Hard X-ray omnidirectional differential phase and dark-field imaging

Abstract

Ever since the discovery of X-rays, tremendous efforts have been made to develop new imaging techniques 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 detail in a weakly absorbing sample than conventional absorption contrast. However, normally only the gradient's component in two mutually orthogonal directions is measurable. In this article, omnidirectional differential phase images, which record the gradient of phase shifts in all directions of the imaging plane, are efficiently generated by scanning an easily obtainable, randomly structured modulator along a spiral path. The retrieved amplitude and main orientation images for differential phase yield more information than the existing imaging methods. Importantly, the omnidirectional dark-field images can be simultaneously extracted to study strongly ordered scattering structures. The proposed method can open up new possibilities for studying a wide range of complicated samples composed of both heavy, strongly scattering atoms and light, weakly scattering atoms.

Keywords: X-ray phase contrast; X-ray speckle; dark field; material science.

Fig. 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 ${\text{ξ}}_{\rho }^{\text{θ}}$ along the polar directions and the maximum of the cross-correlation coefficient ${\gamma }_{max}^{\text{θ}}$ images. (E and F) The differential phase and dark-field signal modulation as the polar angle changes from 0 to $2\pi .$

Fig. 2.

(A and B) The retrieved amplitude $A_1$ and main orientation ${\varphi }_A$ of differential phase. (C) The constructed omnidirectional differential phase, as rendered in an HSV color scheme. (D and E) The corresponding retrieved amplitude $D_1$ and main orientation ${\varphi }_D$ of dark field. (F) The constructed omnidirectional dark field, as rendered in an HSV color scheme. The gray color for A and D indicates the range of normalized amplitude $A_1$ and $D_1$ from 0 (dark) to 1 (bright). For B and E, the gray shades cover the range from 0 (dark) to 2π (bright). (Scale bar, 0.2mm.)

Fig. 3.

(A and B) The retrieved average $D_0$ and amplitude $D_1$ of dark-field signal of a woodlouse sample. The gray color indicates that the normalized $D_0$ and $D_1$ changes from 0 (dark) to 1 (bright). (C) The constructed omnidirectional dark field, as rendered in an HSV color scheme. (D and E) The main orientation ${\varphi }_A\left[0,\hspace{0.17em}2\pi \right]$ and normalized amplitude $A_1\left[0,\hspace{0.17em}1\right]$ of differential phase. (F) The constructed omnidirectional differential phase, as rendered in an HSV color scheme. (G and H) The calculated horizontal and vertical differential phase from $A_1$ and ${\varphi }_A$. The gradient varies from −3 to 3 μrad (bright). (I) The reconstructed phase from G and H, in which the phase ranges from −60 (dark) to 60 rad (bright). (Scale bar, 0.5mm.)