X-ray images of low-density materials, such as soft tissue, provide inherently low contrast due to their subtle attenuation differences. However, differences in phase imparted to x rays can be substantial, giving significantly improved contrast. The barrier to widespread implementation of x-ray phase imaging is that most phase techniques require high spatial coherence of the x-ray beam. We have previously demonstrated that employing structured illumination produced by a stainless steel wire mesh can significantly loosen this coherence requirement. We present a computational model utilizing ray tracing that allows us to explore its design space and to optimize our phase reconstruction algorithms.
X-ray phase imaging can significantly improve image contrast in soft-tissue imaging applications such as mammography where the inherent contrast in conventional attenuation-based imaging is low. A system that employs a stainless steel wire mesh to produce a high-contrast structured illumination pattern reduces the need for source coherence and complex alignments. Phase is reconstructed from distortions in this pattern due to phase-based x-ray deflection. A computational model of this system has been developed that allows exploration of design parameters including source size, mesh period, sample structure, detector pixel size and locations of these system elements. Simulation results are presented and compared with experiment for validation.
X-ray phase imaging has found limited clinical use due to requirements on x-ray coherence that may not be easily translated to clinical practice. Instead, this work employs a conventional source to create structured illumination with a simple wire mesh. A mesh-shifting algorithm that incorporates deconvolution of the source spot width is used to enhance resolution. Polycapillary optics are employed to enhance coherence. The effects of incorporating optics with two different focal lengths are compared. Measurements of fat embedded artificial tumors have been performed.
Quantitative phase imaging (QPI) provides a label free method for imaging live cells and allows quantitative estimates of cell volume. Because the phase of light is not directly measurable at an imaging sensor, QPI techniques involve both hardware and software steps to reconstruct the phase. Digital holographic microscopy (DHM) is a QPI technique that utilizes an interferometer to combine a reference beam with a beam that passes through a specimen. This produces an interference pattern on the image sensor, and the specimen’s phase can be reconstructed using diffraction algorithms. One limitation of DHM is that the images are subject to coherent diffraction artifacts. Transport of intensity (TIE) method, on the other hand, uses the fact that defocused images of a specimen depend on the specimen’s phase to determine the phase from two or more defocused images. Its benefit over DHM is that it is compatible with conventional bright field imaging using sources of relatively low coherence. Although QPI methods can be compared on a variety of static phase targets, these largely consist of phase steps rather than the phase gradients present across cells. In order to compare the QPI methods described above on live cells, rapid switching between QPI modalities is required. We present results comparing DHM and TIE on a custom-built microscope system that allows both techniques to be used on the same cells in rapid succession, which allows the comparison of the accuracy of both measurements.
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 conventional 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 demonstrate two phase imaging techniques compatible with clinical sources: polycapillary focusing optics to enhance source coherence and mesh-based structured illumination.
X-ray phase differences are a thousand times greater than attenuation differences, but phase imaging has found limited clinical use due to requirements on x-ray coherence which may not be easily translated to clinical practice. Instead, this work employs a conventional source to create structured illumination with a simple wire mesh. The system simultaneously collects phase, attenuation, and scatter information. X-ray coherent scatter allows differentiation between tissue types with potentially much higher contrast than conventional radiography. Coherent-scatter images are collected with simple 1D slot-scanning and an angular shield to select signatures of interest from a relatively large region.
X ray phase imaging can offer significantly improved image contrast between materials of similar atomic number compared to traditional imaging, although it typically requires small, low power sources to generate the required spatial coherence. We have demonstrated the use of a simple wire mesh and Fourier transform techniques to overcome this limitation, essentially by observing shifts in the mesh. However, the resolution of that technique is limited by the mesh period. Here we demonstrate greatly improved spatial resolution by the application of wider windowing and appropriate combinations of Fourier components from multiple images acquired while spatially shifting the grid.
Conventional x-ray imaging relies on differences in attenuation in a material to produce image contrast. While useful for differentiating structures with large density variations, the subtle differences in attenuation for low-density materials can be difficult to detect. X-ray phase imaging, on the other hand, relies on differences in phase delay which is typically several orders of magnitude larger than attenuation. However, most methods of producing x-ray phase images rely on specialized synchrotron sources, small and low power microfocus sources or the careful alignment of several precision gratings. We demonstrate that focusing polycapillary optics can produce small focal spots from conventional x-ray sources to enable phase imaging. Moreover, in conjunction with focusing optics, the use of a simple, low cost wire mesh to structure the beam can significantly improve phase reconstructions.
Conventionally, the contrast of X-ray images is due to the attenuation of intensity of X-ray beams after penetrating materials, which is proportional to the imaginary part of the complex refractive index. Subtle density variations within soft tissue or other low-Z materials yield poor attenuation contrast. One method to improve the contrast of X-ray images is to utilize phase information since phase depends depend on the real part of the refractive index, which is typically 1000 times larger than the imaginary part. However, phase imaging relies critically on the spatial coherence of the X-ray beam which traditionally requires synchrotron sources, small-spot, low power laboratory sources, or precisely aligned gratings and multiple exposures.
We will discuss two methods to achieve phase imaging with large-spot sources practical for clinical or security screening. The first method relies on using polycapillary optics to focus the beam and achieve the necessary coherence for traditional propagation-based phase imaging methods based on the transport of intensity equation. The second method relies on a coarse wire mesh which structures the illumination to enhance phase signatures and relax the coherence requirement. We will present recent results from both methods, including computational algorithms for phase contrast, phase retrieval and resolution enhancement.
Conventionally, the contrast of X-ray images is due to the attenuation of intensity of x-ray beams after penetrating materials, which is proportional to the imaginary part of the complex refractive index. Subtle density variations within soft tissue yields poor contrast. One method to improve the contrast of x-ray images is to utilize phase information, which could provide a signature 1000 times larger than attenuation. However, phase imaging relies critically on the spatial coherence of the x-ray beam which traditionally requires synchrotron sources, small-spot, low power laboratory sources, or precisely aligned gratings and multiple exposures. An additional source of tissue-typing information, which is simply discarded in a conventional mammogram, is coherent scatter. Coherent scatter imaging relies on diffraction within the tissue and hence produces a signature that depends on the molecular structure, but as conventionally collected requires raster-scanning of the beam and multiple exposures. None of these methods is compatible with conventional screening mammography.
We will discuss two methods to achieve phase imaging with large-spot sources practical for clinical use. The first uses polycapillary optics to focus x-rays from a large-spot source and achieve the necessary coherence for propagation-based phase imaging. The second uses structured illumination implemented with a coarse wire mesh to enhance phase signatures and relax the coherence requirement. We will present recent results from both methods, including computational algorithms for phase contrast, phase retrieval and resolution enhancement.
We will also present a slot-scanning coherent scatter system which utilizes a slot to shape the beam and shielding placed at specific angles to capture specific coherent scatter signatures in a geometry that is compatible with slot-scan mammograpy.
X-ray phase imaging is known to enhance contrast, particularly for low atomic number materials, for which absorption contrast is low. However, it requires spatial coherence which is typically achieved with a small (10 to 50 µm) source, or a grating placed in front of the source to essentially break it into multiple small sources. In a previous experiment, polycapillary focusing optics were shown to improve coherence when employed to focus x rays from a large spot rotating anode to a smaller secondary source. Edge-enhancement to noise ratios up to a value of 6.5 were obtained, and sufficiently high quality data was obtained from a single image to allow for phase reconstruction using a phase attenuation duality approach. Alternatively, polycapillary optics might operate in place of a source grating to effectively divide the source into a very large number of small channels. In order to examine the potential use of polycapillary optics to enhance phase imaging, the phase and coherence properties of the optic were modeled by observing the fringe visibility in a simulated Young’s double slit experiment. The optic was modeled using simple ray tracing in a Monte Carlo simulation, with the phase advance associated with each photon path computed from the path length and phase changes upon each reflection through the polycapillary tube. Fringes, which disappeared with a large source, were maintained after the optics, implying that beam coherence was observed for both the collimating and focusing polycapillary optics.
Propagation-based phase retrieval using the contrast transfer function (CTF) allows images at any propagation distance to be used when recovering the phase of slowly-varying objects. The CTF suffers from artifacts due to nulls in the transfer function at low spatial frequency and at higher, propagation-distance-dependent frequencies, though the latter can be alleviated by combining measurements at multiple distances. We demonstrate that the use of extended sources can improve low frequency performance. In addition, this method offers source shape as a parameter that can be used when optimizing combinations of measurements to produce robust phase reconstructions.
X-ray coherent scatter imaging has the potential to improve the detection of liquid and powder materials of concern in security screening. While x-ray attenuation is dependent on atomic number, coherent scatter is highly dependent on the characteristic angle for the target material, and thus offers an additional discrimination. Conventional coherent scatter analysis requires pixel-by-pixel scanning, and so could be prohibitively slow for security applications. A novel slot scan system has been developed to provide rapid imaging of the coherent scatter at selected angles of interest, simultaneously with the conventional absorption images. Prior experimental results showed promising capability. In this work, Monte Carlo simulations were performed to assess discrimination capability and provide system optimization. Simulation analysis performed using the measured ring profiles for an array of powders and liquids, including water, ethanol and peroxide. For example, simulations yielded a signal-to-background ratio of 1.63±0.08 for a sample consisting of two 10 mm diameter vials, one containing ethanol (signal) and one water (background). This high SBR value is due to the high angular separation of the coherent scatter between the two liquids. The results indicate that the addition of coherent scatter information to single or dual energy attenuation images improves the discrimination of materials of interest.
Propagation-based phase contrast using the transport of intensity equation (TIE) allows rapid, deterministic phase retrieval from defocused images. For weakly attenuating objects, phase can be retrieved from a single image. However, the TIE suﬀers from significant low frequency artifacts due to enhancement of noise during phase retrieval. We demonstrate that by patterning the illumination source as approximately a modified Bessel function of the 2nd kind of zero order, quantitative phase can be imaged directly at the detector within a spatial frequency band. Outside of that band, Bessel sources still improve low frequency performance in phase retrieval.
Phase contrast and coherent scatter imaging have the potential to improve the detection of materials of interest in x ray screening. While attenuation is dependent on atomic number, phase is highly dependent on electron density, and thus offers an additional discriminant. A major limitation of phase imaging has been the required spatial coherence of the xray illumination, which typically requires a small (10-50 μm) source or multiple images captured with precision gratings, both of which present challenges for high throughput image acquisition. An alternative approach uses a single coarse mesh. This significantly relaxes the source spot size requirement, improving acquisition times and allows near-real-time phase extraction using Fourier processing of the acquired images. Diffraction signatures provide a third approach which yields another set of information to identify materials. Specific angles characteristic of target materials are selected through broad slot apertures for rapid throughput. Depth information can be extracted from stereoscopic imaging using multiple slots. A system capable of simultaneous phase, coherent scatter, and absorption imaging was constructed. Discrimination of materials on the basis of both phase and coherent scatter signatures is demonstrated.
X-ray phase contrast can offer improved contrast in soft tissue imaging at clinical energies. To generate phase contrast in a clinical setting without the need for precisely aligned gratings and multiple exposures has traditionally required the use of specialized sources capable of producing x-ray spots on the order of 10 μm in diameter which necessarily require lengthy exposures due to the low intensity produced. We demonstrate results from two systems capable of overcoming this limitation. In the first, a polycapillary optic is employed to focus a typical clinical source to produce a small secondary source of the size required for phase contrast imaging. In the second, a grid of relatively large pitch is used along with Fourier processing to generate a phase contrast image using a large spot size source.
X–ray phase imaging utilizes a variety of techniques to render phase information as intensity contrast and these
intensity images can in some cases be processed to retrieve quantitative phase. A subset of these techniques
use free space propagation to generate phase contrast and phase can be recovered by inverting differential
equations governing propagation. Two techniques to generate quantitative phase reconstructions from a single
phase contrast image are described in detail, along with regularization techniques to reduce the influence of
noise. Lastly, a recently developed technique utilizing a binary–amplitude grid to enhance signal strength in
propagation–based techniques is described.
Contrast in conventional imaging of soft tissues is often limited due to the very similar attenuation of
tissues to be distinguished. Phase contrast techniques can enable discrimination of tissues with similar attenuation. A
major limitation to the widespread adoption of phase-contrast techniques is that for tabletop sources the required
degree of coherence generally requires a small (10 to 50 μm) source. In this work, a polycapillary optic was
employed to create a small virtual source from a large spot rotating anode. Phase contrast images obtained with two
optics and several pinholes have been analyzed and preliminary results obtained for quantitative phase
A recently developed technique for phase imaging using table top sources is to use multiple fine-pitch gratings.
However, the strict manufacturing tolerences and precise alignment required have limited the widespread adoption
of grating-based techniques. In this work, we employ a technique recently demonstrated by Bennett et al.1 that
ultilizes a single grid of much coarser pitch. Phase is extracted using Fourier processing on a single raw image taken
using a focused mammography grid. The effects on the final image of varying grid, object, and detector distances,
window widths, and of a variety of windowing functions, used to separate the harmonics, were investigated.
We demonstrate a quantitative X-ray phase contrast imaging (XPCI) technique derived from propagation dependent phase change. We assume that the absorption and phase components are correlated and solve the Transport of Intensity Equation (TIE). The experimental setup is simple compared to other XPCI techniques; the only requirements are a micro-focus X-ray source with sufficient temporal coherence and an X-ray detector of sufficient spatial resolution. This method was demonstrated in three scenarios, the first of which entails identification of an index-matched sphere. A rubber and nylon sphere were immersed in water and imaged. While the rubber sphere could be plainly seen on a radiograph, the nylon sphere was only visible in the phase reconstruction. Next, the technique was applied to differentiating liquid samples. In this scenario, three liquid samples (acetone, water, and hydrogen peroxide) were analyzed using both conventional computed tomography (CT) and phase contrast CT. While conventional CT was capable of differentiating between acetone and the other two liquids, it failed to distinguish between water and hydrogen peroxide; only phase CT was capable of differentiating all three samples. Finally, the technique was applied to CT imaging of a human artery specimen with extensive atherosclerotic plaque. This scenario demonstrated the increased sensitivity to soft tissue compared to conventional CT; it also uncovered some drawbacks of the method, which will be the target of future work. In all cases, the signal-to-noise ratio of phase contrast was greatly enhanced relative to conventional attenuation-based imaging.
We give a prescription for defining generalizations of the Wigner function that allow extending the property
of conservation along paths to a wider range of problems, including nonparaxial field propagation and pulse
propagation within general transparent dispersive media.