X-ray phase imaging, radiography, image processing, mammography

The contrast in conventional x-ray imaging is generated by differential attenuation of x rays, which is generally very small in soft tissue. Phase imaging has been shown to improve contrast and signal to noise ratio (SNR) by factors of 100 or more. However, acquiring phase images typically requires a highly spatially coherent source (e.g. a 50 μm or smaller microfocus source or a synchrotron facility), or multiple images acquired with precisely aligned gratings. Here we demonstrate two phase imaging techniques compatible with clinical sources: polycapillary focusing optics to enhance source coherence and mesh-based structured illumination.

The contrast in conventional x-ray imaging is generated by differential attenuation of x rays, which is generally very small in soft tissue. Phase imaging has been shown to improve contrast and signal to noise ratio (SNR) by factors of 100 or more. However, acquiring phase images typically requires a highly spatially coherent source (e.g. a 50 μm or smaller microfocus source or a synchrotron facility), or multiple images acquired with precisely aligned gratings. Here we consider two easily implemented techniques to enable phase imaging with conventional sources.

In the first technique, polycapillary focusing optics are used to produce focal spots which act as secondary sources with sufficient coherence for propagation-based phase imaging. We demonstrate improved contrast and signal-to-noise ratio in mammalian tissue using propagation-based phase images produced by employing focusing optics.

In the second technique, a simple wire mesh is used to structure the x-ray beam. The phase differences created by transmitting through an object deflect x rays and distort the mesh image on the detector. By comparing a reference image of the mesh alone to an image acquired with the object in place, both absorption and phase images can be reconstructed. Conventionally the processing used in this recovery has limited resolution of the reconstructed images to the mesh period. However, we have recently demonstrated a method to combine multiple images acquired with the mesh shifted by half a period to improve the resolution by at least a factor of three. Here, we demonstrate results with this algorithm optimized to recover phase from only 2 images acquired while shifting the mesh.

The first technique is the use of a focusing polycapillary optic, which consists of hollow glass tubes used to focus x rays from a conventional, large spot source onto a small focal spot, as shown in Figure 1.

Fig. 1 An illustration of the polycapillary phase imaging system. A polycapillary optic is used to improve the coherence of the beam. The focal length (lens-to-spot distance) for this lens was 5 cm, with a focal spot of 100 um

This focal spot acts as a secondary source of illumination with sufficient spatial coherence for phase imaging.
By then displacing the detector some distance along the beam axis, a propagation-based phase image can be acquired, where the edges of features in the object show significant contrast enhancement due to phase.

Phase imaging results are shown in Figure 2 for an 550 mAs exposure (most of the beam is lost before the object, so does not contribute to dose) at 40 kV of a preserved ovine eyeball.

Fig. 2 Contact and polycapillary-based phase image of a sheep eyeball

The propagation-based phase image shows significantly higher contrast and reduced noise compared with a conventional contact image acquired immediately after the sample. Phase information is also visible in Figure 3, for example as the dark lines at the edges of the mouse ribs, and the contrast at the edges of the bee legs (which would otherwise not be visible, as the leg itself has little contrast from the background).

Fig. 3 Phase images, from top to bottom, of a bee, fish, and preserved mouse

The second phase imaging technique is to utilize a coarse wire mesh placed after the object, as illustrated in Figure 4.

Fig. 4 Illustration of a mesh-based phase imaging system. The object’s phase deflects the x rays

X rays are deflected after the object by an amount proportional to the gradient of the object phase. The wire mesh serves as a high- contrast sensor for x-ray deflection.

A reference image is initially acquired without an object in place to characterize the mesh and illumination. An image acquired with the object in place will show distortion of the mesh lines which can be attributed to phase. Because a periodic mesh is used, both phase and absorption images can be recovered rapidly by Fourier processing. The Fourier transform of the mesh image produces sharply peaked functions at the grid harmonics, as shown in Figure 5.

Fig. 5 Fourier transform of an image of the mesh. The red square encloses the zeroth order harmonic, the blue (dashed) square, the first order harmonic.
The vertical and horizontal streaks are likely due to the camera

When an object is placed in the path of the beam, its attenuation and phase delay will change the structure of the harmonics, which can be used to reconstruct the phase.

With the object in place, the normalized harmonic image is

where I_n,m is the image obtained by windowing the data in Fourier space around the m,n^th harmonic, and I_mesh; m,n is the same harmonic for the mesh-only image. The scatter-free object attenuation can be obtained from the normalized (0,0) harmonic I_0,0. Differential phase contrast (DPC) images can be found from the ratios of the real and imaginary parts of the higher order harmonics,

Resulting DPC images of small phase objects are shown in Figure 6.

Fig. 6 A mesh-based phase image is proportional to a phase gradient. The first pair show the horizontal component, produced from the horizontal (1,0) Fourier harmonic, of (first) two pieces of a 2.5 mm diameter tube, and (second), a 0.5 mm diameter glass bead. The phase gradient appears as vertical dark and light bands. The next pair are the images produced from the (0,1) harmonic, with horizontal dark and light bands. The last image displays a full 2D phase gradient computed from the sum of the Laplacians of the first two bead images

A limitation of this technique is the loss of resolution. If the window in Fourier space is limited by the magnified separation of the harmonics on detector, 2π/dmag, as shown in Figure 5, then the resolution of the computed image would be limited to the mesh period. A resulting poor resolution image is shown in Figure 7(a).

Fig. 7 Phase image of 0.5 mm diameter glass beads. (a) Using the resolution limitations suggested in Ref. 8 and a single image produces poor resolution. (b) Attempting to improve resolution by using a wider Fourier window introduces significant artifacts. (c) Combining shifted mesh images improves the resolution while removing the artifacts. The phase gradient appears as a diagonal dark then light band at the edge of each bead as the mesh lines were placed at 45° to the image, because the mesh was rotated at 45° to the object. (d) Using only two images instead of 4 still removes the majority of the artifacts for the phase image

The resolution can be improved by increasing the width of the Fourier window, but that results in capturing unwanted harmonics, and hence produces artifacts, as shown in Figure 7(b). To reduce the artifacts, we acquired four images while shifting the position of the mesh by half a period. An appropriate combination of these images allows suppression of all but one of the harmonics, and hence suppression the artifacts, as shown in Figure 7(c). To reduce the required dose, it is possible to use only two images to suppress the zeroth harmonic, as shown in Figure 7(d). The mesh-shifting produces higher resolution with few artifacts.

The phase imaging system, which employs two compatible phase imaging techniques, is illustrated in Figure 8.

Fig. 8 An illustration of the combined optic and mesh phase imaging system. A polycapillary optic is used to improve the coherence of the beam and a wire mesh is placed after the object to improve the phase imaging sensitivity

The addition of the polycapillary optic, which enhances the source coherence, improves the ability of the mesh-based system to retrieve phase results.

One aspect of the improved performance is the ability to determine quantitative phase. In general, computing bot the phase and transmission of an object from a single image requires strong assumptions about the object and the x-ray beam. For example, attempts to compute quantitative phase from the single images of Figure 2 and Figure 3 require either assuming that the objects are weakly attenuating, consist of a single known material, or that Compton scattering is the dominant contributor to attenuation, which are somewhat problematic. Since the mesh-based system produces a signal proportional to the phase gradient, as shown in Figure 6, it is possible to reconstruct a quantitative phase by simple integration. However, if the phase signal is weak, the results can be unreliable. Employing the polycapillary optic results in a better quantitative result, as shown in Figure 9.

Fig. 9 Vertical DPC image of a nylon rod and the resulting integral. The integrated phase was compared along 56 lines through the rod and yielded a mean value of 199 radians, which is within 7% error compared to the expected value of 215 radians for the broadband spectrum with an average energy 13.71keV

The mesh-based system simultaneously produces both phase gradient and scatter-free absorption images. An absorption image is shown in Figure 10.

Fig. 10 Scatter-free absorption image of a toad paw

The images can be combined without registration issues, as they are produced from the same original image. A combined image of the eyeball of Figure 2 is shown in Figure 11.

Fig. 11 Enhanced image created by combining the computed absorption and DPC mesh-based image

We have demonstrated the applicability of polycapillary and mesh-based phase imaging for mammalian tissue.

Results show improved contrast and these methods can be used to produce enhanced contrast at the edges of phase objects. Combining a pair of images (taken with a simple mesh shift, so no image registration is required) allows for high resolution phase imaging.