Trimodal low-dose X-ray tomography

Abstract

X-ray grating interferometry is a coherent imaging technique that bears tremendous potential for three-dimensional tomographic imaging of soft biological tissue and other specimens whose details exhibit very weak absorption contrast. It is intrinsically trimodal, delivering phase contrast, absorption contrast, and scattering ("dark-field") contrast. Recently reported acquisition strategies for grating-interferometric phase tomography constitute a major improvement of dose efficiency and speed. In particular, some of these techniques eliminate the need for scanning of one of the gratings ("phase stepping"). This advantage, however, comes at the cost of other limitations. These can be a loss in spatial resolution, or the inability to fully separate the three imaging modalities. In the present paper we report a data acquisition and processing method that optimizes dose efficiency but does not share the main limitations of other recently reported methods. Although our method still relies on phase stepping, it effectively uses only down to a single detector frame per projection angle and yields images corresponding to all three contrast modalities. In particular, this means that dark-field imaging remains accessible. The method is also compliant with data acquisition over an angular range of only 180° and with a continuous rotation of the specimen.

Fig. 1.

Schematic representation of an X-ray grating interferometer setup. The phase grating (G1) and the absorption grating (G2) are positioned between the sample and the detector. G2 is placed at a distance d from G1 at which the interference pattern generated by G1 exhibits the maximum contrast.

Fig. 2.

Phase-stepping methods represented in the (ω,x_g) coordinate system. Each colored dot or star represents an interferogram recorded by the detector. Interferograms represented by stars are used in more than one phase-stepping scan. (A) Standard phase stepping. (B) Interlaced phase stepping (14). (C) SWZ method: One point of each scan is reused in the next scan. (D) SWI method: All but one point in each scan are reused in the next scan.

Fig. 3.

Comparison of tomographic slices obtained with the different methods, using the same number of simulated noiseless interferograms for each method. (A) ROI of the simulated slice reconstructed with the SWI method; the simulated slice and the ROI reconstructions obtained with the other acquisition schemes are shown in SI. (B) Histograms of the two regions R1 and R2 indicated by rectangles in A. The y axis of the histogram is the number of pixels per histogram bin; the plotted range is from 0 to 200 for the histograms of R1 and 0 to 250 for the histograms of R2. The standard deviation σ of the Gaussian curve obtained by fitting the peaks is reported in the graphs. The value of σ is significantly reduced (of up to 50%) and consequently the contrast-to-noise ratio is substantially increased with the sliding window methods (because the histogram peak positions—i.e., the contrast—are unchanged between the different methods, the peak widths are a direct measure of the contrast-to-noise ratio obtained with the different methods.).

Fig. 4.

Sagittal (Top) and axial (Bottom) views of phase tomograms of a rat heart. A and C show images obtained with the standard method and B and D show images obtained with the SWI method. (E) and (F) Display profiles extracted from the standard and SWI axial slices along the lines shown in C. The two reconstructions show very similar quality despite the high difference in dose delivered in the two tomography scans (the SWI scan was obtained with only 20% the dose than of the standard phase-stepping scan).

Fig. 5.

Sagittal views of phase tomograms of a rat eye obtained with the standard (A) and SWI (B) acquisition schemes; the dose delivered to the sample during the tomography performed with standard stepping was four times higher than the dose given to the sample during the SWI scan. Some of the anatomical features in the images are labeled with capital letters; see main text. The plastic container is indicated with the letter “P.” C and D show enlarged views of the regions indicated by rectangles in A and B, respectively. The profile plots in E show the refractive index in the lens—the δ_r values in this plot go from 0 to 1 × 10^-7. The histograms of the entire sagittal slices are shown in F and G. The δ_r values in the x axis go from -2 × 10^-8 to 8 × 10^-8. The y axis of the histograms represents the frequency of appearance of the gray levels in the slices; its range is the same for the two plots.

Fig. 6.

XGI tomograms in absorption and in-line phase contrast (Left) and dark-field (Right) of an insect in opaque amber. Dark-field images show details that are not fully revealed in the absorption/phase-contrast data, such as the wing of the insect, indicated by arrows in D. The tomograms in the Top were obtained with the standard phase-stepping method, those in the Bottom with the SWI method. The dose and number of raw interferograms were the same for both methods. For both absorption and dark-field signals, the image noise is significantly reduced using the SWI method as shown by the standard deviation (std) of the gray levels in the uniform region at the bottom right of the images.