourier Transform (FFT) is used to retrieve the absorption, differential phase and dark-field information by performing pixel-wise analysis. The absorption contrast is obtained by taking the ratio of the average value of the Fourier transforms of the phase stepping curve obtained with ($a_0^s$) and without ($a_0^r$) the sample, evaluated at the zeroth harmonic

 

Fig. 1 (a) Phase stepping scheme for grating interferometry (b) equivalent speckle scanning scheme in speckle imaging approach. The parameters$a_1^r$, $a_1^s$,$a_0^r$, $a_0^s$,${\varphi }_0^s$, ${\varphi }_0^r$and $\text{ξ}$ are evaluated using the Fourier transform process in case of grating interferometry, while equivalent parameters in speckle scanning technique are obtained using real space correlation. The plot is of signal recorded in detector pixel in absence (square black) and in presence of sample (circle red).

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In contrast, the X-ray speckle-based imaging technique utilises properties of the near-field speckle generated from a random diffuser. The basic concept is to use speckles as wavefront markers and deduce the changes in the speckle pattern due to the sample. Like the moiré fringe analysis mode for GBI, the speckle tracking technique only requires a single speckle image, one with sample and the other without sample [14–16]. While this approach is dose-efficient and easy to implement, it suffers from low angular and spatial sensitivity since a subset size (over tens of pixels) is chosen to apply the cross-correlation algorithm. To overcome this limitation, a speckle scanning scheme has been recently proposed to extract high resolution phase and dark-field images using one-dimensional scan [23, 24]. As shown in the Fig. 1(b), when the diffuser is scanned perpendicular to the beam direction, the intensity at each pixel position oscillates. The intensity oscillation resembles the non-periodic nature of the diffuser. In this sense, this stepping scheme can be considered as a generalization of the phase stepping of a periodic or structured pattern of gratings. In this scheme, the detector signal at each pixel with ($s(r,\epsilon )$) and without ($w(r,\epsilon )$)sample is obtained by scanning the random diffuser (membrane/abrasive paper) with a constant step ($\epsilon$). The displacement vector ($\overrightarrow{\xi }$) of the speckle is calculated using cross-correlation between the two-signals according to the following equation

The absorption image is then obtained by taking the ratio of the average signal recorded in each pixel with and without the object as follows

The decrease in the correlation between the speckles due to the scattering angle distribution of the object, and it can be related to the dark-field signal for SBI technique [23]. The dark-field signal can be written as [25]

3. Experiments

The experiments were performed at the Diamond Light Source’s B16 Test beamline using X-rays from a bending magnet source [26]. X-ray energies from 4 to 21 keV can be selected using either a double multilayer monochromator (DMM) or a double crystal monochromator (DCM). For the characterization of Mammographic accreditation phantom using SBI technique, the data was collected with the DCM at energy of 15keV. For GBI technique, the DCM was replaced by the DMM in order to increase the flux due to the high absorption of the analyzer grating. The same X-ray area detector was used to acquire all sets of images for both the experiments.

Figure 2 shows the schematic layout of experimental setups for grating- and speckle-based experiments. As illustrated in Fig. 2a, the grating interferometer consist a πphase grating and a absorption grating, and the period of the phase grating and the analyzer grating was 4µm and 2µm, respectively. As shown in Fig. 2(c), the complex GBI setup is replaced by a simple diffuser for the SBI technique. Here, a piece of abrasive paper with an average particle size of 5µm was used as the diffuser and mounted on a motorized stage. The specimen was mounted on a motorized sample stage, which was located at 47m from the source. For the Mammographic accreditation phantom shown in Fig. 3, the analyzer grating was kept at the 9th order Talbot distance of 217mm from the phase grating, while the distance between the diffuser and the detector for SBI was 1050mm. Images of the speckle pattern and grating interferograms were recorded using an X-ray area detector with an effective pixel resolution of 2.25 µm × 2.25 µm. While for samples shown in Fig. 4, both the grating inter-distance ($d_m$) and the diffuser-to-detector distance ($L$) were set to 605mm in order to compare the angular sensitivity for the two techniques under the similar experimental conditions, and the X-ray area detector with an effective pixel resolution of 1.8 µm × 1.8 µm was used. For SBI experiments, a set of 80 speckle images for each stack (with and without sample) were collected with the step size of 0.5 µm and data acquisition time of 1s for each image. For GBI experiments, a set of 32 images (with and without sample) were acquired over two periods of the phase grating and the data acquisition time was 10s for each image.

 

Fig. 2 Schematic of the experimental setup for X-ray (a) GBI and (c) SBI. The recorded image on the detector is shown in (b) and (d), respectively. The recorded signals along one column of detector pixels are indicated in (a) and (c) in the absence of sample (solid black) and in the presence of sample (dashed red).

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Fig. 3 Retrieved of results for a nylon fiber from mammography phantom using GBI and SBI. (a) Dark-field image (b) vertical wavefront gradient (c) line profile of vertical wavefront gradient using GBI (circle red). (d) Dark-field image (e) vertical wavefront gradient technique (f) line profile of vertical wavefront gradient along the marked line using SBI (triangle blue). (g) horizontal wavefront gradient using SBI. Reconstructed phase map using (h) SBI and (i) GBI. The scale bar at the top right is 0.5mm long.

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Fig. 4 (a) Absorption (b) dark-field (c) vertical wavefront gradient (d) horizontal wavefront gradient of a test phantom made of rod, tube and a piece of wood using SBI technique. (e) Absorption (f) dark-field (g) unwrapped vertical wavefront gradient using GBI technique. (h) Reconstructed phase map of the test phantom using SBI technique. The scale bar at the bottom right is 0.5mm long.

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4. Results

As a comparison of the two imaging techniques, we first present the results of a standard mammographic accreditation phantom (Gammex 156) for medical imaging applications. This phantom approximates the X-ray attenuation of a 4.2 cm slab of compressed human breast. It is made up of a wax block containing different test objects which represent the different structures or malignancies which may be found when imaging the breast, and it has been studied using GBI with a compact synchrotron light source [27]. In this study, we only selected a nylon fiber (test pattern #5) as a test sample for comparing the two techniques. The results obtained using both the techniques are shown in Fig. 3. For the GBI technique (Fig. 3 (a, b and h)), the phase stepping scheme was used, and the Fourier transform method with pixel-wise analysis was employed to obtain different contrast modalities. In contrast, the real-space cross-correlation algorithm was used for the SBI technique [28], and the speckle analysis was performed by scanning the diffuser in vertical direction. As seen from Fig. 3(a) and 3(d), the dark-field information from both the techniques is mostly caused by the edge enhancement effect due to the finite coherence of the X-ray beam. One way to reduce this is to decrease the detector-to-object distance or inter-grating distance at the cost of the angular sensitivity. Figure 3(b) and Fig. 3(e) show the vertical-wavefront gradient obtained using the GBI and SBI technique, respectively. The profile plot of the vertical wavefront gradients using GBI and SBI along the vertical line is shown in the Fig. 3 (c) and Fig. 3 (f), respectively. The quantitative results retrieved from the two techniques are in good agreement. In contrast to the GBI, the horizontal wavefront gradient image (Fig. 3(g)) can also be produced simultaneously by the SBI technique with 1D scan.

The reconstructed phase maps of the phantom using SBI and GBI technique are shown in Fig. 3(g) and Fig. 3(h), respectively. For GBI, the phase map was generated using conventional 1D integration, while for SBI, the phase map was reconstructed from the two orthogonal phase gradients [29]. The conventional 1D phase integration method suffers from unavoidable streak artefacts due to the presence of statistical noise in raw phase gradient images. On the contrary, such artefacts can be clearly avoided for the one generated by SBI since the two local wavefront gradients are produced simultaneously. Even though one can obtain the two-directional phase gradients by rotating either the sample or the gratings, extra dose has to be delivered to the sample. Thus the SBI technique with single 1D scan can be used to obtain a projected phase map with reduced streak artefact and reduced dose to the sample.

To further compare the capability to retrieve multimodal signals for the two techniques, a test phantom consisting of a small piece of wood, a Polytetrafluoroethylene (PTFE) tube and a PTFE rod was used. The outside diameter of the PTFE tube is 1.0mm with wall thickness of 0.35mm, and the diameter of the PTFE rod is 1.0mm. Figure 4 shows (a) absorption, (b) dark-field, (c) vertical wavefront gradient, (d) horizontal wavefront gradient and (h) reconstructed phase images retrieved with the SBI technique, while the absorption, dark-field and unwrapped vertical wavefront gradient images extracted using the GBI technique are shown in Fig. 4(e), Fig. 4(f) and Fig. 4(g). As shown in Fig. 4(a) and Fig. 4(e), the information obtained from absorption images is consistent between GBI and SBI, and the retrieved dark-field images (Fig. 4(b) and Fig. 4(f)) are also similar to each other. As expected, more scattering signal is observed in the wood sample due to presence of sub-pixel in-homogeneities. It may be further noted that the edges or discontinuities also contribute to the dark-field images for both cases. In addition, the edges of the PTFE rod and tube in both Fig. 4 (a) and Fig. 4 (b) are much sharper than the ones in Fig. 4 (e) and Fig. 4 (f). These findings can be explained by the fact that the spatial resolution of the GBI technique is limited by the shear between the first orders of the diffracting beams due to the phase grating. This shear is given by $2\lambda d_m/p_1$, where $\lambda$ is wavelength, $d_m$ is the distance between the gratings and $p{}_1$ is the period of the phase gratings. The spatial resolution for GBI is therefore 24µm for the current experimental conditions with the detector pixel size of 1.8µm. In contrast, the spatial resolution of the speckle measurements will be limited by the width of first diffraction zone [30], $\sqrt{\lambda L}$, which is about 7µm. Thus, the SBI can provide better spatial resolution for same geometrical setup compared to GBI.

Due to the isotropic nature of speckles, the two orthogonal wavefront gradients were extracted simultaneously with a 1D scan [23]. Even though such information can be obtained by employing two-dimensional (2D) raster scans with 2D gratings using the GBI technique [31], the experimental complexity and data acquisition will be inevitably increased. As shown in Fig. 4(g), the wavefront gradient data from the GBI technique also suffers from the phase wrapping problem [32], and a priori information is often required to correct the phase wrapping errors. Although the issue of unwrapping might be avoided by placing the sample into fluid to reduce the edge enhancement, it will increase the complexity of the experimental setup. In contrast, all these issues will not arise for the SBI technique since the speckle displacements were tracked by using a real space cross-correlation algorithm. As shown in Fig. 4(c) and Fig. 4(d), the retrieved phase gradients are much smoother, and the phase wrapping problem can be avoided. However, it should be pointed out that the necessary scanning range for the SBI technique will be larger than the one for the GBI technique.

Once the two transverse wavefront gradients has been retrieved with the SBI technique, as shown in Fig. 4(h), the phase shift induced by the sample can then be reconstructed. Compared to the absorption contrast image (Fig. 4(a)), enhanced contrast for the tube and rod samples can be clearly observed. As shown in Fig. 4(b) and Fig. 4(h), the dark-field and phase contrast images provide supplementary information for the wood and PTFE samples.

In order to verify the angular sensitivity$\Delta \alpha$, the usual procedure to calculate the standard deviation of wavefront gradient in the empty space was used [24, 33, 34]. In case of GBI technique, from Eq. (3), the minimum detection refraction angle can be express as $\Delta {\alpha }_G=\frac{g_2{\sigma }_G}{2\pi d_m}$ (${\sigma }_G$ is the standard deviation of fringe phase map in the empty space). While the similar relation in case of SBI technique is given by$\Delta {\alpha }_S^y=\frac{\epsilon }{L}{\sigma }_S$ and $\Delta {\alpha }_S^x=\frac{P}{L}{\sigma }_S$ (${\sigma }_S$ is the standard deviation of speckle displacement map in the empty space) according to Eq. (5). The calculated standard deviation in the mark region of interest in Fig. 4(g) is 25 nrad for GBI. In contrast, the one for SBI is 15 nrad and 44 nrad along vertical (Fig. 4(c)) and horizontal (Fig. 4(d) direction, respectively. However, we would like mention that angular sensitivity for both techniques depends upon many experimental parameters [24, 33, 35, 36], and changing any parameter-distances, grating/diffuser properties, and detector properties - may influence the final results. For example, the angular sensitivity for SBI can be further improved by increasing the distance between the random diffuser and the detector at the cost of larger scan range. However, the increase of the inter-grating distance for GBI might get more severe phase wrapping issue.

5. Summary

For comparison, the advantages and limitations for the GBI and SBI techniques are summarized in Table 1. Both of the techniques can work in both single image mode and scanning mode depending upon the requirement of the experiments. Absorption, phase gradient and dark-field images can all be simultaneously retrieved. One of the major advantages of the SBI technique is that it uses a simple filter membrane or abrasive paper rather than high-precision gratings, thus greatly simplifying the experimental setup. Experimental results demonstrate that the SBI technique is quite tolerant of the edge enhancements. The phase unwrapping issue can be avoided for SBI by increasing the scan range. Moreover, thanks to the 2D nature of speckle patterns, two orthogonal wavefront gradients can be simultaneously obtained in a single directional scan, while only one directional wavefront gradient can be retrieved by the GBI technique in this case. It should also be emphasized that the data acquisition time is much shorter for the SBI technique than for the GBI technique since the transmission of the membrane or abrasive paper is much higher than that of a grating. It may be pointed out that the real space cross-correlation algorithm used for SBI is more calculation-intensive than the Fast Fourier Transform (FFT) used for GBI. This hurdle can be overcome by using either a GPU or a cluster to increase the speed of post-processing or by applying the fast cross-correlation algorithm in Fourier space. In summary, SBI has great potential over GBI for high resolution X-ray imaging at synchrotron sources because of its simpler experimental setup and better data quality. The SBI technique provides an alternative and competitive solution for X-ray phase and dark-field contrast imaging in diverse applications for synchrotron community. However, for lab-based imaging applications, SBI can be performed only with a microfocus source [23, 37], whereas GBI can be carried out with the conventional X-ray source by adding a source grating [13]. In addition, GBI is compatible with detectors of large pixel size, which can provide large field of view with reduced dose for those applications where high resolution is not required. Hence, SBI and GBI are expected to be complementary to each other for synchrotron-based and lab-based X-ray imaging applications.

Table 1. Summary of Important Features of GBI and SBI Technique

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