Low-exposure, high-quality multimodal speckle X-ray imaging via an intrinsic gradient-flow approach

Abstract

We present a new approach for retrieving dark-field, phase shift, and attenuation images from speckle-based X-ray imaging data. Speckle-based X-ray imaging (SBXI) exploits sample-induced alterations to a reference near-field speckle pattern produced by a randomly structured mask. Attenuation images allow materials of different densities to be visualised. Phase-shift images are useful because they reveal how materials in a sample refract the X-ray beam, providing contrast between similar low-density structures that are difficult to reconstruct in attenuation images. Dark-field images convey information about structures that are smaller than the spatial resolution and thus invisible in both attenuation and phase-shift images. In previous works, we presented the Multimodal Intrinsic Speckle-Tracking (MIST) algorithm, which recovers the three complementary imaging modes from SBXI data by solving the associated Fokker--Planck equation. In this work, we present a variation of MIST, called ``gradient-flow MIST", which (1) reduces the amount of SBXI data required for image retrieval, (2) maintains the full generality of the X-ray Fokker--Planck equation, and (3) recovers dark-field images with higher quality than the previously proposed variants for weakly attenuating (i.e., low density) samples. We demonstrate the new gradient-flow MIST approach on experimental SBXI data of a knotted bundle of carbon fibres acquired at the Australian synchrotron. This approach is anticipated to be useful in phase-contrast and dark-field applications that require simplicity in experimentation and low sample X-ray exposure.

Figures (5)

• Figure 1: Schematic of a speckle-based X-ray imaging (SBXI) setup, where $Z_{MS}$ is the mask-sample distance, and $Z$ is the sample-detector distance.
• Figure 2: a)--b) SBXI data collected at the Australian synchrotron's Imaging and Medical beamline (IMBL). c)--g) Reconstructed images of a knotted carbon fibre using twenty speckle image pairs with GF-MIST. a) Reference speckle pattern $I_R$, b) sample speckle pattern $I_S$, c) effective diffusion coefficient $D$, d) angle of refraction (corrected for SAXS) in the $x$ direction $\alpha_1$, e) angle of refraction (corrected for SAXS) in the $y$ direction $\alpha_2$, f) transmission $I_\text{ob}^{(2)}$, g) phase-shift $\phi$. The linear greyscale range in [min(black), max(white)] of a)--b) is [0.65, 0.97], c) [0, 78]$\times$$10^{-12}$, d) and e) are [-2.4, 2.4]$\times$$10^{-6}$ radians, f) is [0.87, 1.0], g) [-25, 185] radians.
• Figure 3: Fitted Fourier ring correlation (FRC) curves for the retrieved dark-field and phase-shift images (solid and stripped lines, respectively) in Figure \ref{['carbonknotcomparison']}. The FRC's were fitted to a complementary error function. The spatial resolution was defined as the intersection (labelled) between the FRC curves and a threshold cutoff at 0.143, denoted by the solid horizontal line.
• Figure 4: Retrieved dark-field $D$ and phase-shift $\phi$ images for a carbon-knot with GF-MIST (a)-e) and j)-n)) and RV-MIST (f)-i) and o)-r)) using 2, 4, 6, 8, and 10 speckle-image pairs. The linear greyscale range for images a)--e)$=[0,70]\times10^{-12}$, f)--i)$=[0,30]\times10^{-12}$, j)--r)$=[-185,25]$ radians. The white box in e)(i) and e)(ii) indicates the signal and background area used for the calculation of CNR for images a)--r), respectively.
• Figure 5: a) Dark-field (solid line) and phase-shift (dashed line) spatial resolution of GF-MIST (circles) and RV-MIST (triangles). b) same as in a) but for the measured contrast-to-noise ratio (CNR) using the signal and background as shown in Figs. \ref{['carbonknotcomparison']} and \ref{['carbonknotcomparison']}, respectively.