Diamond Annual Review 2021/22

112 113 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 2 1 / 2 2 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 2 1 / 2 2 than the ones for the dark-field image. In order to show the directional information, the hue-saturation-value (HSV) colour scheme is used with the Hue given by the orientation and the Value equal to the corresponding amplitude. Fig. 2c and Fig. 2f are the directional differential phase and dark-field rendered in a HSV colour scheme. Here, only the edge of the star patterns can be observed from the directional dark-field image, whereas the directional differential phase image also shows the direction of the phase gradient on each bar. The differential phase and phase images of woodlouse sample are presented in Fig. 3. As shown in Fig. 3a and 3b. the higher scattering signals for the edge of the lateral plate are shown in both the average and amplitude of the directional dark-field images for the woodlouse. On the other hand, the lung and part of the thorax (marked with arrows in Fig. 3a) show strong average scattering but only very weak directional scattering. This indicates that the lung tissue and the retained food (containing rotting plants) in the thorax show isotropic scattering signals. The average scattering map shows both isotropic and anisotropic scattering signals, while the directional scattering map shows only the anisotropic scattering signals. In the HSV colourmap of the directional scattering signal in Fig. 3c, the directional scattering of the lateral plane can be clearly identified along different orientations. The corresponding differential phase images from Fig. 3d to Fig. 3e show complementary information to the dark-field images. Consequently, the main orientation angle image for differential phase can provide enhanced contrast to the weak phase signal, and it can be used to study multiple features of complex samples. A 1 antenna  A a b D 1 D 0 c thorax lung lateral plate uropod epimera d e f g h i   y  x retained food lateral plate Advanced X-ray directional imagingwith sandpaper Related publication: Wang, H., & Sawhney, K. Hard X-ray omnidirectional differential phase and dark-field imaging. Proceedings of the National Academy of Sciences 118, (2021). DOI: 10.1073/pnas.2022319118 Publication keywords: X-ray phase contrast; Dark-field; Material science; X-ray speckle X -ray Differential Phase Contrast Imaging, which measures the gradient of a sample’s phase shift, can reveal more detail in a weakly absorbing sample than conventional absorption contrast. However, normally only the gradient’s component in two mutually orthogonal directions for existingmethods is measurable. Diamond Light Source’s scientists have developed a simple method to produce omnidirectional differential phase images, which record the gradient of phase shifts in all directions of the imaging plane. Importantly, the omnidirectional dark-field images can be simultaneously extracted to study strongly ordered scattering structures. Existing methods require special optics, such as advanced phase gratings or absorptionmasks, along with a stringent experimental setup. Over the last decade, the speckle method has been extensively developed for advanced imaging and high precision metrology at the Test Beamline (B16). B16 offers the flexibility of bespoke and novel setups, which was ideal for the R&D work. The technique allows the omnidirectional differential phase and dark-field images to be simultaneously extracted from a single data set with the use of a simple modulator. The omnidirectional differential phase and dark-field images resolve the directional dependence of complex microstructures, which is inaccessible to conventional X-ray imaging techniques. Potentially, the proposed technique could be transferred to laboratory X-ray micro-focus sources for wider application. Using a highly efficient flat panel detector would further reduce the radiation dose. The proposed omni-directional method paves the way for X-ray scattering tensor tomography for the inspection of both biomedical andmaterial science samples. Over the last two decades, various X-ray directional differential phase contrast and dark-field imaging techniques have been developed for unlocking the hidden secrets of our world and enriching our understanding of it. X-ray Differential Phase Contrast Imaging, which measures the gradient of a sample’s phase shift, can reveal more details in a weakly absorbing sample than conventional absorption contrast. In addition, X-ray dark-field images describe the scattering power due to the structural variation and density fluctuation. Therefore, these two techniques can provide complementary information to each other. However, normally only the differential phase contrast and dark field images in two mutually orthogonal directions are measurable 1-3 . As a result, the risk of overlooking structures with strong but varying orientation within the sample is high. Therefore, it will be desirable to generate the omni-directional phase shift changes or dark-field signals to pick up detailed information along all directions 4 . In this study, the researchers describe a new algorithm to extract both the omnidirectional differential phase and dark-field signals with a randomly structured wavefront modulator, such as a sandpaper. To achieve the omnidirectional information and minimise the necessary radiation dose, the modulator is scanned along a spiral trajectory. Fourier analysis is then performed to obtain the phase changes and scattering signal of the sample in all directions of the imaging plane. In addition, the proposed method shows great potential to decouple the isotropic and anisotropic scattering signals by analysing the omnidirectional dark-field images. The experiment was carried out at Diamond Light Source’s B16 Test Beamline. As a demonstration of the capabilities of the proposed technique, a phantom with 36 actinomorphic star patterns was purposefully chosen because its features are distributed along all the directions in the imaging plane. In addition, a woodlouse sample was also tested because it has complex biological structures containing both isotropic and anisotropic scattering properties. The principle of the proposed technique is illustrated in Fig. 1. One stack of reference speckle images was first collected without sample in the beam, and then the same scan was repeated to generate the sample speckle image stack when the sample was moved into the beam. As illustrated in Fig. 1a, for each pixel in the speckle image plane a surrounding subset was selected. The corresponding transformed virtual speckle stack in polar coordinate is shown in Fig. 1b. The correlation coefficient maps were calculated by cross-correlating the two virtual speckle images. As shown in Fig. 1c and 1d, both the differential phase and the dark-field images can be obtained from the same dataset by applying the pixel-wise cross-correlation algorithm by following the above procedure. As demonstrated in Fig.1e and 1f, the Fourier and the phase term can then be extracted by using the Fast Fourier Transform (FFT) analysis for differential phase and dark-field image stacks. Figure 2 shows the retrieved differential phase amplitude and dark-field amplitude; and the corresponding main orientation. Both the amplitude and the main orientation for the differential phase image shows better contrast Optics andMetrology Group Beamline B16 In summary, the researchers have demonstrated that the omnidirectional differential phase and dark-field images can be simultaneously extracted from a single data set with the use of a simple modulator. They have shown that the retrieved multi-modal images from the proposed approach can reveal a wide variety of internal structures within one sample. The directional differential phase images reveal the directional dependence of the weakly absorbed features, complementing the directional dark-field images. In addition, the retrieved main orientation image of the directional differential phase can further improve the contrast for thin samples, while the amplitude image of the directional differential phase shows the phase changes along all directions in the imaging plane at once. Moreover, high-quality horizontal and vertical differential phase images and phase shifts can be automatically calculated from the above amplitude and main orientation images 5 . The omnidirectional differential phase and dark-field images resolve the directional dependence of complex microstructures, which is inaccessible to conventional X-ray imaging techniques. References: 1. Pfeiffer, F. et al. Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources. Nature Physics 2 , 258–261 (2006). DOI: 10.1038/nphys265 2. Wang, H. et al. Hard-X-ray directional dark-field imaging using the speckle scanning technique. Physical Review Letters 114 , 103901 (2015). DOI: 10.1103/PhysRevLett.114.103901 3. Kagias, M. et al. 2D-omnidirectional hard-X-ray scattering sensitivity in a single shot. Physical Review Letters 116 , 093902 (2016). DOI: 10.1103/ PhysRevLett.116.093902 4. Kagias, M. et al. Diffractive small angle X-ray scattering imaging for anisotropic structures. Nature Communications 10 , 5130 (2019). DOI: 10.1038/s41467-019-12635-2 5. Wang, H. et al. Reply to Kagias and Stampanoni: High-sensitivity hard X-ray directional differential phase imaging. Proceedings of the National Academy of Sciences 118, (2021). DOI: 10.1073/pnas.2116067118 Funding acknowledgement: This work was carried out with the support of Diamond Light Source Ltd. Corresponding author: Dr. HongchangWang, Diamond Light Source Ltd, hongchang.wang@ diamond.ac.uk a b c d e f u    �� ��   Subset  0  2   A A 0 A 1 α(  )  0  2   D D 0 D 1 D(  ) �� �� ���      u x y Figure 1: A schematic illustration of the extraction of the directional differential phase and dark-field images of a sample star pattern. (a) the collected stack of speckle images in Cartesian coordinates, (b) the select subset from (a) is transformed into polar coordinates. (c) and (d) the extracted speckle displacement along the polar directions and the maximum of the cross-correlation coefficient images. (e) and (f ) the differential phase and dark-field signal modulation as the polar angle changes from 0 to 2π. a d b e c  D D 1  A A 1 0  /2  3  /2 f 0  /2  3  /2 Figure 2: The omnidirectional differential phase and dark- field images for a phantom with 36 actinomorphic star patterns (a) and (b) The retrieved amplitude and main orientation differential phase. (c) The constructed omni-directional differential phase, as rendered in an HSV colour scheme. (d) and (e) The corresponding retrieved amplitude and main orientation of dark-field. (f ) The constructed omni- directional dark-field, as rendered in an HSV colour scheme. Figure 3: The omnidirectional differential phase and dark-field images for a woodlouse sample(a) and (b) The retrieved average and amplitude of dark-field signal of a woodlouse sample. (c) The constructed omni-directional dark-field, as rendered in an HSV colour scheme. (d) and (e) The main orientation and normalized amplitude of differential phase. (f ) The constructed omni-directional differential phase, as rendered in an HSV colour scheme. (g) and (h), The calculated horizontal and vertical differential phase.