Small-angle scattering computed tomography (SAS-CT) using a Talbot-Lau interferometerand a rotating anode x-ray tube:theory and experiments

Abstract

X-ray differential phase contrast imaging methods, including projection imaging and the corresponding computed tomography (CT), have been implemented using a Talbot interferometer and either a synchrotron beam line or a low brilliance x-ray source generated by a stationary-anode x-ray tube. From small-angle scattering events which occur as an x-ray propagates through a medium, a signal intensity loss can be recorded and analyzed for an understanding of the micro-structures in an image object. This has been demonstrated using a Talbot-Lau interferometer and a stationary-anode x-ray tube. In this paper, theoretical principles and an experimental implementation of the corresponding CT imaging method are presented. First, a line integral is derived from analyzing the cross section of the small-angle scattering events. This method is referred to as small-angle scattering computed tomography (SAS-CT). Next, a Talbot-Lau interferometer and a rotating-anode x-ray tube were used to implement SAS-CT. A physical phantom and human breast tissue sample were used to demonstrate the reconstructed SAS-CT image volumes.

Fig. 1

Illustration of geometry used in deriving the basic equations in SAS-CT.

Fig. 2

Photographs of the grating interferometer x-ray system. Subfigure (a) shows the x-ray tube and the G₀ grating, while (b) shows the detector, G₁, and G₂ gratings.

Fig. 3

Calcification phantom made by filling a PMMA tube with gelatin and placing various sizes of calcifications (indicated on the right) in different layers. A cross section of the phantom is shown on the left, with the approximate arrangement of the calcifications within each layer.

Fig. 4

SAS-CT (a) and absorption contrast CT (b) reconstructions of the calcification phantom. The images shown are both maximal intensity projections (MIP) over the same image volume, with a pixel size of (80 μm)² and a thickness of 1.12 mm. A MIP was used in order to visualize all calcifications within one size layer.

Fig. 5

SAS-CT (a) and absorption contrast CT (b) reconstructions of human breast tissue. Each image shows the same slice from the same data set. An oil cyst is clearly visible in both of the images, with additional contrast from background structure present in the attenuation contrast reconstruction.